{"id": "2606.19594", "title": "Unsupervised Causal Abstractions Discovery", "abstract": "Causal abstractions formalize when a high-level structural causal model (SCM) captures the interventional behavior of a lower-level SCM. Existing applications of this notion largely follow a hypothesis-testing paradigm: an expert proposes a candidate high-level model and then evaluates if the low-level system implements it. We study the complementary problem of learning a high-level model directly from low-level measurements. Our contributions leverage hypotheses from low-rank causal discovery, and can be summarized as follows: (1) we show that observations generated by a low-rank graph induce latents that form a causal abstraction, (2) we provide identifiability results about these latents, and (3) we propose a practical objective to learn this high-level SCM.", "date": "2026-06-17", "categories": []}
{"id": "2606.19610", "title": "Latent Confounded Causal Discovery via Lie Bracket Geometry", "abstract": "Recent work on Kan-Do-Calculus (KDC) has established that the boundary between passive observation and active intervention in causal inference is a category-theoretic bi-adjunction, with interventions modeled by left Kan extensions and conditioning by right Kan extensions. This paper introduces two causal discovery algorithms under latent confounding, building on the information-geometric and categorical consequences of KDC. In smooth statistical settings, Radon-Nikodym derivatives between observational and interventional measures induce local causal vector fields; failures of these fields to close under Lie brackets become computable Frobenius residuals, which we interpret as witnesses of failed visible integrability and possible latent or unmodeled structure. Our first algorithm, BRIDGE (Bracket Residuals for Interventional Discovery and Geometric Estimation), combines an interventional density or Radon-Nikodym-ratio engine with a geometric screen that proposes a high-recall family of admissible arrows, identifies non-closing visible pairs as latent-obstruction candidates, and passes the reduced family to downstream score-based or differentiable discovery routines. The second algorithmic contribution, Spectral Kan-Do Flow Matching (SKFM), learns amortized intervention fields and factors latent curvature spectrally, exposing the direct Lie-space endpoint toward which BRIDGE points. A detailed set of experiments show that both algorithms are capable of discovering causal models with latent confounders while collapsing the super-exponential space of possible DAGs by many orders of magnitude. This paper introduces a new paradigm in causal discovery, where latent structure is inferred directly from the geometry of intervention-induced flows.", "date": "2026-06-17", "categories": []}
{"id": "2606.18506", "title": "Beyond AHI: An Interpretable Causal-Discovery-Guided Framework for Sleep Recovery in Connected Health", "abstract": "Objective sleep assessment relies on polysomnography (PSG), yet clinical impact is often better reflected in patient-reported outcomes (PROs) such as sleepiness and fatigue. Existing summary indices, including the Apnea-Hypopnea Index (AHI), provide limited insight into the multidomain physiology underlying functional recovery. We propose an interpretable, causal-discovery--guided framework for deriving a hierarchical Sleep Recovery Score (SRS) from multimodal PSG. Using two large population cohorts (MESA: n=1540; MrOS: n=825), we apply directed acyclic graph (DAG) learning to identify candidate physiological drivers spanning respiratory burden, hypoxic burden, sleep fragmentation, sleep architecture, and autonomic regulation. Although derived from clinical PSG, these domains map naturally to sensing streams increasingly available in connected health technologies, including wearable ECG, oximetry, and sleep-stage estimation devices. To preserve mechanistic plausibility, we introduce a two-stage screening process that combines physiology-based constraints with constrained LLM-assisted auditing to identify and remove structural confounders and construct-overlapping variables. Across cohorts, these five domains emerge as recurrent physiological domains associated with recovery, and the resulting SRS shows up to 2.5$\\times$ stronger alignment with perceived recovery than AHI. By linking multimodal sleep physiology to patient-centered outcomes through an interpretable, bias-aware, and domain structured framework, this work provides a practical foundation for recovery modeling across both clinical sleep studies and emerging smart and connected health settings.", "date": "2026-06-16", "categories": []}
{"id": "2606.18834", "title": "Identifying Structural Biases from Causal Mechanism Shifts", "abstract": "Causal discovery methods commonly assume that all data is independently and identically distributed (i.i.d.) and that there are no unmeasured variables affecting the system. In practice, these assumptions are often violated, leading to inaccurate inference. In this paper, we study how to identify hidden confounding and selection biases from causal mechanism shifts. In particular, we show that structural biases lead to dependent mechanism shifts. That is, by considering for which variables the mechanisms change given data from different environments, we can tell which variables are unbiased, which are subject to hidden confounding, and which are undergoing selection bias. We formalize this into an empirically testable criterion based on mutual information, and show under which conditions it identifies structural biases. To tell which nodes are subject to what kind of bias, we introduce the StruBI algorithm. Experiments on synthetic and real-world data show that StruBI works well in practice, accurately recovering affected variable sets and types of biases, outperforming the state-of-the-art by a wide margin.", "date": "2026-06-17", "categories": []}
{"id": "2507.11178", "title": "A Gradient-based Causal Discovery Framework with Applications to Complex Industrial Processes", "abstract": "With the advancement of deep learning technologies, various neural network-based Granger causality models have been proposed. Although these models have demonstrated notable improvements, several limitations remain. Most existing approaches adopt the component-wise architecture, necessitating the construction of a separate model for each time series, which results in substantial computational costs. In addition, imposing the sparsity-inducing penalty on the first-layer weights of the neural network to extract causal relationships weakens the model's ability to capture complex interactions. To address these limitations, we propose Gradient Regularization-based Neural Granger Causality (GRNGC), which requires only one time series prediction model and applies $L_{1}$ regularization to the gradient between model's input and output to infer Granger causality. Moreover, GRNGC is not tied to a specific time series forecasting model and can be implemented with diverse architectures such as KAN, MLP, and LSTM, offering enhanced flexibility. Numerical simulations on DREAM, Lorenz-96, fMRI BOLD, and CausalTime show that GRNGC outperforms existing baselines and significantly reduces computational overhead. Meanwhile, experiments on real-world DNA, Yeast, HeLa, and bladder urothelial carcinoma datasets further validate the model's effectiveness in reconstructing gene regulatory networks.", "date": "2025-07-15", "categories": []}
{"id": "2606.17516", "title": "FoundCause: Causal Discovery with Latent Confounders from Observational Data", "abstract": "Causal discovery from observational data remains challenging due to the need to recover directed structure and latent confounding without interventions. We propose FoundCause, an amortized causal discovery model trained entirely on synthetic data that maps datasets directly to causal graphs in a single forward pass. By learning from large collections of simulated structural causal models, FoundCause captures transferable statistical patterns that generalize beyond individual datasets. The architecture incorporates several key inductive biases for causal discovery. It uses a permutation-invariant transformer encoder with alternating attention over samples and variables to jointly model cross-variable dependence and per-variable distributions. Pairwise statistical features derived from classical asymmetry measures are injected through statistics-conditioned attention, guiding the model toward known causal signals. A factorized decoder separates edge existence from direction, while a triangular refinement module enables reasoning over higher-order causal motifs such as chains and colliders. In addition, a dedicated confounder module based on learnable latent tokens explicitly models hidden common causes, and the model explicitly handles missing data via its masked input representation. To our knowledge, FoundCause is the first amortized causal discovery approach to explicitly model latent confounding. FoundCause outperforms 11 classical non-amortized methods (e.g., PC, GES, NOTEARS-style optimization) and 4 amortized causal discovery methods on 15 real-world datasets, achieving +9.6% improvement in $F_1$, +1.2% in AUROC, and an 18.9% reduction in structural Hamming distance relative to the strongest non-amortized methods, while performing inference in a single forward pass.", "date": "2026-06-16", "categories": []}
{"id": "2606.18011", "title": "Fast Nonparametric Conditional Independence Testing via Two-Stage Regression", "abstract": "Constraint-based causal discovery relies on repeated conditional independence tests, but fast nonparametric tests often sacrifice calibration, especially when variables depend on the conditioning set through nonlinear relationships. We introduce BLITZ (Broad-to-Local Independence Testing via residualiZation), a nonparametric conditional independence test designed to run well under a second while maintaining the accuracy needed for the thousands of queries performed by constraint-based causal discovery algorithms. BLITZ first removes broad smooth dependence on the conditioning set using low-order polynomial regression, then applies a small nonlinear feature map and residualizes those features with shallow tree regressions. The resulting statistic tests residual cross-covariance, with a moment-matched chi-square approximation to the null distribution. We show theoretically that the two-stage design reduces the effective complexity faced by the tree residualizers, allowing shallow trees to control residual conditional-mean bias while avoiding excessive overfitting. In simulations, BLITZ provides better null calibration than fast kernel, random-feature, and regression-based competitors while remaining among the fastest methods tested. In causal discovery experiments on synthetic graphs and flow-cytometry data, BLITZ yields more reliable endpoint orientations among retained adjacencies and competitive structural recovery. These results suggest that broad-to-local residualization is a practical route to calibrated, scalable nonparametric conditional independence testing for causal discovery.", "date": "2026-06-16", "categories": []}
{"id": "2606.18074", "title": "Tensor-based second-order causal discovery", "abstract": "Causal discovery seeks to uncover the causal dependencies among variables. For this purpose, we propose an algorithm called Tensor-based Second-order Causal Discovery (TSCD). Its input is a tensor obtained from the covariance matrices of observational and interventional data. Assuming the causal dependencies follow a linear structural equation model on a directed acyclic graph (DAG), TSCD outputs the DAG and the functions on its edges, requiring only that the noise variables are uncorrelated. We also implement a version of the approach for nonlinear models. Our focus on second-order statistics (via the covariance matrices) is motivated by their statistical and computational efficiency relative to higher-order moments, their identifiability relative to first-order statistics, and that they work regardless of whether the variables are Gaussian. We show that TSCD has identifiable causal order and parameters from a number of interventions that is logarithmic in the number of variables. Experiments show that TSCD is robust to noise, competitive with existing methods, and scales to hundreds of variables.", "date": "2026-06-16", "categories": []}
{"id": "2602.21381", "title": "VCDF: A Validated Consensus-Driven Framework for Time Series Causal Discovery", "abstract": "Time series causal discovery is essential for understanding dynamic systems, yet many existing methods remain sensitive to noise, non-stationarity, and sampling variability. We propose the Validated Consensus-Driven Framework (VCDF), a simple and method-agnostic layer that improves robustness by evaluating the stability of causal relations across blocked temporal subsets. VCDF requires no modification to base algorithms and can be applied to methods such as VAR-LiNGAM and PCMCI. Experiments on synthetic datasets show that VCDF improves VAR-LiNGAM by approximately 0.08-0.12 in both window and summary F1 scores across diverse data characteristics, with gains most pronounced for moderate-to-long sequences. The framework also benefits from longer sequences, yielding up to 0.18 absolute improvement on time series of length 1000 and above. Evaluations on simulated fMRI data and IT-monitoring scenarios further demonstrate enhanced stability and structural accuracy under realistic noise conditions. VCDF provides an effective reliability layer for time series causal discovery without altering underlying modeling assumptions.", "date": "2026-02-22", "categories": []}
{"id": "2605.09169", "title": "Prediction Bottlenecks Don't Discover Causal Structure (But Here's What They Actually Do)", "abstract": "A Mamba state-space model trained only for next-step prediction appears to recover Granger-causal structure through a simple readout $S = |W_{out} W_{in}|$, with early experiments suggesting the phenomenon generalized across architectures and benefited from interventional data at $p < 10^{-5}$. We package the protocol used to test that claim -- standardized synthetic generators (VAR/Lorenz/CauseMe-style), three intervention semantics ($do(X=c)$, soft-noise, random-forcing), edge-provenance cards on three real datasets, and size-matched control arms -- as a reusable falsification benchmark, and walk the claim through it in five stages. The method-level claim does not survive: (i) a plain linear bottleneck does as well or better; (ii) tuned Lasso beats the bottleneck on synthetic CauseMe-style benchmarks, and on Lorenz-96 (the only real benchmark with unambiguous ground truth) classical PCMCI and Granger lead a tight cluster in which the bottleneck trails; (iii) the headline intervention advantage is roughly 60% a sample-size confound, and the residual disappears under standard $do(X=c)$ interventions, surviving only under a non-standard random-forcing scheme; (iv) even that residual reproduces, with a larger effect, in classical bivariate Granger -- the effect is method-agnostic. What survives is a narrow characterization result; the benchmark is the lasting artifact, and each stage above is one of its control arms.", "date": "2026-05-09", "categories": []}
{"id": "2606.15559", "title": "SDVDiag: Multimodal Causal Discovery for Online Diagnosis in Software-defined Vehicles", "abstract": "The transition toward software-defined vehicles concentrates an increasing share of vehicle functionality into distributed software services, where failures propagate through service dependencies and the surface symptom is often several causal hops away from the underlying defect. Existing approaches to causal root-cause analysis in such systems address this only partially: they typically reason over a single observability modality and operate in an offline, operator-driven mode that does not match the demands of continuous vehicle operation. This paper presents SDVDiag, a multimodal causal-discovery pipeline that fuses log-based and metric-based service representations into a shared embedding space before graph construction, coupled with an anomaly-driven trigger that converts the diagnostic platform from a manually operated batch tool into a continuously running online system. Evaluation on an Autonomous Valet Parking testbed shows that the multimodal pipeline produces sparser causal graphs than a metrics-only baseline (134 vs. 182 edges on average) and consistently outperforms it in edge-weighted reward against an expert knowledge graph at every stage of human-feedback refinement, showing a 2.4-fold improvement over the baseline after 60 feedback queries. An end-to-end fault-injection scenario further demonstrates that the integrated trigger correctly recovers a true root cause located two causal hops upstream of the observable symptom.", "date": "2026-06-14", "categories": []}
{"id": "2605.26759", "title": "Time Series Causal Discovery via Context-Conditioned and Causality-Augmented Pretraining", "abstract": "Causal discovery from time series is critical for many real-world applications, such as tracing the root causes of anomalies. Existing approaches typically rely on dataset-specific optimization, making it difficult to transfer their causal discovery capabilities to new time series governed by diverse causal mechanisms. In this paper, we propose \\textbf{PTCD}, a novel \\textbf{P}retraining framework for \\textbf{T}ime-series \\textbf{C}ausal \\textbf{D}iscovery, which improves cross-task generalization through context-conditioned modeling and transferable causal augmentation. To model complex temporal causal dependencies, PTCD employs a dual-scale iterative attention mechanism to capture window-level causal relationships, and a Gaussian mixture with a context-level routing mechanism to handle heterogeneous exogenous distributions. To further address distribution shifts across causal graphs, PTCD adopts a pretraining paradigm on synthetic datasets that integrates intervention-based learning and a causal mixup strategy, promoting stable causal discovery and stronger generalization. Extensive experiments on multiple real-world out-of-distribution (OOD) datasets demonstrate that PTCD excels in both causal discovery and root cause identification.", "date": "2026-05-26", "categories": []}
{"id": "2606.02231", "title": "Identifiable Markov Switching Models with Instantaneous Effects and Exponential Families", "abstract": "Temporal systems often exhibit non-stationary behaviour, such as seasonal climate variation or glucose fluctuations in patients with type-1 diabetes. One way to model non-stationarity is through discrete latent regimes, i.e., stationary segments of time. Such systems induce a Markov Switching Model (MSM), a class of Hidden Markov Models with autoregressive dependencies among latent regimes and observed variables. Identifying latent regimes is challenging in the presence of frequent regime switches and nonlinear and non-Gaussian dynamics, particularly when there are instantaneous effects between the variables, e.g., due to slow rates of measurements. In this work, we establish the identifiability of both latent regimes and regime-dependent causal structures under temporal regime dependencies, nonlinear lagged and instantaneous effects, and independent noise from the exponential family. Our identifiability theory subsumes non-temporal mixtures of causal models. Furthermore, we introduce FlowMSM, a regime detection framework that can be paired with any stationary causal discovery method to recover regime-dependent causal structures. Experiments on synthetic benchmarks and a financial economics dataset demonstrate the effectiveness of our approach to detect latent regimes and discover causal structures from non-stationary time series.", "date": "2026-06-01", "categories": []}
{"id": "2606.13024", "title": "CausalMoE: A Billion-Scale Multimodal Foundation Model for Granger Causal Discovery with Pattern-Routed Heterogeneous Experts", "abstract": "Granger Causal Discovery (GCD) is fundamental for analyzing temporal dependencies in complex systems. However, existing neural GCD methods predominantly rely on a \"one-size-fits-all\" paradigm, struggling to capture distribution shifts and dynamic regime changes inherent in real-world time series. This often leads to entangled representations and spurious causal graphs. In this paper, we propose CausalMoE, a billion-scale multimodal Granger causal foundation model that explicitly models patch-level heterogeneity. CausalMoE introduces a Pattern-Routed Mixture of Heterogeneous Experts, which dynamically identifies latent temporal patterns and routes patches to specialized domain experts, effectively decoupling regime-specific mechanisms from shared dynamics. To ensure interpretable graph recovery, we design a Causality-Aware Self-Attention mechanism operating across variables, yielding sparse Granger causal graphs via proximal optimization. Furthermore, CausalMoE is the first to integrate LLMs and VLMs to align numerical signals with textual and visual priors, regularizing causal estimation in complex scenarios. Extensive experiments demonstrate that CausalMoE establishes a new state-of-the-art on fully supervised benchmarks, while effectively generalizing to few-shot settings where traditional methods fail.", "date": "2026-06-11", "categories": []}
{"id": "2606.13532", "title": "Graphical Causal Reasoning for Root Cause Analysis in Cloud Networks", "abstract": "Cloud-computing relies on large-scale networks which are inherently complex systems. In this paper, we present a novel approach to root cause analysis (RCA) of cloud network incidents, leveraging graph-based causal discovery techniques. Our method addresses the limitations of rule-based automation by introducing a spatiotemporal grouping strategy and an automation ontology to reduce the dimensionality of the problem. We construct a causal graph from binary time series data using bivariate Granger causality and conditional independence tests. For inference, we introduce a probabilistic method that assigns edge-specific conditional probabilities as a function of time lag, allowing for interpretable, time-aware root cause scoring via causal graph traversal.\n  We evaluated the system using a labeled dataset of 35 production incidents from a major cloud provider. The model successfully recalled the correct root cause in 85.7% of incidents and produced an exact match in 74.3%. In production, the deployed system has been used in over 800 real-world incidents, with positive qualitative feedback from network engineers. These results highlight the practicality of a data-driven, causal approach to RCA in dynamic and large-scale operational environments.", "date": "2026-06-11", "categories": []}
{"id": "2602.01135", "title": "Your Autoregressive Model Already Reveals the Causal Graph", "abstract": "Autoregressive models trained via next-token prediction implicitly learn the conditional independence structure of their data-generating process. We exploit this observation to perform scalable causal discovery from a single observed sequence of discrete events -- without any task-specific retraining. Such single-stream settings arise naturally in vehicle diagnostics, manufacturing systems, and patient trajectories, yet they remain largely unsolved: the absence of repeated samples, massive event vocabularies, and long-range temporal dependencies render existing methods either inaccurate or computationally intractable. We introduce TRACE, a framework that repurposes any pretrained autoregressive model as a density estimator for conditional mutual information, the fundamental primitive for conditional independence testing. By constructing parallelized CI tests on GPUs, TRACE recovers both the sample-level time causal graph and its summary projection, scaling linearly with the vocabulary size while naturally handling delayed causal effects. Crucially, we prove that minimizing the standard cross-entropy pretraining loss directly minimizes an upper bound on the causal identification error, establishing a duality between sequence prediction and causal discovery. On nonlinear SCMs (|X| = 8000) and real-world vehicle diagnostic logs (|X| = 29100), TRACE is the first applicable method at this scale, outperforming the strongest baseline by over 20 F1 points.", "date": "2026-02-01", "categories": []}
{"id": "2606.09892", "title": "LMT: A Bayesian Framework for Causal Discovery from Textual Alarm Records in Manufacturing Systems", "abstract": "Textual event records, such as alarm logs, have become an increasingly common data source in engineering and manufacturing systems. Beyond identifying correlations or recurring patterns, engineers are often interested in understanding which types of events causally trigger or influence other events during system operation. Textual event descriptions may contain semantic clues about such causal relationships, and recent large language models (LLMs) provide a promising tool for extracting these signals. However, relying solely on LLM-encoded textual information is insufficient for accurate causal discovery, since semantic patterns do not directly reveal causal mechanisms and may confuse causation with correlation or frequent sequential patterns. To address these challenges, we propose \\textbf{LMT}, a Bayesian causal discovery framework for engineering event data that jointly leverages textual descriptions and timestamps. Specifically, LMT first uses LLMs to extract semantic causal signals from event descriptions and constructs a prior distribution over causal graphs among event types or event clusters. It then incorporates temporal evidence through a Poisson-process-based likelihood, allowing the LLM-informed prior to be refined by timestamp-based statistical evidence. By integrating the textual and temporal information, LMT produces a causal graph that is both interpretable and data-supported. Simulation studies show that the proposed framework is effective across different settings and is especially advantageous in small-sample alarm-event scenarios.", "date": "2026-06-03", "categories": []}
{"id": "2606.10607", "title": "Causal Ensemble Agent: Hierarchical Causal Discovery with LLM-guided Expert Reweighting", "abstract": "Causal discovery aims to uncover causal structures from observational data, which is crucial for real-world decision-making. However, different causal discovery algorithms can produce divergent results that conflict with each other, complicating the identification of accurate causal graphs. Traditional approaches rely on numerical values and statistical assumptions, often ignoring rich domain-specific information, such as feature descriptions, which could also help structure learning. While recent works explore using Large Language Models (LLMs) to infer causal relations via direct queries, such methods can be unreliable due to a lack of alignment with the actual data. To address these limitations, we propose Causal Ensemble Agent (CEA), a novel framework that aggregates structural insights from statistical discovery experts across different graph levels via linear opinion pooling, and uses an LLM as a meta-referee to dynamically reweight experts when the aggregated confidence is close to the decision boundary, thereby composing an improved and more complete causal graph. Extensive experiments on both synthetic and real-world datasets demonstrate that CEA achieves the strongest overall performance across a wide range of causal discovery methods, highlighting the effectiveness of using LLMs for meta-analysis in causal discovery.", "date": "2026-06-09", "categories": []}
{"id": "2601.21221", "title": "Causal Discovery for Explainable AI: A Dual-Encoding Approach", "abstract": "Understanding causal relationships among features is fundamental for explaining machine learning model decisions. However, traditional causal discovery methods face challenges with categorical variables due to numerical instability in conditional independence testing. We propose a dual-encoding causal discovery approach that addresses these limitations by running constraint-based algorithms with complementary encoding strategies and merging results through majority voting. Applied to the Titanic dataset, our method identifies causal structures that align with established explainable methods.", "date": "2026-01-29", "categories": []}
{"id": "2601.22736", "title": "UA-DCM: Uncertainty-aware Causal Decision Making via Effect Bound Decomposition", "abstract": "Causal inference from observational data can provide strong evidence for finding the best action in a decision-making scenario without having to perform expensive randomized trials. The causal effect of an action is often not pointwise identifiable even with infinite data due to unobserved confounding factors. Furthermore, having only finitely many samples adds another layer of uncertainty to causal effect estimation. Several existing methods can be used to obtain upper and lower bounds to the causal effect, ranging from symbolic methods to the more recent neural network-based approaches, which implicitly incorporate both sources of uncertainty. However, these methods do not inform whether collecting more samples may or may not help identify the best action from observational data, leaving experts in the dark about their data collection strategies. We address this problem with a novel framework that can distinguish the range of causal effect values that might be eliminated by collecting more samples from the range of values that, with high probability, cannot be eliminated with more observational samples. We show that this partitioning can be obtained by solving max-min and min-max optimization problems. We leverage neural causal models to approximately recover this decomposition in practice. We demonstrate via experiments on synthetic and real-world datasets that our algorithm can determine when collecting more samples will not help determine the best action. Our framework can help practitioners decide when to resort to non-observational studies or seek to measure some of the unmeasured confounders for optimal decision-making.", "date": "2026-01-30", "categories": []}
{"id": "2606.00568", "title": "On the Recoverability of Causal Relations from Bulk Gene Expression Data", "abstract": "Bulk gene expression profiling, which aggregates pooled RNA across cells within a biological sample, remains important in the single-cell era because it is typically less noisy, more sensitive, and more cost-effective than single-cell assays. Accordingly, a growing body of computational methods seeks to recover causal relations among genes from bulk expression data. However, aggregation is a lossy, non-invertible coarsening of the underlying cellular system, and it remains unclear whether and under what conditions causal relations are recoverable from aggregated bulk gene expression data. To answer this, we formalize recoverability under aggregation through two notions of consistency: functional-form consistency and conditional-independence consistency. We then derive necessary and sufficient conditions for recoverability, showing that these properties are preserved only under linear aggregations (e.g., sum/mean) coupled with affine structural equations. To assess the practical plausibility of these conditions, analyses of four bulk and four single-cell gene expression datasets further reveal that the estimated pairwise regulatory functions among genes deviate from linearity in both data types, providing limited empirical support for the linearity assumptions required for recoverability. Together, these results caution against recovering causal relations from aggregated bulk expression data without strong additional assumptions.", "date": "2026-05-30", "categories": []}
{"id": "2606.07525", "title": "Implicit Causal Graph Construction in Text via Chain Discovery", "abstract": "Causal graphs in text are typically populated by observable, predefined events. In contrast, we study implicit causal graph construction from text by treating each described cause-effect pair as the begin- and endpoint of an underlying latent causal graph and using large language models (LLMs) to infer intermediate causal events. We compare end-to-end graph construction with methods that frame the task as causal chain discovery. In the latter, graphs are built either by aggregating inferred chains or by progressively expanding partial chains through an iterative search process. We further explore Wisdom of the Crowd extensions that access causal knowledge from multiple LLMs in post-hoc aggregation and collaborative inference settings. We analyze trade-offs among these approaches and evaluate the validity of inferred causal relations using a manually curated database of 1,560 scientifically validated causal pairs. This database-based evaluation is proposed as reliable, resource-efficient, and transferable to settings where ground-truth graphs are unavailable.", "date": "2026-04-20", "categories": []}
{"id": "2606.08196", "title": "Beyond Additivity: Causal Discovery in Location-Scale Noise Models with Hidden Variables", "abstract": "We study causal discovery from observational data when some variables are hidden and the data-generating process follows a location-scale noise model (LSNM). Existing methods that handle hidden confounders typically assume additive noise, but in practice, causes often modulate not just the mean but also the variance of their effects. We prove that acyclic directed mixed graphs (ADMGs) satisfying a bow-free condition are identifiable under LSNM with hidden variables, establishing the first identifiability result for causally insufficient models beyond noise additivity. We further provide sufficient conditions for identifying causal direction even when the bow-free assumption is violated. Our two-stage algorithm, LSNM-UV, is sound and complete, and experiments demonstrate improved performance over additive baselines on heteroscedastic data.", "date": "2026-06-06", "categories": []}
{"id": "2606.08390", "title": "When Are Neural Interaction Discoveries Real? Identifiability, Recoverability, and a Pre-Fit Diagnostic", "abstract": "When a neural time-series model reports that one variable modulates another's effect on a target, is the discovered interaction a property of the data or an artifact of model flexibility? We argue that this is fundamentally a question of identifiability, governed by the geometry of the observed input support rather than by the specific neural architecture. We study the problem in a multiplicative-gating extension of neural additive vector autoregression (GNAVAR), in which source contributions are modulated by other lagged variables. We show that representational capacity is not identifiability: dependent inputs induce leakage between edge-specific interaction terms, and low-dimensional support permits distinct interaction decompositions that agree on the observed data while differing elsewhere. We then prove a population identifiability theorem for normalized minimal GNAVAR decompositions under explicit support conditions, including settings with shared modulators. The theory yields a simple practitioner-facing diagnostic: the effective rank of the joint lag-block covariance predicts, before fitting, whether interaction recovery is feasible for a given candidate set. When the candidate set is unknown, a two-seed stability check provides a practical operational test. The same support condition organizes empirical outcomes into the three states predicted by the theory. Our results show that interaction recoverability depends on support geometry, that effective rank provides a practical pre-fit diagnostic, and that instability across independent fits is a characteristic signature of non-identifiable interaction discovery. The identifiability phenomenon, the support condition, and the instability signature are model-agnostic; GNAVAR is the vehicle that makes them provable.", "date": "2026-06-07", "categories": []}
{"id": "2606.09672", "title": "Correlation Is Not Enough: Embedding Human Metadata for Individual Causal Discovery", "abstract": "Ask a pretrained biomedical language model whether \"cortisol 28 ug/dL\" and \"stock-market volatility\" are related, and it returns a cosine similarity of 0.83 on a scale where 1.0 means identical. The two share no mechanism. This is not a corner case: every off-the-shelf biomedical encoder we tested (BioBERT, PubMedBERT, BioM-ELECTRA) scores unrelated cross-domain pairs between 0.76 and 0.92 when the answer should be near zero. Accuracy on cross-domain discrimination is 0%.\n  Retrieval systems survive this, because a language model downstream filters the noise. A Large Behavioural Model (LBM), a foundation model whose subject is a person rather than a sentence, does not: it reasons over a graph of a user's life and treats embedding proximity as evidence that two events are causally linked. False proximity writes a false causal edge, and everything downstream inherits the error. Here, embedding geometry is not a tuning knob; it is correctness.\n  We report the fix. A contrastive pass over 72,034 pairs raises PubMedBERT BIOSSES correlation from 0.633 to 0.828 and within-vs-across-domain separation from 1.05x to 1.63x. A second pass, BODHI, mines hard negatives from edges absent in a biomedical knowledge graph and lifts separation to 2.30x and the discrimination gap to +0.392, at a 4.5% BIOSSES cost. On an Intel Xeon 6737P with AMX, OpenVINO cuts single-query latency from 1367 ms to 10 ms (133x) and reaches 555 sentences/sec. One finding contradicts standard advice: FP16 beats INT8 on this silicon at every serving batch size, and we explain why. The same model on a no-AMX Ice Lake instance runs 13-27x slower. We release the benchmark suite, training corpora, the BODHI generator, and the OpenVINO scripts.", "date": "2026-06-08", "categories": []}
{"id": "2606.06464", "title": "Human Adults and LLMs as Scientists: Who Benefits from Active Exploration?", "abstract": "A long-standing finding in the causal learning literature is that adults struggle to identify conjunctive causal rules, where an effect requires the simultaneous presence of multiple causes, while performing better in disjunctive settings. However, most demonstrations of this ``conjunctive handicap'' rely on passive observation paradigms with limited evidence, where learners have no control over evidence generation. This paper asks whether this bias persists when adults are granted agency through active exploration. Using a modified ``blicket detector'' task, adult participants freely intervened to identify causal objects under conjunctive or disjunctive rule structures. We show that active exploration substantially improves adults' conjunctive causal reasoning, although conjunctive rules still require more tests to infer than disjunctive rules. We further compare human performance to a range of large language models in the same setting. While some state-of-the-art models approach human-level performance on hypothesis inference accuracy, they often exhibit less efficient exploration strategies and similar conjunctive-disjunctive performance gaps.", "date": "2026-06-04", "categories": []}
{"id": "2606.06908", "title": "polyDAG: Polynomial Acyclicity Constraints for Efficient Continuous Causal Discovery in Visual Semantic Graphs", "abstract": "Modern image-analysis pipelines often convert images into structured semantic variables, such as facial attributes, object concepts, and scene descriptors. Learning directed dependencies among these variables can produce interpretable visual semantic graphs, but continuous directed acyclic graph learning is limited by the cost of enforcing acyclicity. We present polyDAG, a polynomial acyclicity framework for efficient continuous causal discovery in visual semantic graphs. polyDAG replaces the matrix-exponential acyclicity constraint with a finite polynomial trace constraint and proves that the new constraint is zero exactly for acyclic graphs. We further derive a geometric-series implementation that avoids the explicit summation loop while preserving the same acyclicity condition. Experiments on synthetic Erdos-Renyi graphs and CelebA facial visual attributes show that polyDAG improves efficiency and structure recovery. Averaged over the revised synthetic protocol with d in {100, 200, 500}, polyDAG reduces mean structural Hamming distance from 318.4 to 285.4 and improves mean F1 score from 0.725 to 0.756. At 100 nodes, the geometric variant runs in 3.44 seconds compared with 5.16 seconds for the exponential baseline, corresponding to a 33.4 percent speedup. Code and data are publicly available at https://github.com/wenhaoz-fengcai/polyDAG.", "date": "2026-06-05", "categories": []}
{"id": "2412.11800", "title": "Scalable Temporal Anomaly Causality Discovery in Large Systems: Achieving Computational Efficiency with Binary Anomaly Flag Data", "abstract": "Extracting anomaly causality facilitates diagnostics once monitoring systems detect system faults. Identifying anomaly causes in large systems involves investigating a broader set of monitoring variables across multiple subsystems. However, learning graphical causal models (GCMs) comes with a significant computational burden that restrains the applicability of most existing methods in real-time and large-scale deployments. In addition, modern monitoring applications for large systems often generate large amounts of binary alarm flags, and the distinct characteristics of binary anomaly data -- the meaning of state transition and data sparsity -- challenge existing causality learning mechanisms. This study proposes an anomaly causal discovery approach (AnomalyCD), addressing the accuracy and computational challenges of generating GCMs from temporal binary flag datasets. The AnomalyCD presents several strategies, such as anomaly data-aware causality testing, sparse data and prior link compression, and edge pruning adjustment approaches. We validate the performance of the approach on two datasets: monitoring sensor data from the readout-box system of the Compact Muon Solenoid experiment at CERN, and a public dataset from an information technology monitoring system. The results on temporal GCMs demonstrate a considerable reduction of computation overhead and a moderate enhancement of accuracy on the binary anomaly datasets. Code: https://github.com/muleina/AnomalyCD .", "date": "2024-12-16", "categories": []}
{"id": "2507.12257", "title": "Robust Causal Discovery in Real-World Time Series with Power-Laws", "abstract": "Exploring causal relationships in stochastic time series is a challenging yet crucial task with a vast range of applications, including finance, economics, neuroscience, and climate science. Many algorithms for Causal Discovery (CD) have been proposed; however, they often exhibit a high sensitivity to noise, resulting in spurious causal inferences in real data. In this paper, we observe that the frequency spectra of many real-world time series follow a power-law distribution, notably due to an inherent self-organizing behavior. Leveraging this insight, we build a robust CD method based on the extraction of power-law spectral features that amplify genuine causal signals. Our method consistently outperforms state-of-the-art alternatives on both synthetic benchmarks and real-world datasets with known causal structures, demonstrating its robustness and practical relevance.", "date": "2025-07-16", "categories": []}
{"id": "2603.20980", "title": "From Causal Discovery to Dynamic Causal Inference in Neural Time Series", "abstract": "Time-varying causal models provide a powerful framework for studying dynamic scientific systems, yet most existing approaches assume that the underlying causal network is known a priori - an assumption rarely satisfied in real-world domains where causal structure is uncertain, evolving, or only indirectly observable. This limits the applicability of dynamic causal inference in many scientific settings. We propose Dynamic Causal Network Autoregression (DCNAR), a two-stage neural causal modeling framework that integrates data-driven causal discovery with time-varying causal inference. In the first stage, a neural autoregressive causal discovery model learns a sparse directed causal network from multivariate time series. In the second stage, this learned structure is used as a structural prior for a time-varying neural network autoregression, enabling dynamic estimation of causal influence without requiring pre-specified network structure. We evaluate the scientific validity of DCNAR using behavioral diagnostics that assess causal necessity, temporal stability, and sensitivity to structural change, rather than predictive accuracy alone. Experiments on multi-country panel time-series data demonstrate that learned causal networks yield more stable and behaviorally meaningful dynamic causal inferences than coefficient-based or structure-free alternatives, even when forecasting performance is comparable. These results position DCNAR as a general framework for using AI as a scientific instrument for dynamic causal reasoning under structural uncertainty.", "date": "2026-03-21", "categories": []}
{"id": "2606.05689", "title": "Causal Modeling of Selection in Evolution", "abstract": "Understanding potential selection in data is crucial for causal discovery; we argue that \"selection\" in common narratives takes two forms, which we term static and evolutionary selection, respectively. Static selection refers to a one-shot filtering process where observed data consist of a subset of the population of interest, as in survey volunteer bias. Evolutionary selection, in contrast, operates through repeated rounds of differential fitness in reproduction, where observed data constitute the latest generation shaped by a historical trajectory, as in immune adaptation, antibiotic resistance, and social norm emergence. Existing methods largely conflate these two forms and rely on an identical graphical model of selection. We show that this model is valid for static settings but fails to characterize data under evolution, yielding false discovery results. To address this, we introduce a new model that specifically characterizes evolutionary selection, and develop a sound and complete procedure for identifying such models from data across one or multiple environments or generations. Experimental results validate the method's ability to uncover the relevant mechanisms underlying evolution from data.", "date": "2026-06-04", "categories": []}
{"id": "2606.05942", "title": "EML-CD: Causal Mechanism Recovery via EML Symbolic Trees in Structure Learning", "abstract": "Neural network (NN)-based nonlinear causal discovery methods recover DAG structure but leave each causal mechanism as a black box. Waxman et al. argued that extracting causal mechanisms from NN weights is ill-posed. We propose EML-CD, a framework that integrates the EML operator (capable of composing elementary functions from a single binary operator) into causal structure learning, with interpretable mechanism recovery as the primary objective. EML-CD represents each edge mechanism as a gated EML binary tree and automatically discovers closed-form causal equations. Analytical Jacobians can be directly computed from the output equations, enabling quantitative understanding of causal effects. On real data (Sachs protein signaling, d=11), EML-CD achieves SHD=11.2 +/- 0.4 (5-seed mean; baselines are single deterministic runs), on par with PC/GES within seed variance and below CAM, while attaching closed-form equations to each detected edge (precision 0.756, recall 0.365). In a controlled bivariate test with known mechanisms, EML-CD recovers 10 of 11 elementary function families faithfully (held-out shape correlation >= 0.96; only high-frequency sine is partial). On a symbolic synthetic benchmark, EML-CD attains a substantially lower and more stable held-out mechanism f-MSE than a fixed SINDy dictionary (mean 3.67 vs. 7644, the latter inflated by catastrophic extrapolation on one seed), although its structure recovery (SHD 14.0) only matches the dictionary and stays below specialized optimizers; on the Causal Chambers light-tunnel subset, a depth-2 model improves F1 over linear OLS-BIC (0.444 vs. 0.273).", "date": "2026-06-04", "categories": []}
{"id": "2606.06288", "title": "Discrete Causal Representations from Heterogeneous Domains: A Bayesian Approach with Social Survey Applications", "abstract": "Causal representation learning aims to infer the high-level latent causal concepts that give rise to observed low-level measurements. This is particularly relevant for heterogeneous data from different environments or domains since distribution shifts often arise through sparse, localized changes in some of the underlying causal mechanisms, while other parts of the generative process remain unchanged. Whereas identifiability of causal representations has been studied extensively, practical uncertainty-aware methods and real-world use cases remain less explored. In this work, we propose a Bayesian approach to learning causal representations from multi-environment data, focusing on the case of discrete causal concepts and unknown multi-node soft interventions. To this end, we translate causal assumptions and interpretability desiderata into suitable priors and parametric choices within a hierarchical model. We then devise an inference scheme based on sequential Monte Carlo sampling to approximate the resulting multimodal posterior. We showcase our approach through case studies on social survey data, where latent causal concepts correspond to cultural values or political opinions, measurements to survey responses, and environments to different countries or states. Our model infers meaningful high-level concepts and plausible causal relations among them, demonstrating its utility for learning causal representations of complex real-world data.", "date": "2026-06-04", "categories": []}
{"id": "2606.06440", "title": "Causal Atlases from Entropic Inference: Bayesian Networks beyond Optimal DAGs", "abstract": "Data-driven causal relationship identification is pertinent to advancing understanding of complex systems both within and beyond science. Bayesian networks offer a probabilistic method for modelling generic causal relationships via directed acyclic graphs (DAGs). However, typical techniques for constructing Bayesian networks rely on optimization, which can be ill-suited for learning causal relationships because the underlying data may admit multiple chains of causation. More data-faithful representations of causal relationships would provide frameworks for constructing multiple causal maps that are consistent with the variability that is inherent in underlying data. Here, we show that entropy-based inference generates atlases of plausible causal relationships that are consistent with underlying data. On simulated noisy data of 2- and 20-node linear structural equation models, we sample a maximum-entropy ensemble of graphs that allow us to quantify the inherent structural ambiguity in underlying causal relationships. Our method shows that \"optimized\" DAGs can contain causal artifacts are not consistent across equivalently accurate topologies.", "date": "2026-06-04", "categories": []}
{"id": "2606.04822", "title": "Reconciling Causality and Non-Equilibrium Thermodynamics with Hamiltonian Causal Models", "abstract": "Causal modeling of physical temporal phenomena must handle interventions that act along trajectories, nonstationary induced laws, path-dependent effects, and feedback mediated by dynamics, all challenging in standard causal models. We introduce Hamiltonian Causal Models (HCMs), a trajectory-level framework in which observed variables interact with local environments and interventions act as controls of Hamiltonian mechanisms. HCMs separate immutable equations of motion from intervenable mechanisms and define causal effects as discrepancies between interventional path laws. A key motivation for HCMs is their natural interface with non-equilibrium thermodynamics. Entropy production quantifies the irreversibility of a process and is a central causal observable: it is estimable from data and witnesses causal effects along the system's evolution that are invisible to endpoint and cumulative versions of the standard average treatment effect. As in physics, cause and effect are not primitives of the relation between two random variables but arise from the non-invertibility of the thermodynamic arrow. With this, our paper reconciles the language of statistical causal models and non-stationary thermodynamics, offering new tools to describe causality in a wide range of physical systems.", "date": "2026-06-03", "categories": []}
{"id": "2602.01483", "title": "Causal Preference Elicitation", "abstract": "We propose causal preference elicitation, a Bayesian framework for expert-in-the-loop causal discovery that actively queries local edge relations to concentrate a posterior over directed acyclic graphs (DAGs). From any black-box observational posterior, we model noisy expert judgments with a three-way likelihood over edge existence and direction. Posterior inference uses a flexible particle approximation, and queries are selected by an efficient expected information gain criterion on the expert's categorical response. Experiments on synthetic graphs, protein signaling data, and a human gene perturbation benchmark show faster posterior concentration and improved recovery of directed effects under tight query budgets.", "date": "2026-02-01", "categories": []}
{"id": "2606.03227", "title": "Learning Temporal Causal Structure via Smooth Differentiable Optimization", "abstract": "Causal discovery with instantaneous effects in multivariate time series is challenging, as the instantaneous structure must be acyclic. Prior methods enforce this by either separating instantaneous and lagged estimation into multi-stage pipelines or imposing algebraic acyclicity constraints via complex augmented Lagrangian optimization, both of which incur high computational cost. In this work, we propose a different approach: we learn a differentiable permutation of variables using the Gumbel--Sinkhorn operator and triangularize the instantaneous coefficient matrix of a Structural Vector Autoregressive (SVAR) model in the learned order. This converts acyclicity from a hard constraint into a parameterization and keeps it valid throughout optimization. In doing so, our method enables unified, continuous optimization with gradient-based learning, leading to improved efficiency in time--series causal discovery. Across three real-world benchmarks, our method achieves the best overall performance compared with 12 baselines in both discovery accuracy and efficiency. On the large-scale benchmark, it further demonstrates strong scalability, achieving more than a 6x speedup over competing methods.", "date": "2026-06-02", "categories": []}
{"id": "2606.03602", "title": "CauTion: Knowing When to Trust LLMs for Ensemble Causal Discovery", "abstract": "Causal discovery from observational data remains challenging due to the fundamental limitations of purely statistical methods, such as statistical distinguishability within equivalence classes and sensitivity to finite sample sizes. While large language models (LLMs) offer a promising source of domain knowledge to complement statistical inference, existing LLM-augmented methods are vulnerable to LLM errors and incur high token costs. Moreover, reliance on a single data-centric algorithm can make results sensitive to algorithm-specific biases. To address these limitations, we propose CauTion, a framework that reliably integrates LLM domain knowledge into an ensemble of statistical causal discovery algorithms through consensus filtering and LLM reliability estimation. CauTion proceeds in three stages. First, an algorithm ensemble utilizes a consensus voting to resolve up to 96% of edges on which algorithms agree, achieving near-perfect accuracy on the filtered consensus edges. Second, a trust-calibrated arbitration mechanism estimates the relative reliability of the LLM and the algorithms via an annotation-free trust calibration procedure, which is then utilized to govern a trust-weighted voting process that restricts LLM arbitration exclusively to edges with unreliable algorithmic evidence. Third, a cycle repair step is applied to guarantee the final causal graph is validly acyclic. Experiments on six datasets demonstrate that CauTion consistently outperforms both data-centric and LLM-augmented baselines, with larger gains on larger graphs and strong robustness to LLM errors. Code is available at https://github.com/OpenCausaLab/CauTion.", "date": "2026-06-02", "categories": []}
{"id": "2606.00278", "title": "Evaluating Bivariate Causal Statements Based on Mutual Compatibility", "abstract": "For many real-world systems, causal ground truth is difficult to obtain, making claims about causal effects hard to assess. We develop methods for evaluating collections of $\\binom{n}{2}$ bivariate causal statements over a set of $n$ variables. In the setting of acyclic linear statements, any such collection can be extended to a unique multivariate causal model, but we argue that this induced model is implausible if it imposes substantial additional confounding to explain observed correlations. We introduce a compatibility score that quantifies this notion of plausibility, notably without relying on the faithfulness assumption. Additionally, we define an incompatibility score for purely graphical bivariate causal statements, based on global consistency constraints that are derived from acyclicity and faithfulness assumptions. We give theoretical and empirical evidence that both scores can successfully distinguish correct from incorrect causal statements in generic settings. Moreover, we demonstrate the practical applicability of our methods by analyzing causal claims made by large language models. Our work aims to provide a foundation for assessing the reliability of causal information derived from human experts or artificial intelligence in settings where alternative forms of validation are unavailable.", "date": "2026-05-29", "categories": []}
{"id": "2606.01789", "title": "Consistency evaluation of benchmarks used for causal discovery", "abstract": "In graphical causal model, causal discovery aims to construct a causal graph based on numerical data and domain knowledge in plain text. However, the evaluation of causal discovery methods remains a challenge in the area as the progress of domain researches often makes benchmark causal graphs contain mis-aligned knowledge. This problem especially affects the evaluation of large language model (LLM) based causal discovery methods as they are sensitive to the new discoveries in the literature. This work is the first to systematically study the quality of benchmark causal graphs. Specifically, we design a pipeline that automatically retrieves relevant research papers from scientific databases, and prompts LLMs to check the consistency between the benchmark causal graphs and domain research papers. We evaluate 11 popular real-world benchmarks, for which our pipeline in total proceeds 38,081 domain papers. Our results show that popular benchmarks vary significantly in their consistency with domain research, with clear implications for causal discovery research.", "date": "2026-06-01", "categories": []}
{"id": "2501.02672", "title": "Re-examining Granger Causality with Causal Bayesian Networks and Reichenbachs Principles", "abstract": "Characterising cause-effect relationships in complex systems is fundamental to understanding their underlying mechanisms. Granger causality (GC) remains a widely used computational tool for identifying causal relationships in time series data. However, like other causal discovery methods, GC has limitations and has been criticised for lacking a rigorous causal foundation. In this work, we present a fix to this criticism by reinterpreting GC through the lenses of Reichenbach's principles and causal Bayesian networks. This reinterpretation was implemented as an algorithm we call causalized Granger causality (c-GC). We demonstrate, both theoretically and graphically, that this reformulation endows GC with a robust causal interpretation under specific assumptions. c-GC yields satisfactory results on synthetic data, offering a more principled framework for causal discovery in observational datasets.", "date": "2025-01-05", "categories": []}
{"id": "2512.23626", "title": "Regret-Based Federated Causal Discovery with Unknown Interventions", "abstract": "Most causal discovery methods recover a completed partially directed acyclic graph representing a Markov equivalence class from observational data. Recent work has extended these methods to federated settings to address data decentralization and privacy constraints, but often under idealized assumptions that all clients share the same causal model. Such assumptions are unrealistic in practice, as client-specific policies or protocols, for example, across hospitals, naturally induce heterogeneous and unknown interventions. In this work, we address federated causal discovery under unknown client-level interventions. We propose I-PERI, a novel federated algorithm that first recovers the CPDAG of the union of client graphs and then orients additional edges by exploiting structural differences induced by interventions across clients. This yields a tighter equivalence class, which we call the $\\mathbf{\\Phi}$-Markov Equivalence Class, represented by the $\\mathbf{\\Phi}$-CPDAG. We provide theoretical guarantees on the convergence of I-PERI, as well as on its privacy-preserving properties, and present empirical evaluations on synthetic data demonstrating the effectiveness of the proposed algorithm.", "date": "2025-12-29", "categories": []}
{"id": "2605.31156", "title": "TabCausal: Pretraining Across Causal Environments for Tabular Causal Discovery", "abstract": "Causal discovery aims to recover directed causal relations from observational and interventional data, providing a basis for mechanistic understanding and reliable decision-making. Causal discovery foundation models (CDFMs) seek to amortize this problem by mapping a dataset directly to a causal graph in a single forward pass, avoiding per-dataset testing, search, or optimization. However, existing CDFMs remain limited, often failing to consistently match strong classical methods, and we find that a key bottleneck is how causal pretraining tasks are constructed. Based on this observation, we propose TabCausal, a data-driven CDFM trained with broad causal pretraining over diverse graph priors, structural mechanisms, noise models, dimensions, sample sizes, and intervention regimes. A dynamic task construction strategy composes these causal environments into varied discovery tasks, enabling more transferable structural learning from observational and mixed-interventional data. On large-scale synthetic benchmarks, TabCausal achieves better macro-averaged performance than a diverse set of causal discovery baselines. To further bridge abstract synthetic generators and realistic causal reasoning scenarios, we introduce a protocol-guided and LLM-audited semantic causal environment benchmark, where domain-grounded SCMs generate interpretable observational and interventional datasets for out-of-distribution analysis. Across both synthetic and semantic environments, TabCausal demonstrates robust structure recovery, especially under interventional evidence, highlighting broad causal pretraining as a key ingredient for transferable amortized causal discovery.", "date": "2026-05-29", "categories": []}
{"id": "2605.26029", "title": "CausaLab: A Scalable Environment for Interactive Causal Discovery Toward AI Scientists", "abstract": "We introduce CausaLab, a scalable environment for evaluating interactive causal discovery by LLM agents. Unlike prior evaluations, CausaLab evaluates both whether an agent can solve a problem using causal evidence and whether its answer is grounded in a faithful recovered causal mechanism. Each episode places an agent in a synthetic laboratory: it receives prior measurement records, intervenes on a manipulator crystal, and predicts the resonance frequency of a held-out reactor crystal governed by the same mechanism. The hidden data-generating process is a randomly sampled structural causal model (SCM), so success requires recovering both a causal graph and structural equations rather than recalling prior knowledge.\n  Experiments show a persistent gap between prediction and mechanism recovery: in the purely observational 6-node setting, GPT-5.2-high reaches 92% task accuracy but only 0.471 all-edge $F_1$. Mixed observation-intervention strategies improve structural fidelity, while pure intervention remains difficult even for strong agents. We identify premature stopping as a major weakness and show that consistency verification mitigates it. CausaLab therefore separates predictive success from causal understanding and exposes current LLM agents' limits as experimental causal reasoners.", "date": "2026-05-25", "categories": []}
{"id": "2605.26408", "title": "Function-Valued Causal Influence in Nonlinear Time Series", "abstract": "Causal discovery in time series is increasingly performed using nonlinear machine-learning models, yet the resulting causal relationships are almost always summarized by scalar edge scores. We argue that this practice obscures the true object learned by nonlinear autoregressive models: a state-dependent function whose effect varies across regimes, magnitudes, and contexts. We formalize function-valued causal influence for additive, contribution-decomposable architectures and show that scalar causal scores constitute a severe information bottleneck, conflating between-state variation with within-state residual noise. Using Neural Additive Vector Autoregression as a representative architecture, we introduce a practical framework based on Individual Conditional Expectation for estimating causal response functions directly from trained models. Through controlled synthetic experiments, we demonstrate that edges with indistinguishable scalar scores can exhibit qualitatively different functional behaviors, including monotonic, thresholded, saturating, and sign-changing effects. An applied case study on democratic development further shows that function-valued analysis reveals regime-specific and asymmetric causal structure systematically missed by score-centric approaches.", "date": "2026-05-26", "categories": []}
{"id": "2605.28880", "title": "Towards Continuous-time Causal Foundation Models", "abstract": "Extending discrete-time causal Prior-data Fitted Networks for time series to continuous time invites writing the mechanism as a stochastic differential equation (SDE) -- but if the SDE is integrated \\emph{once per observation gap}, the trajectory law depends on when it is observed, and the prior remains a discrete-time Markov model in SDE clothing.\n  We propose a precise continuity criterion -- trajectory-law invariance to the observation schedule -- together with a three-tier taxonomy (discrete; naive observation-grid integration; fine-grid integration with decoupled observation) and a construction realising the top tier on a random DAG with OU or small-MLP nonlinear drifts, irregular observation schedules, and hard / soft / time-varying interventions.\n  A $2 \\times 2$ encoder $\\times$ integrator ablation, run independently on a linear and a nonlinear prior, finds fine-grid integration beats naive on 8/8 cells (sign-consistency $p < 1/256$) with the gap growing as the eval grid refines; the encoder axis is null with fine integration but time-aware-leading with naive.\n  We release the prior and a preliminary zero-shot protocol on pharmacokinetic and physical-system data.", "date": "2026-05-26", "categories": []}
{"id": "2605.29008", "title": "Causal Intelligence for Constraint-Aware Intervention Design to Induce State Transitions", "abstract": "Driving a system from one state to another through targeted interventions is a fundamental challenge in science, yet most predictive models offer limited mechanistic insight and no principled framework for decision-making. Here we present COAST (Causally Optimal Actions for State Transitions), a causal-intelligence approach for the in-silico design of constrained interventions that induce user-defined state transitions. Given data characterizing source and target states, COAST learns context-specific causal graphs and structural causal models, attributes observed distributional shifts to mechanism-level causal drivers, and introduces a novel constraint-aware multi-objective optimization formulation that balances transition efficacy, intervention complexity, and target-state stability. The approach is modular and domain-agnostic, integrating feature selection, causal discovery, causal modeling, and intervention identification and evaluation through interchangeable components. Across synthetic benchmarks and real biological datasets, COAST recovers key causal drivers and identifies robust single- and multi-target intervention strategies that achieve desired state transitions, accompanied by transparent mechanistic rationales to guide experimental validation.", "date": "2026-05-27", "categories": []}
{"id": "2605.30015", "title": "Test Time Training for Supervised Causal Learning", "abstract": "Supervised Causal Learning (SCL) has shown promise in causal discovery by framing it as a supervised learning problem. However, it suffers from significant out-of-distribution generalization challenges. We reveal three limitations of previous SCL practices: a significant performance gap between synthetic benchmarks and real-world data, fragility to distribution shifts, and failure in compositional generalization, collectively questioning its real-world applicability. To address this, we propose Test-Time Training for Supervised Causal Learning (TTT-SCL), a novel framework that dynamically generates training sets explicitly aligned with any specific test instance. We demonstrate the correlation between TTT-SCL and score-based methods, and design an efficient module for generating training sets based on the classic scoring function. Experiments on synthetic benchmarks, pseudo-real and real-world datasets demonstrate that TTT-SCL significantly outperforms existing SCL and traditional causal discovery methods.", "date": "2026-05-28", "categories": []}
{"id": "2503.11477", "title": "Heterogeneous Causal Discovery of Repeated Undesirable Health Outcomes", "abstract": "Understanding the factors that trigger or prevent undesirable health outcomes across patient subpopulations is essential for designing targeted interventions. While randomized controlled trials and expert-led patient interviews are standard methods for identifying these factors, they can be time-consuming or infeasible. Causal discovery offers an alternative to conventional approaches by generating cause-and-effect hypotheses from observational data, yet its practical utility is limited by strong or untestable assumptions. This work presents a novel, end-to-end framework that uniquely integrates an ensemble of causal structure learning (CSL) algorithms with heterogeneous causal effect estimation. By aggregating results across multiple algorithms, the framework identifies robust causal relationships that persist under different modeling assumptions while simultaneously revealing how these effects vary across specific patient contexts. The proposed heterogeneous causal discovery framework improves robustness and provides practitioners with a prioritized set of actionable, clinically interpretable hypotheses. We demonstrate the framework's effectiveness through two large-scale healthcare applications: identifying drivers and inhibitors of repeat emergency department visits among diabetic patients and hospital readmissions among ICU patients, using insurance claims and electronic health record datasets. Our results, across both settings, identify chronic disease management and care coordination as key interventions, while revealing that intervention effectiveness depends on specific patient-level modifiers. We employ a multi-layered validation strategy, including ground-truth recovery via simulations, alignment with clinical literature, validation by expert clinicians, and portability in modern healthcare systems using an external dataset, to demonstrate the framework's practical utility.", "date": "2025-03-14", "categories": []}
{"id": "2602.23602", "title": "Moment Matters: Mean and Variance Causal Graph Discovery from Heteroscedastic Observational Data", "abstract": "Heteroscedasticity -- where the variance of a variable changes with other variables -- is pervasive in real data, and elucidating why it arises from the perspective of statistical moments is crucial in scientific knowledge discovery and decision-making. However, standard causal discovery does not reveal which causes act on the mean versus the variance, as it returns a single moment-agnostic graph, limiting interpretability and downstream intervention design. We propose a Bayesian, moment-driven causal discovery framework that infers separate \\textit{mean} and \\textit{variance} causal graphs from observational heteroscedastic data. We first derive the identification results by establishing sufficient conditions under which these two graphs are separately identifiable. Building on this theory, we develop a variational inference method that learns a posterior distribution over both graphs, enabling principled uncertainty quantification of structural features (e.g., edges, paths, and subgraphs). To address the challenges of parameter optimization in heteroscedastic models with two graph structures, we take a curvature-aware optimization approach and develop a prior incorporation technique that leverages domain knowledge on node orderings, improving sample efficiency. Experiments on synthetic, semi-synthetic, and real data show that our approach accurately recovers mean and variance structures and outperforms state-of-the-art baselines.", "date": "2026-02-27", "categories": []}
{"id": "2605.27477", "title": "Iterative Causal Discovery: Per-Edge Impossibility Certificates, Tier-Aware Oracle Queries, and the $1+K$ Lower Bound", "abstract": "Causal-discovery algorithms return a directed graph, yet provide no principled means of distinguishing edge directions identified by the data from those assigned without an identifying assumption. Under the standard Markov and faithfulness conditions, the observational distribution identifies only a Markov equivalence class; orientations within that class are not determined by the joint distribution and cannot be recovered from additional samples alone, but require either a functional restriction or an intervention. We introduce a protocol for observational causal discovery on continuous data that attaches to each candidate edge a discrete impossibility certificate: a RESOLVED code records the identifiability theorem under which the direction was committed, while an IMPOSSIBLE code records the failure mode together with the specific question a domain expert must answer to resolve it. The bivariate cascade is extended with five gated identifiability tiers LSNM, IGCI, Stein, MDL, and PEIT that abstain when their precondition test rejects. Two oracle primitives, the meta-hub query and the node-children query, jointly establish an upper bound of $1+K$ expert interactions sufficient to recover any DAG, where $K$ denotes the number of non-leaf vertices. Under an ideal-oracle assumption, the bound is met exactly on the asia, sachs, child, and alarm benchmarks.", "date": "2026-05-26", "categories": []}
{"id": "2605.27567", "title": "Why LLMs Fail at Causal Discovery and How Interventional Agents Escape", "abstract": "Causal discovery is a cornerstone of scientific reasoning, yet whether large language models can perform it reliably remains an open question. Recent benchmarks show that even fine-tuned models plateau on simple causal graphs and degrade as complexity grows, but why they fail has not been established. We prove the failure is fundamental: supervised fine-tuning, direct preference optimization, and in-context learning all produce predictors that cannot distinguish between causal graphs generating similar observational data, and any attempt to do so requires the model's internal representations to grow unboundedly, violating the very conditions under which these methods work. We formalize this as a kernel obstruction theorem, establishing that the limitation is intrinsic to the learning paradigm, \\emph{not any particular model or dataset}. We propose Agentic Causal Bayesian Optimization (A-CBO), wherein a frozen language model serves as an interventional oracle answering targeted queries about intervention effects, while an external Bayesian loop concentrates beliefs over candidate graphs in logarithmically many rounds. Because the decision operates outside the space where the obstruction applies, A-CBO provably converges while the underlying model remains unchanged. On Corr2Cause, A-CBO matches fine-tuned baselines without any training. On Extended Corr2Cause, a new benchmark scaling to 24 variables with 18K test samples, A-CBO significantly outperforms both fine-tuning and preference optimization, with the advantage growing", "date": "2026-05-26", "categories": []}
{"id": "2407.15073", "title": "Multi-Agent Causal Discovery Using Large Language Models", "abstract": "Causal discovery aims to identify causal relationships between variables and is a fundamental problem across the sciences. Traditional statistical causal discovery (SCD) methods rely solely on observational data and ignore the contextual information available in metadata, whereas recent LLM-based methods exploit metadata but treat the large language model (LLM) as a single agent, leaving its judgments vulnerable to memorized or biased associations. To address this gap, we introduce MAC (Multi-Agent Causal Discovery Framework), which casts causal discovery as a multi-agent debate coupled with the autonomous selection of an SCD algorithm. MAC combines two complementary modules, bridged by a Meta Fusion mechanism: a Debate-Coding Module (DCM) that grounds an initial graph in data by autonomously selecting and executing the best-suited SCD algorithm, and a Meta-Debate Module (MDM) that refines the graph through an adversarial Affirmative-Negative-Judge debate over the metadata. Across five benchmark datasets and three metrics (F1, SHD, NHD), MAC achieves the best aggregate performance among five statistical and four LLM-based baselines, ranking first on 10 of 15 evaluation points with Gemini-2.0-Flash -- including a perfect reconstruction of the Earthquake graph -- and remains robust across three backbone LLMs.", "date": "2024-07-21", "categories": []}
{"id": "2512.16111", "title": "BUILD with Precision: Bottom-Up Inference of Linear DAGs", "abstract": "Learning the structure of directed acyclic graphs (DAGs) from observational data is a central problem in causal discovery, statistical signal processing, and machine learning. Under a linear Gaussian structural equation model (SEM) with equal noise variances, the problem is identifiable and we show that the ensemble precision matrix of the observations exhibits a distinctive structure that facilitates DAG recovery. Exploiting this property, we propose BUILD (Bottom-Up Inference of Linear DAGs), a deterministic stepwise algorithm that identifies leaf nodes and their parents, then prunes the leaves by removing incident edges to proceed to the next step, exactly reconstructing the DAG from the true precision matrix. In practice, precision matrices must be estimated from finite data, and ill-conditioning may lead to error accumulation across BUILD steps. As a mitigation strategy, we periodically re-estimate the precision matrix (with less variables as leaves are pruned), trading off runtime for enhanced robustness. Reproducible results on challenging synthetic benchmarks demonstrate that BUILD compares favorably to state-of-the-art DAG learning algorithms, while offering an explicit handle on complexity.", "date": "2025-12-18", "categories": []}
{"id": "2604.18751", "title": "Beyond Coefficients: Forecast-Necessity Testing for Interpretable Causal Discovery in Nonlinear Time-Series Models", "abstract": "Nonlinear machine-learning models are increasingly used to discover causal relationships in time-series data, yet the interpretation of their outputs remains poorly understood. In particular, causal scores produced by regularized neural autoregressive models are often treated as analogues of regression coefficients, leading to misleading claims of statistical significance.\n  In this paper, we argue that causal relevance in nonlinear time-series models should be evaluated through forecast necessity rather than coefficient magnitude, and we present a practical evaluation procedure for doing so. We present an interpretable evaluation framework based on systematic edge ablation and forecast comparison, which tests whether a candidate causal relationship is required for accurate prediction. Using Neural Additive Vector Autoregression as a case study model, we apply this framework to a real-world case study of democratic development, modeled as a multivariate time series of panel data - democracy indicators across 139 countries. We show that relationships with similar causal scores can differ dramatically in their predictive necessity due to redundancy, temporal persistence, and regime-specific effects.\n  Our results demonstrate how forecast-necessity testing supports more reliable causal reasoning in applied AI systems and provides practical guidance for interpreting nonlinear time-series models in high-stakes domains.", "date": "2026-04-20", "categories": []}
{"id": "2605.27022", "title": "ORCA: An End-to-End Interactive Copilot for Optimized Root Cause Analysis", "abstract": "Causal analysis is a crucial task in many domains, including manufacturing, social science, and medicine. However, despite recent progress, the conceptual and methodological complexity of causal methods makes them largely inaccessible to domain experts. This gap prevents experts from leveraging these advances and hinders researchers who lack access to real-world data for validation. To bridge this divide, we introduce ORCA, a copilot for end-to-end causal analysis. ORCA orchestrates agents to understand the user's goals and guide them through the most appropriate causal analysis workflow, from fully automatic to highly user-guided execution. It features causal discovery, causal effect estimation, explainability and Root-Cause-Analysis (RCA). ORCA evaluates and compares performance, generates key metrics and diagrams, and generates insights through structured reports. We highlight its effectiveness across several real-world use-cases.", "date": "2026-05-26", "categories": []}
{"id": "2605.25211", "title": "Evolving Causal Regulatory Networks (ECR-Net)", "abstract": "Modern machine learning models excel at pattern recognition but remain brittle, often failing to generalize out of distribution (OOD) because they capture spurious correlations rather than the underlying causal data-generating process. Current causal discovery methods, while powerful, typically assume a static graph structure, rendering them unable to model systems that adapt or undergo structural changes across different environments. We introduce ECR-Net, Evolving Causal Regulatory Networks, a novel, bio-inspired framework for adaptive causal mechanism discovery. Our approach models the data-generating process not as a static graph, but as a dynamic system analogous to a Gene Regulatory Network (GRN), composed of localized, recursive functions where variables can activate and inhibit one another. To discover the latent structure of this network, we employ an evolutionary search algorithm that evolves a population of candidate regulatory graphs, optimizing for a fitness function that measures how well the simulated system dynamics reconstruct the observed data. The key innovation of ECR-Net is its ability to model structural adaptation, it explicitly ingests shifts in the data's statistical properties as signals of an environmental shock. In response, the evolutionary search identifies parsimonious modifications to the causal graph topology, such as link inhibitions or activations that explain the new data regime. We posit that ECR-Net represents a new class of adaptive Structural Causal Models capable of discovering how and why a system's fundamental rules change, offering a path toward robust generalization in complex, non-stationary systems.", "date": "2026-05-24", "categories": []}
{"id": "2605.25998", "title": "Causal methods for LLM development and evaluation", "abstract": "Large language model (LLM) development is currently driven by large-scale empirical iteration over data mixtures, reward models, routing strategies, and evaluation pipelines. Here, we argue that many central questions in LLM development and evaluation are inherently causal: What is the effect of adding a data domain during pretraining? How do annotator preferences change when LLMs generate text in a different style? Should a prompt be routed to a larger or smaller model given inference cost constraints? In general, causal methods are well-suited to such settings where interventions change outcomes but, surprisingly, are underrepresented in LLM development. Our contribution is threefold: (1) We explain how causal methods can help develop modern LLM development and evaluation: LLM development relies heavily on logged data, which are often subject to confounding and distribution shifts; evaluation uses learned but potentially biased judges; and deployment environments are non-stationary. These conditions make purely predictive approaches fragile and create opportunities for principled identification and estimation methods from causal inference. (2) We further map opportunities for causal methods in the entire LLM development pipeline, including pretraining, alignment, routing, agentic workflows, and evaluation. (3) We discuss new research opportunities around leveraging causal methods for LLM development and evaluation. Overall, we argue that causal methods are potentially underutilized for the LLM development and evaluation pipeline, despite the fact that such methods can ensure a reliable and scientifically grounded design.", "date": "2026-05-25", "categories": []}
{"id": "2502.07646", "title": "Causal Additive Models with Unobserved Causal Paths and Backdoor Paths", "abstract": "Causal additive models provide a tractable yet expressive framework for causal discovery in the presence of hidden variables. When unobserved backdoor or causal paths exist between two variables, their causal relationship is often unidentifiable under existing theories. We establish sufficient conditions under which causal directions can be identified in many such cases. These conditions rely on new characterizations of regression sets to determine independence among regression residuals and conditional independencies among observed variables. Building on these results, we introduce a search algorithm that incorporates these innovations and prove its soundness and completeness. Empirical evaluations demonstrate its competitive performance against state-of-the-art methods.", "date": "2025-02-11", "categories": []}
{"id": "2605.21846", "title": "Causal Discovery in Structural VAR Models Under Equal Noise Variance", "abstract": "Causal discovery from multivariate time series is challenging when causal effects may occur both across time and within the same sampling interval. This issue is especially important in applications such as neuroscience, where the sampling rate may be coarse relative to the underlying dynamics and contemporaneous effects need not form an acyclic graph. We study causal discovery in linear Gaussian structural VAR models under an equal noise variance assumption, meaning that the structural noise terms have a common variance. Unlike the DAG-based cross-sectional equal noise variance setting, the time-series setting considered here does not generally yield point identification of a unique causal graph. Instead, multiple structural VAR parameterizations can induce the same stationary observed process law. We introduce a notion of observational equivalence tailored to this setting and show that the corresponding equivalence class is characterized by orthogonal transformations of the structural equations together with a global positive scale. This characterization leads to an equivalence-aware model discrepancy, the observational alignment discrepancy, which compares structural models modulo transformations that preserve the observed law. Building on this theory, we propose ENVAR, a sparsity-based procedure that searches over the induced observational equivalence class for a sparse normalized structural representative. We evaluate the proposed methodology on synthetic structural VAR data and on an fMRI dataset.", "date": "2026-05-21", "categories": []}
{"id": "2605.22335", "title": "Learning Causal Orderings for In-Context Tabular Prediction", "abstract": "In-context learning for tabular data sets strong predictive standards in observational settings; it however primarily relies on correlational structure, which becomes unreliable under distribution shift or intervention. While established methods to discover causal structure exist, they are often focused on structure identifiability and decoupled from the predictive architectures that could benefit from them.\n  To bridge these perspectives, we study how to simultaneously infer and enforce causal structure in the form of topological variable orderings into tabular prediction. Unlike standard architectures, our model TabOrder uses causal order-constrained attention, basing predictions only on features that precede a target under a learned causal order. Similar to causal discovery methods, TabOrder learns the optimal variable ordering in an unsupervised manner through a likelihood-based objective. We justify this choice under standard functional model classes and also study how sample missingness, a common challenge in tabular data, interacts with causal direction identification. Empirically, we confirm that TabOrder recovers accurate variable orderings while addressing prediction and imputation tasks, as well as gives insight into real-world biological data under intervention.", "date": "2026-05-21", "categories": []}
{"id": "2602.04907", "title": "Causal Discovery from Heteroscedastic Stochastic Dynamical Systems under Imperfect Physical Models", "abstract": "Causal discovery is a data-driven paradigm for analyzing complex systems, while physics-based models, such as ordinary differential equations (ODEs), provide mechanistic structure for real-world dynamical processes. Integrating these paradigms can improve identifiability, stability, and robustness. However, real dynamical systems often exhibit cyclic interactions and nonstationarity, whereas many causal discovery methods rely on acyclicity, stationarity, or equilibrium assumptions. We propose an integrative causal discovery framework for dynamical systems that leverages partial physical knowledge through stochastic differential equations (SDEs). The drift term encodes known ODE dynamics, while the diffusion term captures unknown causal couplings beyond the prescribed physics. We develop a scalable sparsity-inducing maximum quasi-likelihood estimator with a theoretically justified stabilization technique to improve the optimization landscape. Under mild conditions, we establish causal graph recovery guarantees for both stable and unstable SDEs. We also analyze robustness of our causal graph estimate to ODE misspecification and clarify how the introduced stabilization technique balances numerical stability and statistical recoverability. Experiments on linear SDEs and nonlinear benchmarks, including Lotka-Volterra and Lorenz dynamics with acyclic and cyclic structures, show improved graph recovery and robustness over data-driven baselines. We also demonstrate practical utility on real-world epidemic data by reconstructing stochastic SIR dynamics within our causal discovery framework.", "date": "2026-02-03", "categories": []}
{"id": "2605.20396", "title": "Score-Based Causal Discovery of Latent Variable Causal Models", "abstract": "Identifying latent variables and the causal structure involving them is essential across various scientific fields. While many existing works fall under the category of constraint-based methods (with e.g. conditional independence or rank deficiency tests), they may face empirical challenges such as testing-order dependency, error propagation, and choosing an appropriate significance level. These issues can potentially be mitigated by properly designed score-based methods, such as Greedy Equivalence Search (GES) (Chickering, 2002) in the specific setting without latent variables. Yet, formulating score-based methods with latent variables is highly challenging. In this work, we develop score-based methods that are capable of identifying causal structures containing causally-related latent variables with identifiability guarantees. Specifically, we show that a properly formulated scoring function can achieve score equivalence and consistency for structure learning of latent variable causal models. We further provide a characterization of the degrees of freedom for the marginal over the observed variables under multiple structural assumptions considered in the literature, and accordingly develop both exact and continuous score-based methods. This offers a unified view of several existing constraint-based methods with different structural assumptions. Experimental results validate the effectiveness of the proposed methods.", "date": "2026-05-19", "categories": []}
{"id": "2605.20400", "title": "Understanding Deterioration Random Effects for Causal Discovery in Infrastructure Management", "abstract": "Infrastructure deterioration poses significant challenges for asset management, yet existing approaches rely on population-averaged models that overlook equipment-specific heterogeneity. We present a novel framework that combines Bayesian hierarchical hazard modeling with causal discovery to identify operational patterns that drive heterogeneous deterioration rates in pump equipment. Our approach first estimates pump-specific random effects $u_i$ using GPU-accelerated No-U-Turn Sampling (NUTS), achieving 3--5$\\times$ speedup over CPU implementations. We then employ DirectLiNGAM to discover causal relationships between 22 engineered time-series features and deterioration rates, stratified by positive ($u_i > 0$, faster deterioration) versus negative ($u_i \\leq 0$, slower deterioration) random effects. Analyzing 112 pumps with 92,861 observations over 650 days, we uncover striking heterogeneity: the negative group exhibits causal effects 400$\\times$ larger than the positive group, with standard deviation (std) showing a strong positive causal effect ($+1.515$) on deterioration rates in low-risk equipment. We validate linearity assumptions through NonlinearLiNGAM comparison and demonstrate practical scalability through GPU acceleration. Our findings enable targeted maintenance strategies by revealing that different operational regimes require fundamentally distinct management approaches, advancing predictive maintenance from population-averaged to heterogeneity-aware decision making.", "date": "2026-05-19", "categories": []}
{"id": "2605.20782", "title": "Causal Machine Learning Is Not a Panacea: A Roadmap for Observational Causal Inference in Health", "abstract": "Objective: The growing availability of large-scale observational clinical datasets and challenges in conducting randomized controlled trials have spurred enthusiasm in using causal machine learning (ML) for causal inference in observational data. We present a roadmap for applying causal ML to observational data. Materials and methods: We outline the importance of assessing validity assumptions within available data and applying causal ML responsibly for clinical experts using causal ML and ML practitioners with limited clinical expertise. Observations: Despite advances in causal ML, its limitations remain largely under-appreciated across disciplines. This gap in shared knowledge may impact the validity of findings. Discussion: Causal assumptions must be satisfied and modeling choices justified. Otherwise, these approaches risk producing biased or misleading results, with consequences for clinical research and patient care. Conclusion: Causal ML can be a powerful tool for generating causal hypotheses. We provide a template to strengthen the rigor and interpretability of causal analyses.", "date": "2026-05-20", "categories": []}
{"id": "2605.19313", "title": "A Unified Framework for Structure-Aware Clustering and Heterogeneous Causal Graph Learning", "abstract": "In complex multivariate systems, interactions among variables are defined by dependency structures, often encoded as directed acyclic graphs ($\\text{DAGs}$). However, dependency structures can vary across subjects, and ignoring this structural heterogeneity introduces bias and obscures subpopulation-specific dependencies. To address this, we propose Directed Acyclic Graph-based Dependency Clustering via Alternating Direction Method of Multipliers (DAG-DC-ADMM), a unified framework built upon Structural Equation Modeling (SEM) that jointly learns cluster assignments and cluster-specific dependency structures. We encode acyclicity via a smooth constraint and integrate a groupwise truncated Lasso fusion penalty (gTLP) to cluster subjects based on their structural similarity. This yields a nonconvex optimization problem that incorporates sparsity, acyclicity, and structural consensus constraints. We address the nonconvexity by using the augmented Lagrangian method and solve it with an adapted version of the Alternating Direction Method of Multipliers (ADMM) for difference-of-convex programs. For certain graph structures, such as upper triangular adjacency matrices, our algorithm is guaranteed to converge to a Karush-Kuhn-Tucker (KKT) point. Experiments demonstrate that our method recovers cluster-specific causal dependency structures with a high true positive rate and a low false discovery rate. This capability enables the robust discovery of heterogeneous dependencies across subjects where the subpopulation label is unknown.", "date": "2026-05-19", "categories": []}
{"id": "2605.19947", "title": "Exploiting Non-Negativity in DAG Structure Learning", "abstract": "This work addresses the problem of learning directed acyclic graphs (DAGs) from nodal observations generated by a linear structural equation model. DAG learning is a central task in signal processing, machine learning, and causal inference, but it remains challenging because acyclicity is a global combinatorial property. Continuous acyclicity constraints have led to important algorithmic advances by replacing the discrete DAG constraint with smooth equality constraints. However, existing formulations still involve difficult non-convex optimization landscapes and may suffer from degenerate first-order optimality conditions. Here, we restrict attention to DAGs with non-negative edge weights and exploit this additional structure to obtain a simpler characterization of acyclicity. Building on this characterization, we formulate a regularized non-negative DAG learning problem and develop an algorithm based on the method of multipliers. We further analyze the benign optimization landscape induced by non-negativity. In the population regime, we show that the true DAG is the unique global minimizer of the proposed augmented-Lagrangian formulation; moreover, the landscape contains no spurious interior stationary points, and the true DAG is the only acyclic KKT point. Numerical experiments on synthetic and real-world data show that the proposed method improves over state-of-the-art continuous DAG-learning alternatives.", "date": "2026-05-19", "categories": []}
{"id": "2307.09575", "title": "Causal Influences over Social Learning Networks", "abstract": "This paper investigates causal influences between agents linked by a social graph and interacting over time. In particular, the work examines the dynamics of social learning models and distributed decision-making protocols, and derives expressions that reveal the causal relations between pairs of agents and explain the flow of influence over the network. The results turn out to be dependent on the graph topology and the level of information that each agent has about the inference problem they are trying to solve. Using these conclusions, the paper proposes an algorithm to rank the overall influence between agents to discover highly influential agents. It also provides a method to learn the necessary model parameters from raw observational data. The results and the proposed algorithm are illustrated by considering both synthetic data and real social media data.", "date": "2023-07-13", "categories": []}
{"id": "2602.02830", "title": "SC3D: Dynamic and Differentiable Causal Discovery for Temporal and Instantaneous Graphs", "abstract": "Discovering causal structures from multivariate time series is a key problem because interactions span across multiple lags and possibly involve instantaneous dependencies. Additionally, the search space of the dynamic graphs is combinatorial in nature. In this study, we propose Stable Causal Dynamic Differentiable Discovery (SC3D), a two-stage differentiable framework that jointly learns lag-specific adjacency matrices and, if present, an instantaneous directed acyclic graph (DAG). In Stage 1, SC3D performs edge preselection through node-wise prediction to obtain masks for lagged and instantaneous edges, whereas Stage 2 refines these masks by optimizing a likelihood with sparsity along with enforcing acyclicity on the instantaneous block. Numerical results across synthetic SVAR systems, nonlinear and chaotic benchmarks, nonstationary dynamics and real-world datasets demonstrate that SC3D achieves improved stability and more accurate recovery of both lagged and instantaneous causal structures compared to existing baselines.", "date": "2026-02-02", "categories": []}
{"id": "2605.16620", "title": "SCOUT: Cyclic Causal Discovery Under Soft Interventions with Unknown Targets", "abstract": "Learning causal relationships between variables from data is a fundamental research area with many applications across disciplines. Most existing causal discovery algorithms rely on the assumptions that (i) the underlying system is acyclic, (ii) the exogenous noise variables are Gaussian, and (iii) the intervention targets for the data-generating experiments are known. While these assumptions simplify the analysis, they are violated in real-life systems. Most existing methods that address these issues either assume the underlying model is linear or are constrained to operate in limited interventional settings. To that end, we propose SCOUT, a novel causal discovery framework for learning nonlinear cyclic causal relationships from soft interventional data with unknown targets. Our approach maximizes the data log-likelihood to recover the graph structure, using two normalizing-flow architectures: contractive residual flows and neural spline flows. Through experiments on synthetic and real-world data, we show that SCOUT outperforms state-of-the-art methods in both causal graph recovery and unknown target recovery across various interventional and noise settings.", "date": "2026-05-15", "categories": []}
{"id": "2605.17465", "title": "TriOpt: A Scalable Algorithm for Linear Causal Discovery", "abstract": "Learning causal relations from observational data is challenging because the graph search space grows super-exponentially with the number of variables. Ordering-based methods reduce this space by first identifying the topological ordering, whereas continuous optimization methods explore most likely regions of the space by casting DAG learning as a differentiable objective with an acyclicity constraint. Despite their conceptual appeal, both paradigms face significant scalability limitations in high-dimensional settings, restricting their practical applicability. In this work, we introduce a new formulation for linear causal discovery that tightly integrates these two paradigms to achieve substantial gains in scalability without sacrificing accuracy. Our approach, TriOpt, decomposes the problem into two efficient stages. First, it recovers the topological ordering by exploiting the Sherman-Morrison rank-1 downdate together with the additive structure of linear kernels, enabling fast and scalable ordering estimation. Second, given this ordering, we reformulate structure learning as a convex continuous optimization problem that entirely avoids the need for enforcing costly acyclicity constraints. We theoretically show that, under the true ordering, TriOpt exactly recovers the underlying linear DAG. Empirically, across synthetic, semi-synthetic, and real-world datasets, TriOpt achieves orders-of-magnitude speedups over state-of-the-art linear causal discovery methods in high-dimensional regimes, while maintaining comparable or superior accuracy.", "date": "2026-05-17", "categories": []}
{"id": "2605.15353", "title": "PACER: Acyclic Causal Discovery from Large-Scale Interventional Data", "abstract": "Inferring the structure of directed acyclic graphs (DAGs) from data is a central challenge in causal discovery, particularly in modern high-dimensional settings where large-scale interventional data are increasingly available. While interventional data can improve identifiability, existing methods remain limited by soft acyclicity constraints, leading to optimization over invalid cyclic graphs, numerical instability, and reduced scalability. We introduce PACER (Perturbation-driven Acyclic Causal Edge Recovery), a scalable framework for causal discovery that guarantees acyclicity by construction. PACER parameterizes a distribution over DAGs through a joint model of variable permutations and edge probabilities, enabling direct optimization over valid causal structures without surrogate penalties. The framework supports a unified likelihood-based treatment of observational and interventional data, flexible conditional density models, and the incorporation of structural prior knowledge. For linear-Gaussian mechanisms, we derive closed-form expressions for the expected interventional log-likelihood and its gradients, yielding substantial computational gains. Empirically, PACER matches or exceeds state-of-the-art methods on protein signaling and large-scale genetic perturbation benchmarks, while scaling efficiently to networks with thousands of variables and achieving up to two orders of magnitude speedups over penalty-based differentiable approaches. These results demonstrate that exact and scalable causal discovery from high-dimensional perturbation data is achievable through principled search space design.", "date": "2026-05-14", "categories": []}
{"id": "2510.13583", "title": "On the Identifiability of Causal Graphs with the Invariance Principle", "abstract": "Causal discovery from i.i.d. observational data is known to be generally ill-posed. We demonstrate that if we have access to the distribution {induced} by a structural causal model, and additional data from (in the best case) \\textit{only two} environments that sufficiently differ in the noise statistics, the unique causal graph is identifiable. Notably, this is the first result in the literature that guarantees the entire causal graph recovery with a constant number of environments and arbitrary nonlinear mechanisms. Our only constraint is the Gaussianity of the noise terms; however, we propose potential ways to relax this requirement. Of interest on its own, we expand on the well-known duality between independent component analysis (ICA) and causal discovery; recent advancements have shown that nonlinear ICA can be solved from multiple environments, at least as many as the number of sources: we show that the same can be achieved for causal discovery while having access to much less auxiliary information.", "date": "2025-10-15", "categories": []}
{"id": "2605.15133", "title": "Causal Foundation Models with Continuous Treatments", "abstract": "Causal inference, estimating causal effects from observational data, is a fundamental tool in many disciplines. Of particular importance across a variety of domains is the continuous treatment setting, where the variable of intervention has a continuous range. This setting is far less explored and represents a substantial shift from the binary treatment setting, with models needing to represent effects across a continuum of treatment values. In this paper, we present the first causal foundation model for the continuous treatment setting. Our model meta-learns the ability to predict causal effects across a wide variety of unseen tasks without additional training or fine-tuning. First, we design a novel prior over data-generating processes with continuous treatment variables in order to generate a rich causal training corpus. We then train a transformer to reconstruct individual treatment-response curves given only observational data, leveraging in-context learning to amortize expensive Bayesian posterior inference. Our model achieves state-of-the-art performance on individual treatment-response curve reconstruction tasks compared to causal models which are trained specifically for those tasks.", "date": "2026-05-14", "categories": []}
{"id": "2605.13589", "title": "Causal Learning with the Invariance Principle", "abstract": "Causal discovery, the problem of inferring the direction of causality, is generally ill-posed. We use the language of structural causal models (SCM) to show that assuming that the causal relations are acyclic and invariant across multiple environments (e.g., the way minimum wage affects employment rate is stable across different geographical regions), \\textit{only} two auxiliary environments are sufficient to infer the causal graph for arbitrary nonlinear mechanisms. Moreover, we demonstrate that this implies identifiability of the SCM functional mechanisms: as a corollary, we show that \\textit{two} auxiliary environments are sufficient to guarantee correct counterfactual inference. We empirically support our theoretical results on synthetic data.", "date": "2026-05-13", "categories": []}
{"id": "2602.13004", "title": "Towards Uncertainty-Aware Federated Granger Causal Learning", "abstract": "Granger causality recovers directed interactions from time-series data, but in many distributed systems, the data are vertically partitioned across clients, with each client observing only the variables of its own subsystem. Federated Granger causality (FedGC) recovers cross-client interactions without sharing raw data. Existing FedGC methods, however, return deterministic point estimates with no calibrated measure of uncertainty, leaving operators without a principled basis for identifying reliable cross-client interactions. We address this limitation by characterizing how uncertainty propagates through the FedGC framework. We derive closed-form covariance recursions for the cross-covariances induced by the coupled client-server feedback loop, and establish spectral-radius-based convergence conditions yielding closed-form expressions for the steady-state variances at both the client and server. Under mild stability conditions, we prove that the steady-state uncertainty depends only on client data statistics (aleatoric) and is independent of the priors placed on the model parameters (epistemic). Building on this asymptotic characterization, we construct a post-training hypothesis testing procedure that separates genuine cross-client interactions from spurious edges. Experiments on synthetic and real-world datasets show that the predicted uncertainty propagation matches the theory across multiple operating regimes, while consistently outperforming the state-of-the-art federated causal structure learning baselines.", "date": "2026-02-13", "categories": []}
{"id": "2506.16234", "title": "Sequential Causal Discovery with Noisy Language Model Priors", "abstract": "Causal discovery from observational data typically assumes access to complete data and availability of perfect domain experts. In practice, data often arrive in batches, are subject to sampling bias, and expert knowledge is scarce. Language Models (LMs) offer a surrogate for expert knowledge but suffer from hallucinations, inconsistencies, and bias. We present a hybrid framework that bridges these gaps by adaptively integrating sequential batch data with LM-derived noisy, expert knowledge while accounting for both data-induced and LM-induced biases. We propose a representation shift from Directed Acyclic Graph (DAG) to Partial Ancestral Graph (PAG), that accommodates ambiguities within a coherent framework, allowing grounding the global LM knowledge in local observational data. To guide LM interactions, we use a sequential optimization scheme that adaptively queries the most informative edges. Across varied datasets and LMs, we outperform prior work in structural accuracy and extend to parameter estimation, showing robustness to LM noise.", "date": "2025-06-19", "categories": []}
{"id": "2507.03310", "title": "Causal Discovery for Irregularly Time Series with Consistency Guarantees", "abstract": "This paper studies causal discovery in irregularly sampled time series-a key challenge in risk-sensitive domains like finance, healthcare, and climate science, where missing data and inconsistent sampling frequencies distort causal mechanisms. The main challenge comes from the interdependence between missing data imputation and causal structure recovery: errors in imputation and structure learning can reinforce each other, leading to an inaccurate causal graph. Existing methods either impute first and then discover, or jointly optimize both via neural representation learning, but lack explicit mechanisms to ensure mutual consistency of imputation and structure learning. We address this challenge with ReTimeCausal, an EM-based framework that alternates between imputation and structure learning, which encourages structural consistency throughout the optimization process. Our framework provides theoretical consistency guarantees for structure recovery and extends classical results to settings with irregular sampling and high missingness. ReTimeCausal combines kernel-based sparse regression and structural constraints in an alternating process that updates the completed data and the causal graph in turn. Experiments on synthetic and real-world datasets show that ReTimeCausal is more effective than existing methods under challenging irregular sampling and missing data.", "date": "2025-07-04", "categories": []}
{"id": "2603.02678", "title": "Causal Discovery Should Embrace the Wisdom of the Crowd", "abstract": "This paper argues for recognizing an emerging paradigm of causal learning by wisdom of the crowd. Recent developments in government, industry, and research point to the rise of decentralized and crowd-based approaches within causal modeling, where causal knowledge distributed across many contributors can be systematically elicited and integrated with causal learning workflows. In this paradigm, causal learning becomes a distributed decision-making problem: each participant contributes partial and potentially noisy knowledge, while collective contributions help construct a global causal structure. This direction is enabled by advances in crowdsourcing platforms, expert knowledge elicitation, aggregation techniques, and large language model (LLM)-augmented information acquisition. Its promise is increasingly visible in early research and emerging real-world practices. Building on this momentum, we outline a framework for crowd-based causal learning spanning elicitation, modeling, aggregation, and optimization. We further discuss the opportunities and challenges introduced by this paradigm and call for interdisciplinary collaboration across causal learning, collective intelligence, human-AI interaction, and decision science.", "date": "2026-03-03", "categories": []}
{"id": "2605.05743", "title": "Fourier Feature Methods for Nonlinear Causal Discovery: FFML Scoring, TRFF Scoring, and FFCI Testing in Mixed Data", "abstract": "Gaussian process (GP) marginal likelihood scores and kernel conditional independence tests are theoretically appealing for nonlinear causal discovery but computationally prohibitive at scale. We present three complementary RFF-based methods forming a practical toolkit for score-based, constraint-based, and hybrid causal discovery.\n  The Fourier Feature Marginal Likelihood (FFML) score approximates the exact GP marginal likelihood by replacing the $n x n$ kernel Gram matrix with a finite-dimensional feature representation, reducing cost to $O(nm^2 + m^3)$ while retaining the probabilistic interpretation and automatic complexity penalty of the exact score. FFML extends to mixed (continuous and discrete) parent sets via a product-kernel construction, with a Kronecker path for small discrete parent sets and a Hadamard-product path otherwise.\n  The Tetrad Random Fourier Feature (TRFF) score is a complementary BIC-style alternative using penalized Student-t regression with random Fourier features. TRFF offers robustness to heavy-tailed noise and faster runtime than FFML. Empirically, TRFF and FFML exhibit a complementary precision-recall profile: TRFF achieves higher precision while FFML achieves better recall and lower SHD overall.\n  The Fourier Feature Conditional Independence (FFCI) test is a fast nonparametric CI test for mixed data, using ridge residualization in feature space and a Frobenius-norm cross-covariance statistic approximated as a weighted sum of chi-squared variables. Empirically, BOSS+FFML achieves the lowest SHD on nonlinear data, while BOSS+TRFF offers the highest precision. When run through PC-Max, FFCI and RCIT exhibit complementary precision-recall profiles: RCIT is more precise while FFCI achieves better recall and substantially lower SHD, at approximately twice the runtime.", "date": "2026-05-07", "categories": []}
{"id": "2605.08111", "title": "TTCD:Transformer Integrated Temporal Causal Discovery from Non-Stationary Time Series Data", "abstract": "The widespread availability of complex time series data in various domains such as environmental science, epidemiology, and economics demands robust causal discovery methods that can identify intricate contemporaneous and lagged relationships in non-stationary, nonlinear, and noisy settings. Existing constraint-based methods often rely heavily on conditional independence tests that degrade for limited data samples and complex distributions, while score-based methods impose strong statistical assumptions. Recent methods address special cases such as change point detection or distribution shifts, but struggle to provide a unified solution. We propose the Transformer Integrated Temporal Causal Discovery (TTCD) Framework, a novel end-to-end approach that learns contemporaneous and lagged causal relations from non-stationary time series. TTCD introduces a Non-Stationary Feature Learner integrating temporal and frequency-domain attention with dynamic non-stationarity profiling, and a custom Causal Structure Learner. A key innovation is reconstruction-guided causal signal distillation, to distill essential causal signals through the reconstruction process of the transformer decoder, which mitigates noise and spurious correlations while preserving meaningful dependencies. The Causal Structure Learner operates on distilled reconstructed signals to infer the underlying causal graph without restrictive assumptions on noise distributions or data generation processes. Experiments on synthetic, benchmark, and real world datasets show that TTCD consistently outperforms state-of-the-art baselines in both accuracy and consistency with domain knowledge, demonstrating the approach's effectiveness for causal discovery in challenging real world contexts.", "date": "2026-04-27", "categories": []}
{"id": "2605.08197", "title": "ReplaySCM: A Benchmark for Executable Causal Mechanism Induction from Interventions", "abstract": "Most causal benchmarks for language models score local answers or graph structure. We introduce ReplaySCM, a 1,300 item benchmark for executable causal mechanism induction from finite interventional evidence. Each item contains binary worlds generated by a latent fully observed acyclic Boolean structural causal model (SCM). A system must output a mechanism map in a restricted Boolean DSL; the submission is parsed, checked for legality and acyclicity, and replayed on training and held-out intervention worlds. Scoring uses replay behavior rather than formula strings, so syntactically different mechanisms receive credit when they behave correctly. ReplaySCM varies the structural information disclosed to the model through Ordered, Block-order, Hidden-order, and Hidden-roots settings, and includes Alternative-SCM tasks that supply a valid reference SCM and ask for a semantically distinct alternative that fits the training worlds, together with a separating intervention and witness. Frontier LLMs infer parts of the functional-parent structure, but held-out replay drops sharply when order or root structure is hidden. We also evaluate a matched support-audit ladder: Original, Extra Worlds, and Counterexample Audit (CEx), that raises mean local predecessor-pattern coverage from 0.8949 to 0.9815 to 1.0; under the audited searches, no discovered semantic alternative remains consistent with the training worlds. The Ordered/Hidden-order gap persists under this stronger evidence. ReplaySCM complements answer-level causal reasoning and graph-discovery benchmarks by evaluating executable replay generalization from finite interventional evidence, without claiming unique identification of the latent SCM.", "date": "2026-05-05", "categories": []}
{"id": "2605.09870", "title": "Intervention-Based Time Series Causal Discovery via Simulator-Generated Interventional Distributions", "abstract": "We propose SVAR-FM (Structural VAR with Flow Matching), a framework for time series causal discovery that treats a physics-based simulator as a mechanical realization of Pearl's do operator. Clamping a variable inside the simulator physically severs confounding paths, producing interventional data by construction. Conditional Flow Matching then learns the nonlinear interventional conditionals. Theoretically, we prove that the full structural VAR becomes identifiable under a coverage condition on the simulator-clampable variables, and derive an end-to-end error bound that decomposes into Monte Carlo, simulator fidelity, and Flow Matching terms. A sign-flip corollary predicts that when simulator accuracy falls below a threshold, the estimated causal effect reverses sign. Empirically, a benchmark across four scientific domains confirms that SVAR-FM recovers the correct causal sign where observational methods produce sign-reversed estimates due to confounding. A case study in ultrafast laser physics verifies the sign-flip prediction by physically varying the accuracy level of a first-principles quantum solver: the low-accuracy setting reverses the causal sign, while the high-accuracy setting recovers the correct direction (R-squared = 0.983, zero bias).", "date": "2026-05-11", "categories": []}
{"id": "2605.10163", "title": "Coarsening Linear Non-Gaussian Causal Models with Cycles", "abstract": "Recent work on causal abstraction, in particular graphical approaches focusing on causal structure between clusters of variables, aims to summarize a high-dimensional causal structure in terms of a low-dimensional one. Existing methods for learning such summaries from data assume that both the high- and low-dimensional structures are acyclic, which is helpful for causal effect identification and reasoning but excludes many high-dimensional models and thus limits applicability. We show that in the linear non-Gaussian (LiNG) setting, the high-dimensional acyclicity assumption can be relaxed while still allowing recovery of a low-dimensional causal directed acyclic graph (DAG). We further connect identifiability of this low-dimensional DAG to existing results: LiNG models with cycles are observationally identifiable only up to an equivalence class whose members differ by reversals of directed cycles; our low-dimensional DAG, which is invariant across all members of a given equivalence class, thus forms a natural representative of the class. While existing approaches for learning this observational equivalence class over high-dimensional variables have exponential time complexity, our low-dimensional summary is learned in worst-case cubic time and comes with explicit bounds on the sample complexity. We provide open source code and experiments on synthetic data to corroborate our theoretical results.", "date": "2026-05-11", "categories": []}
{"id": "2605.10651", "title": "A Recursive Decomposition Framework for Causal Structure Learning in the Presence of Latent Variables", "abstract": "Constraint-based causal discovery is widely used for learning causal structures, but heavy reliance on conditional independence (CI) testing makes it computationally expensive in high-dimensional settings. To mitigate this limitation, many divide-and-conquer frameworks have been proposed, but most assume causal sufficiency, i.e., no latent variables. In this paper, we show that divide-and-conquer strategies can be theoretically generalized beyond causal sufficiency to settings with latent variables. Specifically, we propose a recursive decomposition framework, termed DiCoLa, that enables divide-and-conquer causal discovery in the presence of latent variables. It recursively decomposes the global learning task into smaller subproblems and integrates their solutions through a principled reconstruction step to recover the global structure. We theoretically establish the soundness and completeness of the proposed framework. Extensive experiments on synthetic data demonstrate that our approach significantly improves computational efficiency across a range of causal discovery algorithms, while experiments on a real-world dataset further illustrate its practical effectiveness.", "date": "2026-05-11", "categories": []}
{"id": "2602.09034", "title": "Latent-Space Causal Discovery from Indirect Neuroimaging Observations", "abstract": "Neuroimaging does not observe causal variables directly: hemodynamics and volume conduction distort signals so that statistical dependence need not reflect latent neural influence. Before estimating graphs, one must specify under what assumptions delayed directed structure can be studied from such indirect observations. We formalize a conditional setting - recoverable inversion under modality physics together with nonstationary latent dynamics - and derive an inversion-error propagation bound under explicit assumptions. Building on this framing, we propose INCAMA (INdirect CAusal MAmba): physics-aware inversion coupled with a delay-aware Mamba encoder that uses mechanism shifts as informative variation for directed graph scoring. We use controlled simulations for quantitative validation and HCP motor-task fMRI as a zero-shot external transfer check based on anatomical and task-network consistency. Across TVB simulations, INCAMA improves directed-structure recovery by 2-3x in F1 over observation-space and two-stage baselines, and on HCP motor-task fMRI it produces sparse directed estimates concentrated in canonical visuo-motor pathways.", "date": "2026-01-30", "categories": []}
{"id": "2603.00041", "title": "Econometric vs. Causal Structure-Learning for Time-Series Policy Decisions: Evidence from the UK COVID-19 Policies", "abstract": "Causal machine learning (ML) recovers graphical structures that inform us about potential cause-and-effect relationships. Most progress has focused on cross-sectional data with no explicit time order, whereas recovering causal structures from time series data remains the subject of ongoing research in causal ML. In addition to traditional causal ML, this study assesses econometric methods that some argue can recover causal structures from time series data. The use of these methods can be explained by the significant attention the field of econometrics has given to causality, and specifically to time series, over the years. This presents the possibility of comparing the causal discovery performance between econometric and traditional causal ML algorithms. We seek to understand if there are lessons to be incorporated into causal ML from econometrics, and provide code to translate the results of these econometric methods to the most widely used Bayesian Network R library, bnlearn. We investigate the benefits and challenges that these algorithms present in supporting policy decision-making, using the real-world case of COVID-19 in the UK as an example. Four econometric methods are evaluated in terms of graphical structure, model dimensionality, and their ability to recover causal effects, and these results are compared with those of eleven causal ML algorithms. Amongst our main results, we see that econometric methods provide clear rules for temporal structures, whereas causal-ML algorithms offer broader discovery by exploring a larger space of graph structures that tends to lead to denser graphs that capture more identifiable causal relationships.", "date": "2026-02-09", "categories": []}
{"id": "2605.04081", "title": "Time series causal discovery with variable lags", "abstract": "Causal Bayesian Networks (CBNs) are a powerful tool for reasoning under uncertainty about complex real-world problems. Such problems evolve over time, responding to external shocks as they occur. To support decision-making, CBNs require a cause-and-effect map of the variables under consideration, known as the network's structure. Learning the graphical structure of a causal model from data remains challenging; learning it from time-series data is even harder because dependencies may arise at different time lags. Existing time-series causal discovery methods often assume a fixed lag window and do not explicitly optimise edge-specific lags. We propose a Tabu-based structure learning algorithm that searches for a time-ordered directed structure (i.e., where every edge respects time) while allowing edge-specific lags up to a specified maximum lag. The approach uses a decomposable BIC-based score with node-specific effective sample sizes and an explicit lag-length penalty encouraging parsimonious delay assignments while preserving efficient local score updates. We provide theoretical guarantees of validity and local optimality, and we also describe a parallel implementation for improved scalability. In simulations, the method recovered graph structure competitively and estimated lags accurately when true adjacencies were recovered. On a real-world UK COVID-19 policy dataset, the learnt structure was dominated by short delays while retaining a substantial minority of longer-lag dependencies, consistent with delayed behavioural and epidemiological effects.", "date": "2026-04-15", "categories": []}
{"id": "2605.07204", "title": "Arrow: A Foundation Model for Causal Discovery", "abstract": "We introduce Arrow, a foundation model for zero-shot causal discovery on observational tabular data. Arrow factorizes a directed acyclic graph into an undirected skeleton and a topological order, guaranteeing acyclicity by construction. Given a new dataset, it uses a transformer-based architecture to contextualize variables within and across observations, then predicts skeleton edge probabilities and node order scores that together define a graph. Arrow is trained in a supervised fashion on synthetic datasets with ground-truth graphs, using an end-to-end differentiable directed edge composite likelihood induced by the skeleton-order factorization. The training distribution spans diverse graph families, functional forms, noise models, and dataset shapes. Across in- and out-of-distribution synthetic, semi-synthetic, and real datasets, Arrow matches or outperforms existing causal discovery methods at substantially lower inference cost than competitive alternatives. Our results demonstrate that large-scale pretraining on diverse synthetic data can yield zero-shot causal discovery models that are fast, accurate, and reusable on new datasets.", "date": "2026-05-08", "categories": []}
{"id": "2605.07267", "title": "PerCaM-Health: Personalized Dynamic Causal Graphs for Healthcare Reasoning", "abstract": "Personalized healthcare decisions require reasoning about how physiological and behavioral variables influence an individual patient over time. Existing temporal causal discovery methods are poorly matched to this setting: cohort-level models provide stable but non-personalized structures, while per-patient discovery is unreliable because individual trajectories are short, noisy, irregular, and non-stationary. This creates a fundamental gap between population-level causal modeling and the patient-specific, time-varying mechanisms needed for intervention reasoning. We introduce PerCaM-Health, a framework for learning personalized dynamic causal graphs from longitudinal health data. The framework learns a knowledge-guided population temporal graph, then conservatively adapts and evolves it using patient-specific temporal evidence and rolling-window updates, producing interpretable and auditable graph sequences. By coupling these graphs with temporal structural equations, the framework enables patient-level counterfactual queries, such as estimating short-horizon outcome changes under hypothetical behavioral interventions. Experiments on a semi-synthetic dynamic health benchmark show that PerCaM-Health improves graph recovery, dynamic edge tracking, and intervention direction accuracy compared to cohort-level, per-patient, and non-personalized temporal baselines. These results demonstrate that jointly modeling personalization and temporal evolution yields more reliable causal structure and intervention reasoning.", "date": "2026-05-08", "categories": []}
{"id": "2605.07280", "title": "Mask2Cause: Causal Discovery via Adjacency Constrained Causal Attention", "abstract": "Leveraging deep learning for causal discovery in time series remains challenging because existing neural methods predominantly rely on component-wise architectures that fail to capture shared system dynamics or employ decoupled post-hoc graph extraction that risks overfitting to spurious correlations. We propose $\\textbf{Mask2Cause}$, an end-to-end framework that recovers the underlying causal graph directly during the forecasting forward pass. Our approach introduces an Inverted Variable Embedding and an Adjacency-Constrained Masked Attention mechanism, trained with homoscedastic or heteroscedastic objectives to capture causal influences in both mean and variance. Empirical results on diverse benchmarks, from synthetic chaotic dynamics to realistic biological simulations, demonstrate state-of-the-art causal discovery with significantly reduced parameter complexity compared to standard baselines. We further show that inferred causal structures can be used to reduce parameter count of forecasting models by more than 70% on average while maintaining predictive accuracy.", "date": "2026-05-08", "categories": []}
{"id": "2605.07467", "title": "Physical Simulators as Do-Operators: Causal Discovery under Latent Confounders for AI-for-Science", "abstract": "Existing interventional causal discovery methods -- IGSP, DCDI, ENCO -- assume causal sufficiency (no latent confounders) and rely on virtual interventions in synthetic simulators. In AI-for-Science settings such as molecular design and materials science, latent confounders are ubiquitous and real interventions (e.g., physics-based simulations) require hours to days per data point. We propose CFM-SD (Causal Flow Matching with Simulation Data), which uses first-principles physical simulators as do-operators in Pearl's interventional calculus to simultaneously handle latent confounders and real interventional data. Theoretically, $d$-variable causal structure is identifiable with $O(d)$ single-variable interventions -- the minimum under physical realizability constraints. In Intrinsic Evaluation on synthetic data ($\\gamma=0.2$--$0.8$), CFM-SD achieves average F1$=0.800$ vs. F1$=0.127$--$0.562$ for all baselines. In Extrinsic Evaluation on real scientific data, CFM-SD achieves 57--58\\% bias reduction in molecular toxicity prediction and battery electrolyte optimization, demonstrating practical value beyond synthetic benchmarks.", "date": "2026-05-08", "categories": []}
{"id": "2409.00417", "title": "Learning linear acyclic causal model including Gaussian noise using ancestral relationships", "abstract": "This paper discusses algorithms for learning causal DAGs. The PC algorithm makes no assumptions other than the faithfulness to the causal model and can identify only up to the Markov equivalence class. LiNGAM assumes linearity and continuous non-Gaussian disturbances for the causal model, and the causal DAG defining LiNGAM is shown to be fully identifiable. The PC-LiNGAM, a hybrid of the PC algorithm and LiNGAM, can identify up to the distribution-equivalence pattern of a linear causal model, even in the presence of Gaussian disturbances. However, in the worst case, the PC-LiNGAM has factorial time complexity for the number of variables. In this paper, we propose an algorithm for learning the distribution-equivalence patterns of a linear causal model with a lower time complexity than PC-LiNGAM, using the causal ancestor finding algorithm in Maeda and Shimizu, which is generalized to account for Gaussian disturbances.", "date": "2024-08-31", "categories": []}
{"id": "2601.16715", "title": "Dynamic Expert-Guided Model Averaging for Causal Discovery", "abstract": "Would-be practitioners of causal discovery face a dizzying array of algorithms without a clear best choice. This abundance of competitive methods makes ensembling a natural strategy for practical applications. At the same time, real-world use cases frequently violate the assumptions on which common causal discovery algorithms are based, forcing reliance on expert knowledge. Inspired by recent work on dynamically requested expert knowledge and large language models (LLMs) as experts, we present a flexible model averaging method that integrates selective expert querying to ensemble a diverse set of causal discovery algorithms. Crucially, we distinguish between edge existence and orientation, enabling the method to leverage the complementary strengths of data-driven discovery and expert input. We further consider the realistic setting of limited access to an imperfect expert, using disagreement among algorithms to query the expert in cases of greater uncertainty. Experiments demonstrate that our method consistently outperforms strong baselines on both clean and noisy data. Code and data are available at https://anonymous.4open.science/r/expert-cd-ensemble-3282/.", "date": "2026-01-23", "categories": []}
{"id": "2605.01669", "title": "PRCD-MAP: Learning How Much to Trust Imperfect Priors in Causal Discovery", "abstract": "External priors of unknown reliability create a brittle trade-off in causal discovery: blind trust amplifies errors, blind rejection wastes signal. Real priors are also heterogeneously reliable -- physical laws are trustworthy, LLM-suggested edges are speculative -- yet existing methods either ignore priors or impose them through globally uniform trust. We propose PRCD-MAP, a soft prior-consumption layer that assigns per-edge trust to an imperfect prior and uses it to modulate a prior-aware $\\ell_1$ and prior-weighted $\\ell_2$ regularizer in a MAP objective. Trust is calibrated by empirical Bayes on a Laplace-approximated marginal likelihood and propagated along the prior graph by an MLP, so data-confirmed neighborhoods boost trust and contradictions suppress it. PRCD-MAP enjoys a population-level safety guarantee: it is $\\varepsilon$-safe in expectation over the prior-generation distribution, with $\\varepsilon\\leq C\\cdot\\mathrm{acc}(1{-}\\mathrm{acc})\\cdot d^2/T$ at the parametric $T^{-1}$ rate and vanishing at the prior-quality endpoints. When the prior is uninformative, learned trust provably collapses to its floor and the method recovers a no-prior baseline. Empirically, on real CausalTime data PRCD-MAP exploits informative LLM priors (LLM-prior gain $+0.067/+0.089$ AUROC on AQI/Medical over a no-prior PRCD-MAP backbone; combined backbone+prior lead $+0.123/+0.043$ over PCMCI+), auto-attenuates on the anonymous-variable Traffic stress test, and retains a lead at $d{=}300$; against BayesDAG, the closest soft-Bayesian baseline, PRCD-MAP wins on every CausalTime dataset under a matched $W_0$-only protocol. A four-way ablation isolates each component: EB calibration and MLP trust propagation jointly carry the plurality of the gain, with positive sign on every dataset. Extensions to nonlinear (NAM) and cross-sectional settings show the calibrated-trust principle is setting-agnostic.", "date": "2026-05-03", "categories": []}
{"id": "2605.05568", "title": "Relaxed Sparsest-Permutation Formulation for Causal Discovery at Scale", "abstract": "Despite the growing availability of large datasets, causal structure learning remains computationally prohibitive at scale. We revisit sparsest-permutation learning for linear structural equation models and show that exact Cholesky factorization is unnecessary for structure recovery. This observation motivates a support-level relaxation that searches for sparse triangular factors over a precision-support screening graph. The relaxed formulation can be efficiently evaluated via masked zero-fill incomplete Cholesky factorization, enabling scalable comparison of candidate orderings. At the population level, we establish soundness for Markov equivalence class (MEC) recovery under no-cancellation and sparsest Markov representation assumptions, as well as robustness to ordering misspecification. Motivated by these guarantees, we introduce SCOPE, a sparse-Cholesky pipeline that provides a scalable implementation of the relaxed formulation. Experiments on synthetic and real datasets demonstrate that SCOPE matches the MEC recovery accuracy of substantially slower baselines, while achieving significantly reduced runtime and scaling to 10k variables.", "date": "2026-05-07", "categories": []}
{"id": "2605.06288", "title": "A Topological Sorting Criterion for Random Causal Directed Acyclic Graphs", "abstract": "Random directed acyclic graphs (DAGs) based on imposing an order on Erd\\H{o}s-R\\'enyi and scale free random graphs are widely used for evaluating causal discovery algorithms. We show that in such DAGs, the set of nodes reachable via open paths, termed relatives, increases monotonically along the causal order. We assess the prevalence of this pattern numerically, and demonstrate that it can be exploited for causal order recovery via sorting by the estimated number of relatives. We note that many simulations in the literature feature settings where this yields an excellent proxy for the causal order, and show that a strict increase of relatives along the causal order leads to a singular Markov equivalence class. We propose sampling time-series DAGs as a possible alternative and discuss implications for causal discovery algorithms and their evaluation on synthetic data.", "date": "2026-05-07", "categories": []}
{"id": "2605.06335", "title": "Eliciting associations between clinical variables from LLMs via comparison questions across populations", "abstract": "The training data of large language models (LLMs) comprises a wide range of biomedical literature, reflecting data from many different patient populations. We investigate how it might be possible to recover information on correlation and causal links between patient characteristics, as a key building block for medical decision making. To avoid the pitfalls of direct elicitation, we propose an approach based on structured comparison questions, specifically patient comparison triplet questions. This is combined with a statistical model for the LLM representation that provides estimates of correlations without access to activations or model internals. Intuitively, we consider how similarity decisions of LLMs based on a first variable are affected by providing information on a second variable for one of the patients being assessed. We then induce prompt-level environment shifts to obtain correlation estimates for different subpopulations, which enables an invariant causal prediction (ICP) approach to obtain conservative candidate parent links. We demonstrate the method in two clinical domains, chronic obstructive pulmonary disease (COPD) and multiple sclerosis (MS). Across prompted environments, the elicited correlations are smooth, stable, and clinically interpretable, yet vary in a statistically significant way that supports downstream invariance testing, such that ICP provides a small set of candidate invariant parent links. These results show that indirect elicitation via triplet comparisons can recover meaningful association structure from LLMs and offer a cautious route from implicit correlations to causal statements that are congruent with LLM answering patterns.", "date": "2026-05-07", "categories": []}
{"id": "2605.04191", "title": "Heterogeneous Ordinal Structure Learning with Bayesian Nonparametric Complexity Discovery", "abstract": "Public attitudes toward artificial intelligence are heterogeneous, ordinally measured, and poorly captured by any single dependency graph. Existing ordinal structure learners assume a shared directed acyclic graph (DAG) across all respondents; recent heterogeneous ordinal graphical-model approaches focus on subgroup discovery rather than confirmatory cluster-specific DAG estimation; and latent profile analyses discard dependency structure entirely. We introduce a heterogeneous ordinal structure-learning framework combining monotone Gaussian score embedding, Bayesian nonparametric (BNP) complexity discovery via a truncated stick-breaking prior, and confirmatory fixed-K estimation with cluster-specific sparse DAG learning. The key methodological insight is a discovery-to-confirmation workflow: the nonparametric stage calibrates plausible archetype complexity, while inner-validated confirmatory refitting yields stable, interpretable structural estimates. On the 2024 Pew American Trends Panel AI attitudes survey, Wave 152 (W152) survey, (N = 4,788, 8 ordinal items), the confirmatory K*=5 model reduces holdout transformed-score mean squared error (MSE) by 25.8% over a single-graph baseline and by 4.6% over mixture-only clustering. A controlled tiered semi-synthetic benchmark calibrated to W152 structure validates recovery across difficulty regimes and transparently reveals failure modes under stress conditions.", "date": "2026-05-05", "categories": []}
{"id": "2605.04381", "title": "Causal discovery under mean independence and linearity", "abstract": "Causal discovery methods such as LiNGAM identify causal structure from observational data by assuming mutually independent disturbances. This assumption is fragile: shared volatility, common scale effects, or other forms of dependence can cause the methods to recover the wrong causal order, even with infinite data. We introduce the Linear Mean-Independent Acyclic Model (LiMIAM), which replaces full independence with weaker one-sided mean-independence restrictions on the disturbances. Under finite-order consequences of these restrictions, source nodes are generically identifiable, and hence a compatible causal order can be recovered recursively. Our proof is constructive and leads to DirectLiMIAM, a sequential residual-based algorithm for causal discovery under dependent noise. In simulations with mean-independent but dependent disturbances, DirectLiMIAM outperforms LiNGAM methods. A large-scale empirical application to the oil market highlights the implausibility of the independence assumption and the ability of DirectLiMIAM to recover a realistic causal ordering, from policy to production and from prices to inflation.", "date": "2026-05-06", "categories": []}
{"id": "2605.04838", "title": "PAIR-CI: Calibrated Conditional Independence Testing for Causal Discovery with Incomplete Data", "abstract": "The standard constraint-based paradigm for causal discovery with incomplete data -- impute first, test second -- is frequently miscalibrated: any consistent conditional independence (CI) test rejects a true null with probability approaching 1 when imputation error induces spurious conditional dependence. We introduce PAIR-CI, a nonparametric CI test that restores calibration by integrating multiple imputation directly into the inferential procedure via a paired permutation design. PAIR-CI compares cross-validated models that include and exclude the candidate variable while receiving the same imputed conditioning set, forcing imputation error to cancel in their loss difference rather than contaminate the test statistic. A provably consistent variance estimator jointly accounts for uncertainty arising from cross-validation and multiple imputation -- to our knowledge, the first formal unification of these two inferential frameworks. In simulations, existing imputation-based CI tests exhibit false positive rates of 28--45% when data are missing not at random (MNAR), whereas PAIR-CI averages below the nominal 5% level across data-generating processes and missingness mechanisms. These gains are largest in nonlinear settings and grow with causal graph size: when integrated into the PC algorithm, PAIR-CI reduces structural Hamming distance by 8% on 10-variable nonlinear graphs, 15% on 30-variable equivalents, and up to 44% on the 56-variable HAILFINDER network, with stable performance in all settings.", "date": "2026-05-06", "categories": []}
{"id": "2605.03045", "title": "TCD-Arena: Assessing Robustness of Time Series Causal Discovery Methods Against Assumption Violations", "abstract": "Causal Discovery (CD) is a powerful framework for scientific inquiry. Yet, its practical adoption is hindered by a reliance on strong, often unverifiable assumptions and a lack of robust performance assessment. To address these limitations and advance empirical CD evaluation, we present TCD-Arena, a modularized, highly customizable, and extendable testing kit to assess the robustness of time series CD algorithms against stepwise more severe assumption violations. For demonstration, we conduct an extensive empirical study comprising around 30 million individual CD attempts and reveal nuanced robustness profiles for 33 distinct assumption violations. Further, we investigate CD ensembles and find that they have the potential to improve general robustness, which has implications for real-world applications. With this, we strive to ultimately facilitate the development of CD methods that are reliable for a diverse range of synthetic and potentially real-world data conditions.", "date": "2026-05-04", "categories": []}
{"id": "2605.03267", "title": "Partial Effective Information Decomposition for Synergistic Causality", "abstract": "Causality is a central topic in scientific inquiry, yet for complex systems, the identification and analysis of synergistic causation remain a challenging and fundamental problem. In the context of causal relations among multivariate variables, a decomposition framework grounded in interventionist causation is still lacking. To address this gap, this paper proposes Partial Effective Information Decomposition (PEID), a framework that decomposes the influence of multiple source variables on a target variable under maximum-entropy interventions into unique and synergistic information, thereby providing a unified and computable characterization of synergistic causal relations. Theoretically, in the three-variable case, the proposed framework is compatible with the major axioms of Partial Information Decomposition (PID). Empirically, under maximum-entropy interventions, correlations among input variables are removed, causing redundancy to vanish and thereby enabling PEID to compute synergistic relations. Furthermore, based on this framework, it is possible to define causal graphs containing hyperedges as well as downward causation, thus offering a unified toolkit for analyzing cross-scale and multivariate causal mechanisms in complex systems. Finally, applying the framework to a machine-learning-based air quality forecasting task on KnowAir-V2, we demonstrate that PEID can extract interpretable inter-station causal structures from a learned dynamical model. These results suggest that PEID provides a general interventionist information-theoretic tool for analyzing multivariate and synergistic causal mechanisms in complex systems.", "date": "2026-05-05", "categories": []}
{"id": "2605.03268", "title": "Partially Observed Structural Causal Models", "abstract": "Here we introduce Partially Observed Structural Causal Models (POSCMs) that formalize causal systems where latent contexts co-determine both the interaction structure and downstream mechanisms on observed variables. POSCMs provide an extension of structural causal models (SCMs), as a self-contained causal modeling framework for endogenous graphs, allowing for an intervention hierarchy spanning node- and edge-level context and endogenous variable interventions. To enable surgical edge interventions, we adopt a Kolmogorov-Arnold-Sprecher edge-functional decomposition, an existence theorem for representing each node mechanism as a sum of univariate functions of its parents, yielding an explicit parametrization of dyadic functional contributions. We provide an identifiability theory that clarifies which intervention families would suffice to disentangle structure formation from mechanisms. We empirically validate these predictions in a biophysically detailed virtual human retina simulator, constructing intervention protocols that (i) reproduce the non-identifiability predicted when context is latent and no context-level interventions are available, (ii) exhibit structure-mechanism confounding under latent edges when only node interventions are observed, and (iii) recover synaptic input-output relationships via targeted node interventions, consistent with our positive kernel identifiability result. Our work generalizes SCMs in a way that allows it to work in a world closer to the one we live in.", "date": "2026-05-05", "categories": []}
{"id": "2605.02318", "title": "Can Causal Discovery Algorithms Help in Generating Legal Arguments?", "abstract": "In 2011, Judea Pearl received the Turing Award, considered the Nobel Prize in Computing, for fundamental contributions to artificial intelligence through the development of a calculus for probabilistic and causal reasoning. It includes pioneering the development of causal discovery algorithms. These computer algorithms can analyze large multivariate datasets and automatically discover the causal relationships among the constituent variables. They have been widely used in many critical fields such as medicine and economics to support decisions. However, to our knowledge, they have not been leveraged in law. This paper attempts to alleviate this gap by investigating whether causal discovery algorithms can be leveraged for automated generation of legal arguments. To that end, a novel legal dataset is prepared by identifying 17 legal concepts, such as physical assault and property dispute. A curated collection of 150 homicide cases are annotated with these concepts, e.g., a case is annotated with physical assault only if a physical assault had been reported in that case. Subsequently, a selected set of widely-used causal discovery algorithms is applied to the annotated dataset to discover the causal relationships between the legal concepts. Additionally, the degrees of belief associated with the discovered relationships are quantified in mathematical probabilities. It is shown that some of the causal relationships help generate viable legal arguments, e.g., if one could establish that a physical assault has not taken place during a homicide, it should be a sufficient condition (with probability 1) to establish that the homicide has not been committed due to a property-related dispute. Thus, this paper shows that causal discovery algorithms can be helpful in generating legal arguments, opening up avenues for promising future endeavors.", "date": "2026-05-04", "categories": []}
{"id": "2510.04378", "title": "Score-based Greedy Search for Structure Identification of Partially Observed Linear Causal Models", "abstract": "Identifying the structure of a partially observed causal system is essential to various scientific fields. Recent advances have focused on constraint-based causal discovery to solve this problem, and yet in practice these methods often face challenges related to multiple testing and error propagation. These issues could be mitigated by a score-based method and thus it has raised great attention whether there exists a score-based greedy search method that can handle the partially observed scenario. In this work, we propose the first score-based greedy search method for the identification of structure involving latent variables with identifiability guarantees. Specifically, we propose Generalized N Factor Model and establish the global consistency:\n  the true structure including latent variables can be identified up to the Markov equivalence class by using score. We then design\n  Latent variable Greedy Equivalence Search (LGES), a greedy search algorithm for this class of model with well-defined operators,\n  which search very efficiently over the graph space to find the optimal structure. Our experiments on both synthetic and real-life data validate the effectiveness of our method (code will be publicly available).", "date": "2025-10-05", "categories": []}
{"id": "2605.00398", "title": "M-CaStLe: Uncovering Local Causal Structures in Multivariate Space-Time Gridded Data", "abstract": "Causal graph discovery for space-time systems is challenging in high-dimensional gridded data, which often has many more grid cells than temporal observations per cell. The Causal Space-Time Stencil Learning (CaStLe) meta-algorithm was developed to address that niche under space-time locality and stationarity assumptions, but it is currently limited to univariate analyses. In this work, we present M-CaStLe. M-CaStLe generalizes the local embedding and parent-identification phases of CaStLe to jointly model local within-variable and cross-variable space-time causal structures in gridded data. Like CaStLe, by constraining candidate parents to a constant-size space-time neighborhood and pooling spatial replicates, M-CaStLe increases effective sample size to make discovery tractable in high-dimensional settings. We further decompose the resulting multivariate stencil graph into reaction and spatial graphs to aid interpretation in complex settings.\n  We study M-CaStLe in four settings: a multivariate space-time vector autoregression benchmark with known ground truth, an advective-diffusive-reaction partial differential equation verification problem with derived physical reference structure, an atmospheric chemistry case study in a low-temporal-sample regime, and an El Ni\\~{n}o Southern Oscillation study on reanalysis data, identifying phase-dependent ocean--atmosphere coupling. Across these settings, M-CaStLe more accurately recovers multivariate causal structure in controlled settings and identifies important physical dynamics in real-world case studies. Overall, M-CaStLe advances causal discovery for multivariate space-time systems while retaining interpretability at the grid level.", "date": "2026-05-01", "categories": []}
{"id": "2602.07915", "title": "CausalCompass: Evaluating the Robustness of Time-Series Causal Discovery in Misspecified Scenarios", "abstract": "Causal discovery from time series is a fundamental task in machine learning. However, its widespread adoption is hindered by a reliance on untestable causal assumptions and by the lack of robustness-oriented evaluation in existing benchmarks. To address these challenges, we propose CausalCompass, a flexible and extensible benchmark framework designed to assess the robustness of time-series causal discovery (TSCD) methods under violations of modeling assumptions. To demonstrate the practical utility of CausalCompass, we conduct extensive benchmarking of representative TSCD algorithms across eight assumption-violation scenarios. Our experimental results indicate that no single method consistently attains optimal performance across all settings. Nevertheless, the methods exhibiting superior overall performance across diverse scenarios are almost invariably deep learning-based approaches. We further provide hyperparameter sensitivity analyses to deepen the understanding of these findings. We additionally conduct ablation experiments to explain the strong performance of deep learning-based methods under assumption violations. We also find, somewhat surprisingly, that NTS-NOTEARS relies heavily on standardized preprocessing in practice, performing poorly in the vanilla setting but exhibiting strong performance after standardization. Finally, our work aims to provide a comprehensive and systematic evaluation of TSCD methods under assumption violations, thereby facilitating their broader adoption in real-world applications. The user-friendly implementation, documentation and datasets are available at https://anonymous.4open.science/r/CausalCompass-anonymous-5B4F/.", "date": "2026-02-08", "categories": []}
{"id": "2510.06735", "title": "Incorporating Expert Knowledge into Bayesian Causal Discovery of Mixtures of Directed Acyclic Graphs", "abstract": "Bayesian causal discovery benefits from prior information elicited from domain experts, and in heterogeneous domains any prior knowledge would be badly needed. However, so far prior elicitation approaches have assumed a single causal graph and hence are not suited to heterogeneous domains. We propose a causal elicitation strategy for heterogeneous settings, based on Bayesian experimental design (BED) principles, and a variational mixture structure learning (VaMSL) method -- extending the earlier differentiable Bayesian structure learning (DiBS) method -- to iteratively infer mixtures of causal Bayesian networks (CBNs). We construct an informative graph prior incorporating elicited expert feedback in the inference of mixtures of CBNs. Our proposed method successfully produces a set of alternative causal models (mixture components or clusters), and achieves an improved structure learning performance on heterogeneous synthetic data when informed by a simulated expert. Finally, we demonstrate that our approach is capable of capturing complex distributions in a breast cancer database.", "date": "2025-10-08", "categories": []}
{"id": "2602.01433", "title": "DCD: Decomposition-based Causal Discovery from Autocorrelated and Non-Stationary Temporal Data", "abstract": "Multivariate time series in domains such as finance, climate science, and healthcare often exhibit long-term trends, seasonal patterns, and short-term fluctuations, complicating causal inference under non-stationarity and autocorrelation. Existing causal discovery methods typically operate on raw observations, making them vulnerable to spurious edges and misattributed temporal dependencies. We introduce a decomposition-based causal discovery framework that separates each time series into trend, seasonal, and residual components and performs component-specific causal analysis. Trend components are assessed using stationarity tests, seasonal components using kernel-based dependence measures, and residual components using constraint-based causal discovery. The resulting component-level graphs are integrated into a unified multi-scale causal structure. This approach isolates long- and short-range causal effects, reduces spurious associations, and improves interpretability. Across extensive synthetic benchmarks and real-world climate data, our framework more accurately recovers ground-truth causal structure than state-of-the-art baselines, particularly under strong non-stationarity and temporal autocorrelation.", "date": "2026-02-01", "categories": []}
{"id": "2604.25295", "title": "Optimization-Free Topological Sort for Causal Discovery via the Schur Complement of Score Jacobians", "abstract": "Continuous causal discovery typically couples representation learning with structural optimization via non-convex acyclicity penalties, which subjects solvers to local optima and restricts scalability in high-dimensional regimes. We propose a decoupled paradigm that shifts the causal discovery bottleneck from non-convex optimization to statistical score estimation. We introduce the Score-Schur Topological Sort (SSTS), an algorithm that extracts topological order directly from unconstrained generative models, bypassing constrained structure optimization. We establish that the causal hierarchy leaves a geometric signature within the score function: iterative graph marginalization is mathematically equivalent to computing the Schur complement of the Score-Jacobian Information Matrix (SJIM) under linear conditions. This translates the acyclicity constraint into an algebraic procedure with a dominant cost of O(d^3) operations. For non-linear systems, we formulate the expectation gap of Schur marginalization and introduce Block-SSTS to compress extraction depth, bounding structural error. Empirically, SSTS allows causal structural analysis on non-linear graphs up to d=1000. At this scale, our framework indicates that once the non-convex optimization bottleneck is mathematically bypassed, the structural fidelity of continuous causal discovery is bounded by the finite-sample estimation variance of the global score geometry. By reducing graph extraction to matrix operations, this work reframes scalable causal discovery from a constrained optimization problem to a statistical estimation challenge.", "date": "2026-04-28", "categories": []}
{"id": "2604.23633", "title": "Causal Discovery as Dialectical Aggregation: A Quantitative Argumentation Framework", "abstract": "Constraint-based causal discovery is brittle in finite-sample regimes because erroneous conditional-independence (CI) decisions can cascade into substantial structural errors. We propose Quantitative Argumentation for Causal Discovery (QACD), a semantics-driven framework that represents CI outcomes as graded, defeasible arguments rather than irreversible constraints. QACD maps statistical test outcomes to argument strengths and aggregates conflicting evidence through connectivity-mediated witness propagation, producing a fixed-point acceptability labeling over candidate adjacencies. Experiments on standard benchmark Bayesian networks suggest that QACD improves structural coherence and interventional reliability in several noisy or inconsistent CI regimes, while remaining competitive with classical constraint-based, hybrid, and prior argumentation-based baselines.", "date": "2026-04-26", "categories": []}
{"id": "2604.23800", "title": "Causal Representation Learning from General Environments under Nonparametric Mixing", "abstract": "Causal representation learning aims to recover the latent causal variables and their causal relations, typically represented by directed acyclic graphs (DAGs), from low-level observations such as image pixels. A prevailing line of research exploits multiple environments, which assume how data distributions change, including single-node interventions, coupled interventions, or hard interventions, or parametric constraints on the mixing function or the latent causal model, such as linearity. Despite the novelty and elegance of the results, they are often violated in real problems. Accordingly, we formalize a set of desiderata for causal representation learning that applies to a broader class of environments, referred to as general environments. Interestingly, we show that one can fully recover the latent DAG and identify the latent variables up to minor indeterminacies under a nonparametric mixing function and nonlinear latent causal models, such as additive (Gaussian) noise models or heteroscedastic noise models, by properly leveraging sufficient change conditions on the causal mechanisms up to third-order derivatives. These represent, to our knowledge, the first results to fully recover the latent DAG from general environments under nonparametric mixing. Notably, our results match or improve upon many existing works, but require less restrictive assumptions about changing environments.", "date": "2026-04-26", "categories": []}
{"id": "2604.22416", "title": "From Local to Cluster: A Unified Framework for Causal Discovery with Latent Variables", "abstract": "Latent variables pose a fundamental challenge to causal discovery and inference. Conventional local methods focus on direct neighbors but fail to provide macro level insights. Cluster level methods enable macro causal reasoning but either assume clusters are known a priori or require causal sufficiency. Moreover, directly applying single variable causal discovery methods to cluster level problems violates causal sufficiency and leads to incorrect results. To overcome these limitations, this paper proposes L2C (Local to Cluster Causal Abstraction), a unified framework that bridges local structure learning and cluster level causal discovery. Unlike prior work that requires a complete manual assignment of micro variables to clusters, L2C discovers the partition automatically from local causal patterns. Our solution leverages a cluster reduction theorem to reduce any cluster to at most three nodes without loss of causal information, applies local causal discovery to identify direct causes, effects, and V structures in the presence of latent variables, and performs macro level causal inference via cluster level calculus on the learned cluster graph. L2C does not assume causal sufficiency, as latent variables are handled through local discovery. Theoretical analysis shows that L2C ensures soundness, atomic completeness, and computational efficiency. Extensive experiments on synthetic and real world data demonstrate that L2C accurately recovers ground truth clusters and achieves superior macro causal effect identification compared to existing baselines.", "date": "2026-04-24", "categories": []}
{"id": "2506.05590", "title": "Nonlinear Causal Discovery through a Sequential Edge Orientation Approach", "abstract": "Recent advances have established the identifiability of a directed acyclic graph (DAG) under additive noise models (ANMs), spurring the development of various causal discovery methods. However, most existing methods make restrictive model assumptions, rely heavily on general independence tests, or require substantial computational time. To address these limitations, we propose a sequential procedure to orient undirected edges in a completed partial DAG (CPDAG), representing an equivalence class of DAGs, by leveraging the pairwise additive noise model (PANM) to identify their causal directions. We prove that this procedure can recover the true causal DAG assuming a restricted ANM. Building on this result, we develop a novel constraint-based algorithm for learning causal DAGs under nonlinear ANMs. Given an estimated CPDAG, we develop a ranking procedure that sorts undirected edges by their adherence to the PANM, which defines an evaluation order of the edges. To determine the edge direction, we devise a statistical test that compares the log-likelihood values, evaluated with respect to the competing directions, of a sub-graph comprising just the candidate nodes and their identified parents in the partial DAG. We further establish the structural learning consistency of our algorithm in the large-sample limit. Extensive experiments on synthetic and real-world datasets demonstrate that our method is computationally efficient, robust to model misspecification, and consistently outperforms many existing nonlinear DAG learning methods.", "date": "2025-06-05", "categories": []}
{"id": "2407.01621", "title": "Deciphering interventional dynamical causality from non-intervention complex systems", "abstract": "Detecting and quantifying causality is a focal topic in the fields of science, engineering, and interdisciplinary studies. However, causal studies on non-intervention systems attract much attention but remain extremely challenging. Delay-embedding technique provides a promising approach. In this study, we propose a framework named Interventional Dynamical Causality (IntDC) in contrast to the traditional Constructive Dynamical Causality (ConDC). ConDC, including Granger causality, transfer entropy and convergence of cross-mapping, measures the causality by constructing a dynamical model without considering interventions. A computational criterion, Interventional Embedding Entropy (IEE), is proposed to measure causal strengths in an interventional manner. IEE is an intervened causal information flow but in the delay-embedding space. Further, the IEE theoretically and numerically enables the deciphering of IntDC solely from observational (non-interventional) time-series data, without requiring any knowledge of dynamical models or real interventions in the considered system. In particular, IEE can be applied to rank causal effects according to their importance and construct causal networks from data. We conducted numerical experiments to demonstrate that IEE can find causal edges accurately, eliminate effects of confounding, and quantify causal strength robustly over traditional indices. We also applied IEE to real-world tasks. IEE performed as an accurate and robust tool for causal analyses solely from the observational data. The IntDC framework and IEE algorithm provide an efficient approach to the study of causality from time series in diverse non-intervention complex systems.", "date": "2024-06-29", "categories": []}
{"id": "2502.08531", "title": "On Different Notions of Redundancy in Conditional-Independence-Based Discovery of Graphical Models", "abstract": "Conditional-independence-based discovery uses statistical tests to identify a graphical model that represents the independence structure of variables in a dataset. These tests, however, can be unreliable, and algorithms are sensitive to errors and violated assumptions. Often, there are tests that were not used in the construction of the graph. In this work, we show that these redundant tests have the potential to detect or sometimes correct errors in the learned model. But we further show that not all tests contain this additional information and that such redundant tests have to be applied with care. Precisely, we argue that the conditional (in)dependence statements that hold for every probability distribution are unlikely to detect and correct errors - in contrast to those that follow only from graphical assumptions.", "date": "2025-02-12", "categories": []}
{"id": "2604.14691", "title": "CAMO: An Agentic Framework for Automated Causal Discovery from Micro Behaviors to Macro Emergence in LLM Agent Simulations", "abstract": "LLM-empowered agent simulations are increasingly used to study social emergence, yet the micro-to-macro causal mechanisms behind macro outcomes often remain unclear. This is challenging because emergence arises from intertwined agent interactions and meso-level feedback and nonlinearity, making generative mechanisms hard to disentangle. To this end, we introduce \\textbf{\\textsc{CAMO}}, an automated \\textbf{Ca}usal discovery framework from \\textbf{M}icr\\textbf{o} behaviors to \\textbf{M}acr\\textbf{o} Emergence in LLM agent simulations. \\textsc{CAMO} converts mechanistic hypotheses into computable factors grounded in simulation records and learns a compact causal representation centered on an emergent target $Y$. \\textsc{CAMO} outputs a computable Markov boundary and a minimal upstream explanatory subgraph, yielding interpretable causal chains and actionable intervention levers. It also uses simulator-internal counterfactual probing to orient ambiguous edges and revise hypotheses when evidence contradicts the current view. Experiments across four emergent settings demonstrate the promise of \\textsc{CAMO}.", "date": "2026-04-16", "categories": []}
{"id": "2604.14856", "title": "ClimateCause: Complex and Implicit Causal Structures in Climate Reports", "abstract": "Understanding climate change requires reasoning over complex causal networks. Yet, existing causal discovery datasets predominantly capture explicit, direct causal relations. We introduce ClimateCause, a manually expert-annotated dataset of higher-order causal structures from science-for-policy climate reports, including implicit and nested causality. Cause-effect expressions are normalized and disentangled into individual causal relations to facilitate graph construction, with unique annotations for cause-effect correlation, relation type, and spatiotemporal context. We further demonstrate ClimateCause's value for quantifying readability based on the semantic complexity of causal graphs underlying a statement. Finally, large language model benchmarking on correlation inference and causal chain reasoning highlights the latter as a key challenge.", "date": "2026-04-16", "categories": []}
{"id": "2412.07469", "title": "Score-matching-based Structure Learning for Temporal Data on Networks", "abstract": "Causal discovery is a crucial initial step in establishing causality from empirical data and background knowledge. Numerous algorithms have been developed for this purpose. Among them, the score-matching method has demonstrated superior performance across various evaluation metrics, particularly for the commonly encountered Additive Nonlinear Causal Models. However, current score-matching-based algorithms are primarily designed to analyze independent and identically distributed (i.i.d.) data. More importantly, they suffer from high computational complexity due to the pruning step required for handling dense Directed Acyclic Graphs (DAGs). To enhance the scalability of score matching, we have developed a new parent-finding subroutine for leaf nodes in DAGs, significantly accelerating the most time-consuming part of the process: the pruning step. This improvement results in an efficiency-lifted score matching algorithm, termed Parent Identification-based Causal structure learning for both i.i.d. and temporal data on networKs, or PICK. The new score-matching algorithm extends the scope of existing algorithms and can handle static and temporal data on networks with weak network interference. Our proposed algorithm can efficiently cope with increasingly complex datasets that exhibit spatial and temporal dependencies, commonly encountered in academia and industry. The proposed algorithm can accelerate score-matching-based methods while maintaining high accuracy in real-world applications.", "date": "2024-12-10", "categories": []}
{"id": "2510.02050", "title": "Multidata Causal Discovery for Statistical Hurricane Intensity Forecasting", "abstract": "Improving statistical forecasts of tropical cyclone (TC) intensity is limited by complex nonlinear interactions and difficulty in identifying relevant predictors. Conventional methods prioritize correlation or fit, often overlooking confounding variables and limiting generalizability to unseen TCs. To address this, we leverage a multidata causal discovery framework with a replicated dataset based on Statistical Hurricane Intensity Prediction Scheme (SHIPS) using ERA5 meteorological reanalysis. We conduct experiments to identify and select predictors causally linked to TC intensity changes. We then train multiple linear regression models to compare causal feature selection with correlation, random forest feature importance, and no feature selection, across five forecast lead times from 1 to 5 days (24 to 120 hours). Causal feature selection consistently outperforms on unseen test cases, especially for lead times shorter than 3 days. Top causal features include vertical shear, mid-tropospheric potential vorticity and surface moisture conditions, which are physically significant yet often underutilized in TC intensity predictions. We build an extended predictor set (SHIPS+) by adding selected features to the standard SHIPS predictors. SHIPS+ yields increased short-term predictive skill at lead times of 24, 48, and 72 hours. Adding nonlinearity using a multilayer perceptron further extends skill to longer lead times, despite our framework being purely regional and not requiring global forecast data. Operational SHIPS tests confirm that three of the six added causally discovered predictors improve forecast skill, with the largest gains at longer lead times. Our results demonstrate that causal discovery improves TC intensity prediction and pave the way toward more empirical forecasts.", "date": "2025-10-02", "categories": []}
{"id": "2604.10371", "title": "Structural Gating and Effect-aligned Lag-resolved Temporal Causal Discovery Framework with Application to Heat-Pollution Extremes", "abstract": "This study proposes Structural Gating and Effect-aligned Discovery for Temporal Causal Discovery (SGED-TCD), a novel and general framework for lag-resolved causal discovery in complex multivariate time series. SGED-TCD combines explicit structural gating, stability-oriented learning, perturbation-effect alignment, and unified graph extraction to improve the interpretability, robustness, and functional consistency of inferred causal graphs.\n  To evaluate its effectiveness in a representative real-world setting, we apply SGED-TCD to teleconnection-driven compound heatwave--air-pollution extremes in eastern and northern China. Using large-scale climate indices, regional circulation and boundary-layer variables, and compound extreme indicators, the framework reconstructs weighted causal networks with explicit dominant lags and relative causal importance. The inferred networks reveal clear regional and seasonal heterogeneity: warm-season extremes in Eastern China are mainly linked to low-latitude oceanic variability through circulation, radiation, and ventilation pathways, whereas cold-season extremes in Northern China are more strongly governed by high-latitude circulation variability associated with boundary-layer suppression and persistent stagnation.\n  These results show that SGED-TCD can recover physically interpretable, hierarchical, and lag-resolved causal pathways in a challenging climate--environment system. More broadly, the proposed framework is not restricted to the present application and provides a general basis for temporal causal discovery in other complex domains.", "date": "2026-04-11", "categories": []}
{"id": "2604.08935", "title": "A novel hybrid approach for positive-valued DAG learning", "abstract": "Causal discovery from observational data remains a fundamental challenge in machine learning and statistics, particularly when variables represent inherently positive quantities such as gene expression levels, asset prices, company revenues, or population counts, which often follow multiplicative rather than additive dynamics. We propose the Hybrid Moment-Ratio Scoring (H-MRS) algorithm, a novel method for learning directed acyclic graphs (DAGs) from positive-valued data by combining moment-based scoring with log-scale regression. The key idea is that for positive-valued variables, the moment ratio $\\frac{\\mathbb{E}[X_j^2]}{\\mathbb{E}[(\\mathbb{E}[X_j \\mid S])^2]}$ provides an effective criterion for causal ordering, where $S$ denotes candidate parent sets. H-MRS integrates log-scale Ridge regression for moment-ratio estimation with a greedy ordering procedure based on raw-scale moment ratios, followed by Elastic Net-based parent selection to recover the final DAG structure. Experiments on synthetic log-linear data demonstrate competitive precision and recall. The proposed method is computationally efficient and naturally respects positivity constraints, making it suitable for applications in genomics and economics. These results suggest that combining log-scale modeling with raw-scale moment ratios provides a practical framework for causal discovery in positive-valued domains.", "date": "2026-04-10", "categories": []}
{"id": "2407.19426", "title": "Causal Discovery in Linear Models with Unobserved Variables and Measurement Error", "abstract": "The presence of unobserved common causes and measurement error poses two major obstacles to causal structure learning, since ignoring either source of complexity can induce spurious causal relations among variables of interest. We study causal structure learning in linear systems where both challenges may occur simultaneously. We introduce a causal model called LV-SEM-ME, which contains four types of variables: directly observed variables, variables that are not directly observed but are measured with error, the corresponding measurements, and variables that are neither observed nor measured. Under a separability condition-namely, identifiability of the mixing matrix associated with the exogenous noise terms of the observed variables-together with certain faithfulness assumptions, we characterize the extent of identifiability and the corresponding observational equivalence classes. We provide graphical characterizations of these equivalence classes and develop recovery algorithms that enumerate all models in the equivalence class of the ground truth. We also establish, via a four-node union model that subsumes instrumental variable, front-door, and negative-control-outcome settings, a form of identification robustness: the target effect remains identifiable in the broader LV-SEM-ME model even when the assumptions underlying the specialized identification formulas for the corresponding submodels need not all hold simultaneously.", "date": "2024-07-28", "categories": []}
{"id": "2505.02781", "title": "Local Markov Equivalence for PC-style Local Causal Discovery and Identification of Controlled Direct Effects", "abstract": "Identifying controlled direct effects (CDEs) is crucial across numerous scientific domains. While existing methods can identify these effects from causal directed acyclic graphs (DAGs), the true DAG is often unknown in practice. Essential graphs, which represent a Markov equivalence class of DAGs characterized by the same set of conditional independencies, provide a more practical and realistic alternative, and the PC algorithm is one of the most widely used method to learn them using conditional independence tests. However, learning the full essential graph is computationally intensive and relies on strong, untestable assumptions. In this work, we adapt the PC algorithm to recover only the portion of the graph needed for identifying CDEs. In particular, we introduce the local essential graph (LEG), a graph structure defined relative to a target variable, and present LocPC, an algorithm that learns the LEG using solely local conditional independence tests. Building on this, we develop LocPC-CDE, which extracts precisely the portion of the LEG that is both necessary and sufficient for identifying a CDE. Compared to global methods, our algorithms require less conditional independence tests and operate under weaker assumptions while maintaining theoretical guarantees. We illustrate the effectiveness of our approach on synthetic and real data.", "date": "2025-05-05", "categories": []}
{"id": "2603.11090", "title": "Interventional Time Series Priors for Causal Foundation Models", "abstract": "Prior-data fitted networks (PFNs) have emerged as powerful foundation models for tabular causal inference, yet their extension to time series remains limited by the absence of synthetic data generators that provide interventional targets. Existing time series benchmarks generate observational data with ground-truth causal graphs but lack the interventional data required for training causal foundation models. To address this, we propose \\textbf{CausalTimePrior}, a principled framework for generating synthetic temporal structural causal models (TSCMs) with paired observational and interventional time series. Our prior supports configurable causal graph structures, nonlinear autoregressive mechanisms, regime-switching dynamics, and multiple intervention types (hard, soft, time-varying). We demonstrate that PFNs trained on CausalTimePrior can perform in-context causal effect estimation on held-out TSCMs, establishing a pathway toward foundation models for time series causal inference.", "date": "2026-03-11", "categories": []}
{"id": "2604.05136", "title": "Non-monotonic causal discovery with Kolmogorov-Arnold Fuzzy Cognitive Maps", "abstract": "Fuzzy Cognitive Maps constitute a neuro-symbolic paradigm for modeling complex dynamic systems, widely adopted for their inherent interpretability and recurrent inference capabilities. However, the standard FCM formulation, characterized by scalar synaptic weights and monotonic activation functions, is fundamentally constrained in modeling non-monotonic causal dependencies, thereby limiting its efficacy in systems governed by saturation effects or periodic dynamics. To overcome this topological restriction, this research proposes the Kolmogorov-Arnold Fuzzy Cognitive Map (KA-FCM), a novel architecture that redefines the causal transmission mechanism. Drawing upon the Kolmogorov-Arnold representation theorem, static scalar weights are replaced with learnable, univariate B-spline functions located on the model edges. This fundamental modification shifts the non-linearity from the nodes' aggregation phase directly to the causal influence phase. This modification allows for the modeling of arbitrary, non-monotonic causal relationships without increasing the graph density or introducing hidden layers. The proposed architecture is validated against both baselines (standard FCM trained with Particle Swarm Optimization) and universal black-box approximators (Multi-Layer Perceptron) across three distinct domains: non-monotonic inference (Yerkes-Dodson law), symbolic regression, and chaotic time-series forecasting. Experimental results demonstrate that KA-FCMs significantly outperform conventional architectures and achieve competitive accuracy relative to MLPs, while preserving graph- based interpretability and enabling the explicit extraction of mathematical laws from the learned edges.", "date": "2026-04-06", "categories": []}
{"id": "2604.05829", "title": "Bivariate Causal Discovery Using Rate-Distortion MDL: An Information Dimension Approach", "abstract": "Approaches to bivariate causal discovery based on the minimum description length (MDL) principle approximate the (uncomputable) Kolmogorov complexity of the models in each causal direction, selecting the one with the lower total complexity. The premise is that nature's mechanisms are simpler in their true causal order. Inherently, the description length (complexity) in each direction includes the description of the cause variable and that of the causal mechanism. In this work, we argue that current state-of-the-art MDL-based methods do not correctly address the problem of estimating the description length of the cause variable, effectively leaving the decision to the description length of the causal mechanism. Based on rate-distortion theory, we propose a new way to measure the description length of the cause, corresponding to the minimum rate required to achieve a distortion level representative of the underlying distribution. This distortion level is deduced using rules from histogram-based density estimation, while the rate is computed using the related concept of information dimension, based on an asymptotic approximation. Combining it with a traditional approach for the causal mechanism, we introduce a new bivariate causal discovery method, termed rate-distortion MDL (RDMDL). We show experimentally that RDMDL achieves competitive performance on the T\\\"ubingen dataset. All the code and experiments are publicly available at github.com/tiagobrogueira/Causal-Discovery-In-Exchangeable-Data.", "date": "2026-04-07", "categories": []}
{"id": "2410.18918", "title": "MissNODAG: Differentiable Cyclic Causal Graph Learning from Incomplete Data", "abstract": "Causal discovery in real-world systems, such as biological networks, is often complicated by feedback loops and incomplete data. Standard algorithms, which assume acyclic structures or fully observed data, struggle with these challenges. To address this gap, we propose MissNODAG, a differentiable framework for learning both the underlying cyclic causal graph and the missingness mechanism from partially observed data, including data missing not at random. Our framework integrates an additive noise model with an expectation-maximization procedure, alternating between imputing missing values and optimizing the observed data likelihood, to uncover both the cyclic structures and the missingness mechanism. We establish consistency guarantees under exact maximization of the score function in the large sample setting. Finally, we demonstrate the effectiveness of MissNODAG through synthetic experiments and an application to real-world gene perturbation data.", "date": "2024-10-24", "categories": []}
{"id": "2507.13920", "title": "Causal Process Models: Reframing Dynamic Causal Graph Discovery as a Reinforcement Learning Problem", "abstract": "Most neural models of causality assume static causal graphs, failing to capture the dynamic and sparse nature of physical interactions where causal relationships emerge and dissolve over time. We introduce the Causal Process Framework and its neural implementation, Causal Process Models (CPMs), for learning sparse, time-varying causal graphs from visual observations. Unlike traditional approaches that maintain dense connectivity, our model explicitly constructs causal edges only when objects actively interact, dramatically improving both interpretability and computational efficiency. We achieve this by casting dynamic interaction-graph construction for world modeling as a multi-agent reinforcement learning problem, where specialized agents sequentially decide which objects are causally connected at each timestep. Our key innovation is a structured representation that factorizes object and force vectors along three learned dimensions (mutability, causal relevance, and control relevance), enabling the automatic discovery of semantically meaningful encodings. We demonstrate that a CPM significantly outperforms dense graph baselines on physical prediction tasks, particularly for longer horizons and varying object counts.", "date": "2025-07-18", "categories": []}
{"id": "2509.12981", "title": "Causal Discovery via Quantile Partial Effect", "abstract": "Quantile Partial Effect (QPE) is a statistic associated with conditional quantile regression, measuring the effect of covariates at different levels. Our theory demonstrates that when the QPE of cause on effect is assumed to lie in a finite linear span, cause and effect are identifiable from their observational distribution. This generalizes previous identifiability results based on Functional Causal Models (FCMs) with additive, heteroscedastic noise, etc. Meanwhile, since QPE resides entirely at the observational level, this parametric assumption does not require considering mechanisms, noise, or even the Markov assumption, but rather directly utilizes the asymmetry of shape characteristics in the observational distribution. By performing basis function tests on the estimated QPE, causal directions can be distinguished, which is empirically shown to be effective in experiments on a large number of bivariate causal discovery datasets. For multivariate causal discovery, leveraging the close connection between QPE and score functions, we find that Fisher Information is sufficient as a statistical measure to determine causal order when assumptions are made about the second moment of QPE. We validate the feasibility of using Fisher Information to identify causal order on multiple synthetic and real-world multivariate causal discovery datasets.", "date": "2025-09-16", "categories": []}
{"id": "2603.22620", "title": "Causal Discovery in Action: Learning Chain-Reaction Mechanisms from Interventions", "abstract": "Causal discovery is challenging in general dynamical systems because, without strong structural assumptions, the underlying causal graph may not be identifiable even from interventional data. However, many real-world systems exhibit directional, cascade-like structure, in which components activate sequentially and upstream failures suppress downstream effects. We study causal discovery in such chain-reaction systems and show that the causal structure is uniquely identifiable from blocking interventions that prevent individual components from activating. We propose a minimal estimator with finite-sample guarantees, achieving exponential error decay and logarithmic sample complexity. Experiments on synthetic models and diverse chain-reaction environments demonstrate reliable recovery from a few interventions, while observational heuristics fail in regimes with delayed or overlapping causal effects.", "date": "2026-03-23", "categories": []}
{"id": "2604.04290", "title": "DAGAF: A directed acyclic generative adversarial framework for joint structure learning and tabular data synthesis", "abstract": "Understanding the causal relationships between data variables can provide crucial insights into the construction of tabular datasets. Most existing causality learning methods typically focus on applying a single identifiable causal model, such as the Additive Noise Model (ANM) or the Linear non-Gaussian Acyclic Model (LiNGAM), to discover the dependencies exhibited in observational data. We improve on this approach by introducing a novel dual-step framework capable of performing both causal structure learning and tabular data synthesis under multiple causal model assumptions. Our approach uses Directed Acyclic Graphs (DAG) to represent causal relationships among data variables. By applying various functional causal models including ANM, LiNGAM and the Post-Nonlinear model (PNL), we implicitly learn the contents of DAG to simulate the generative process of observational data, effectively replicating the real data distribution. This is supported by a theoretical analysis to explain the multiple loss terms comprising the objective function of the framework. Experimental results demonstrate that DAGAF outperforms many existing methods in structure learning, achieving significantly lower Structural Hamming Distance (SHD) scores across both real-world and benchmark datasets (Sachs: 47%, Child: 11%, Hailfinder: 5%, Pathfinder: 7% improvement compared to state-of-the-art), while being able to produce diverse, high-quality samples.", "date": "2026-04-05", "categories": []}
{"id": "2402.01207", "title": "Efficient Causal Graph Discovery Using Large Language Models", "abstract": "We propose a novel framework that leverages LLMs for full causal graph discovery. While previous LLM-based methods have used a pairwise query approach, this requires a quadratic number of queries which quickly becomes impractical for larger causal graphs. In contrast, the proposed framework uses a breadth-first search (BFS) approach which allows it to use only a linear number of queries. We also show that the proposed method can easily incorporate observational data when available, to improve performance. In addition to being more time and data-efficient, the proposed framework achieves state-of-the-art results on real-world causal graphs of varying sizes. The results demonstrate the effectiveness and efficiency of the proposed method in discovering causal relationships, showcasing its potential for broad applicability in causal graph discovery tasks across different domains.", "date": "2024-02-02", "categories": []}
{"id": "2604.02488", "title": "Causal-Audit: A Framework for Risk Assessment of Assumption Violations in Time-Series Causal Discovery", "abstract": "Time-series causal discovery methods rely on assumptions such as stationarity, regular sampling, and bounded temporal dependence. When these assumptions are violated, structure learning can produce confident but misleading causal graphs without warning. We introduce Causal-Audit, a framework that formalizes assumption validation as calibrated risk assessment. The framework computes effect-size diagnostics across five assumption families (stationarity, irregularity, persistence, nonlinearity, and confounding proxies), aggregates them into four calibrated risk scores with uncertainty intervals, and applies an abstention-aware decision policy that recommends methods (e.g., PCMCI+, VAR-based Granger causality) only when evidence supports reliable inference. The semi-automatic diagnostic stage can also be used independently for structured assumption auditing in individual studies. Evaluation on a synthetic atlas of 500 data-generating processes (DGPs) spanning 10 violation families demonstrates well-calibrated risk scores (AUROC > 0.95), a 62% false positive reduction among recommended datasets, and 78% abstention on severe-violation cases. On 21 external evaluations from TimeGraph (18 categories) and CausalTime (3 domains), recommend-or-abstain decisions are consistent with benchmark specifications in all cases. An open-source implementation of our framework is available.", "date": "2026-04-02", "categories": []}
{"id": "2601.10531", "title": "Coarsening Causal DAG Models", "abstract": "Directed acyclic graphical (DAG) models are a powerful tool for representing causal relationships among jointly distributed random variables, especially concerning data from across different experimental settings. However, it is not always practical or desirable to estimate a causal model at the granularity of given features in a particular dataset. There is a growing body of research on causal abstraction to address such problems. We contribute to this line of research by (i) providing novel graphical identifiability results for practically-relevant interventional settings, (ii) proposing an efficient, provably consistent algorithm for directly learning abstract causal graphs from interventional data with unknown intervention targets, and (iii) uncovering theoretical insights about the lattice structure of the underlying search space, with connections to the field of causal discovery more generally. As proof of concept, we apply our algorithm on synthetic and real datasets with known ground truths, including measurements from a controlled physical system with interacting light intensity and polarization.", "date": "2026-01-15", "categories": []}
{"id": "2604.02250", "title": "Smoothing the Landscape: Causal Structure Learning via Diffusion Denoising Objectives", "abstract": "Understanding causal dependencies in observational data is critical for informing decision-making. These relationships are often modeled as Bayesian Networks (BNs) and Directed Acyclic Graphs (DAGs). Existing methods, such as NOTEARS and DAG-GNN, often face issues with scalability and stability in high-dimensional data, especially when there is a feature-sample imbalance. Here, we show that the denoising score matching objective of diffusion models could smooth the gradients for faster, more stable convergence. We also propose an adaptive k-hop acyclicity constraint that improves runtime over existing solutions that require matrix inversion. We name this framework Denoising Diffusion Causal Discovery (DDCD). Unlike generative diffusion models, DDCD utilizes the reverse denoising process to infer a parameterized causal structure rather than to generate data. We demonstrate the competitive performance of DDCDs on synthetic benchmarking data. We also show that our methods are practically useful by conducting qualitative analyses on two real-world examples. Code is available at this url: https://github.com/haozhu233/ddcd.", "date": "2026-04-02", "categories": []}
{"id": "2408.07575", "title": "A General Framework on Conditions for Constraint-based Causal Learning", "abstract": "Most constraint-based causal learning algorithms provably return the correct causal graph under certain correctness conditions, such as faithfulness. By representing any constraint-based causal learning algorithm using the notion of a property, we provide a general framework to obtain and study correctness conditions for these algorithms. From the framework, we provide exact correctness conditions for the PC algorithm, which are then related to the correctness conditions of some other existing causal discovery algorithms. The framework also suggests a paradigm for designing causal learning algorithms which allows for the correctness conditions of algorithms to be controlled for before designing the actual algorithm, and has the following implications. We show that the sparsest Markov representation condition is the weakest correctness condition for algorithms that output ancestral graphs or directed acyclic graphs satisfying any existing notions of minimality. We also reason that Pearl-minimality is necessary for meaningful causal learning but not sufficient to relax the faithfulness condition and, as such, has to be strengthened, such as by including background knowledge, for causal learning beyond faithfulness.", "date": "2024-08-14", "categories": []}
{"id": "2601.20589", "title": "Exact Graph Learning via Integer Programming", "abstract": "Learning the dependence structure among variables in complex systems is a central problem across medical, natural, and social sciences. These structures can be naturally represented by graphs, and the task of inferring such graphs from data is known as graph learning or causal discovery. Existing approaches typically rely on restrictive assumptions about the data-generating process, employ greedy oracle algorithms, or solve approximate formulations of the graph learning problem. Therefore, they are either sensitive to violations of central assumptions or fail to guarantee globally optimal solutions. We address these limitations by introducing a nonparametric graph learning framework based on conditional independence testing and integer programming. We reformulate the graph learning problem as a mixed-integer program and prove that solving this integer-programming problem provides a globally optimal solution to the original graph learning problem. Our method leverages efficient encodings of graphical separation criteria, enabling the exact recovery of larger graphs than was previously feasible. We provide an open-source R package 'glip' which supports learning (acyclic) directed (mixed) graphs and chain graphs. We demonstrate that our approach is often faster than existing exact graph learning procedures and achieves state-of-the-art performance on simulated and benchmark data across all aforementioned classes of graphs.", "date": "2026-01-28", "categories": []}
{"id": "2510.14582", "title": "Local Causal Discovery for Statistically Efficient Causal Inference", "abstract": "Causal discovery methods can identify valid adjustment sets for causal effect estimation for a pair of target variables, even when the underlying causal graph is unknown. Global causal discovery methods focus on learning the whole causal graph and therefore enable the recovery of optimal adjustment sets, i.e., sets with the lowest asymptotic variance, but they quickly become computationally prohibitive as the number of variables grows. Local causal discovery methods offer a more scalable alternative by focusing on the local neighborhood of the target variables, but are restricted to statistically suboptimal adjustment sets. In this work, we propose Local Optimal Adjustments Discovery (LOAD), a sound and complete causal discovery approach that combines the computational efficiency of local methods with the statistical optimality of global methods. First, LOAD identifies the causal relation between the targets and tests if the causal effect is identifiable by using only local information. If it is identifiable, it finds the possible descendants of the treatment and infers the optimal adjustment set as the parents of the outcome in a modified forbidden projection. Otherwise, it returns the locally valid parent adjustment sets. In our experiments on synthetic and realistic data LOAD outperforms global methods in scalability, while providing more accurate effect estimation than local methods.", "date": "2025-10-16", "categories": []}
{"id": "2603.24436", "title": "Enes Causal Discovery", "abstract": "Enes The proposed architecture is a mixture of experts, which allows for the model entities, such as the causal relationships, to be further parameterized. More specifically, an attempt is made to exploit a neural net as implementing neurons poses a great challenge for this dataset. To explain, a simple and fast Pearson coefficient linear model usually achieves good scores. An aggressive baseline that requires a really good model to overcome that is. Moreover, there are major limitations when it comes to causal discovery of observational data. Unlike the sachs one did not use interventions but only prior knowledge; the most prohibiting limitation is that of the data which is addressed. Thereafter, the method and the model are described and after that the results are presented.", "date": "2026-03-25", "categories": []}
{"id": "2412.14019", "title": "Retrieving Classes of Causal Orders with Inconsistent Knowledge Bases", "abstract": "Traditional causal discovery methods often depend on strong, untestable assumptions, making them unreliable in real-world applications. In this context, Large Language Models (LLMs) have emerged as a promising alternative for extracting causal knowledge from text-based metadata, effectively consolidating domain expertise. However, LLMs are prone to hallucinations, necessitating strategies that account for these limitations. One effective approach is to use a consistency measure as a proxy of reliability. Moreover, LLMs do not clearly distinguish direct from indirect causal relationships, complicating the discovery of causal Directed Acyclic Graphs (DAGs), which are often sparse. This ambiguity is evident in the way informal sentences are formulated in various domains. For this reason, focusing on causal orders provides a more practical and direct task for LLMs. We propose a new method for deriving abstractions of causal orders that maximizes a consistency score obtained from an LLM. Our approach begins by computing pairwise consistency scores between variables, from which we construct a semi-complete partially directed graph that consolidates these scores into an abstraction. Using this structure, we identify both a maximally oriented partially directed acyclic graph and an optimal set of acyclic tournaments that maximize consistency across all configurations. We further demonstrate how both the abstraction and the class of causal orders can be used to estimate causal effects. We evaluate our method on a wide set of causal DAGs extracted from scientific literature in epidemiology and public health. Our results show that the proposed approach can effectively recover the correct causal order, providing a reliable and practical LLM-assisted causal framework.", "date": "2024-12-18", "categories": []}
{"id": "2502.14950", "title": "Symmetric observations without symmetric causal explanations", "abstract": "Inferring causal models from observed correlations is a challenging task, crucial to many areas of science. In order to alleviate the computational effort when sifting through possible causal explanations for some given observations, it is important to know whether symmetries in the observations correspond to symmetries in the underlying realization so that one can quickly discard impossible explanations. Via an explicit example, we demonstrate that, in general, symmetries cannot be exploited to reduce the hypothesis space. We use a tripartite probability distribution over binary events that is realized by using three (different) independent sources of classical randomness. We prove that even removing the condition that the sources distribute systems described by classical physics, the requirements that (i) the sources distribute the same physical systems, (ii) these physical systems respect relativistic causality, and (iii) the correlations are the observed ones are incompatible.", "date": "2025-02-20", "categories": []}
{"id": "2603.25796", "title": "Beyond identifiability: Learning causal representations with few environments and finite samples", "abstract": "We provide explicit, finite-sample guarantees for learning causal representations from data with a sublinear number of environments. Causal representation learning seeks to provide a rigourous foundation for the general representation learning problem by bridging causal models with latent factor models in order to learn interpretable representations with causal semantics. Despite a blossoming theory of identifiability in causal representation learning, estimation and finite-sample bounds are less well understood. We show that causal representations can be learned with only a logarithmic number of unknown, multi-node interventions, and that the intervention targets need not be carefully designed in advance. Through a careful perturbation analysis, we provide a new analysis of this problem that guarantees consistent recovery of (a) the latent causal graph, (b) the mixing matrix and representations, and (c) \\emph{unknown} intervention targets.", "date": "2026-03-26", "categories": []}
{"id": "2603.26024", "title": "Identification of Bivariate Causal Directionality Based on Anticipated Asymmetric Geometries", "abstract": "Identification of causal directionality in bivariate numerical data is a fundamental research problem with important practical implications. This paper presents two alternative methods to identify direction of causation by considering conditional distributions: (1) Anticipated Asymmetric Geometries (AAG) and (2) Monotonicity Index. The AAG method compares the actual conditional distributions to anticipated ones along two variables. Different comparison metrics, such as correlation, cosine similarity, Jaccard index, K-L divergence, K-S distance, and mutual information have been evaluated. Anticipated distributions have been projected as normal based on dual response statistics: mean and standard deviation. The Monotonicity Index approach compares the calculated monotonicity indexes of the gradients of conditional distributions along two axes and exhibits counts of gradient sign changes. Both methods assume stochastic properties of the bivariate data and exploit anticipated unimodality of conditional distributions of the effect. It turns out that the tuned AAG method outperforms the Monotonicity Index and reaches a top accuracy of 77.9% compared to ANMs accuracy of 63 +/- 10% when classifying 95 pairs of real-world examples (Mooij et al, 2014). The described methods include a number of hyperparameters that impact accuracy of the identification. For a given set of hyperparameters, both the AAG or Monotonicity Index method provide a unique deterministic outcome of the solution. To address sensitivity to hyperparameters, tuning of hyperparameters has been done by utilizing a full factorial Design of Experiment. A decision tree has been fitted to distinguish misclassified cases using the input data's symmetrical bivariate statistics to address the question of: How decisive is the identification method of causal directionality?", "date": "2026-03-27", "categories": []}
{"id": "2410.20894", "title": "Working Paper: Active Causal Structure Learning with Latent Variables: Towards Learning to Detour in Autonomous Robots", "abstract": "Artificial General Intelligence (AGI) Agents and Robots must be able to cope with everchanging environments and tasks. They must be able to actively construct new internal causal models of their interactions with the environment when new structural changes take place in the environment. Thus, we claim that active causal structure learning with latent variables (ACSLWL) is a necessary component to build AGI agents and robots. This paper describes how a complex planning and expectation-based detour behavior can be learned by ACSLWL when, unexpectedly, and for the first time, the simulated robot encounters a sort of transparent barrier in its pathway towards its target. ACSWL consists of acting in the environment, discovering new causal relations, constructing new causal models, exploiting the causal models to maximize its expected utility, detecting possible latent variables when unexpected observations occur, and constructing new structures-internal causal models and optimal estimation of the associated parameters, to be able to cope efficiently with the new encountered situations. That is, the agent must be able to construct new causal internal models that transform a previously unexpected and inefficient (sub-optimal) situation, into a predictable situation with an optimal operating plan.", "date": "2024-10-28", "categories": []}
{"id": "2512.10152", "title": "Rethinking Bivariate Causal Discovery Through the Lens of Exchangeability", "abstract": "Causal discovery methods have traditionally been developed under two different modeling assumptions: independent and identically distributed (i.i.d.) data and time series data. In this paper, we focus on the i.i.d. setting, arguing that it should be reframed in terms of exchangeability, a strictly more general symmetry principle. For that goal, we propose an exchangeable hierarchical model that builds upon the recent Causal de Finetti theorem. Using this model, we show that both the uncertainty regarding the causal mechanism and the uncertainty in the distribution of latent variables are better captured under the broader assumption of exchangeability. In fact, we argue that this is most often the case with real data, as supported by an in-depth analysis of the T\\\"ubingen dataset. Exploiting this insight, we introduce a novel synthetic dataset that mimics the generation process induced by the proposed exchangeable hierarchical model. We show that our exchangeable synthetic dataset mirrors the statistical and causal structure of the T\\\"ubingen dataset more closely than other i.i.d. synthetic datasets. Furthermore, we introduce SynthNN, a neural-network-based causal-discovery method trained exclusively on the proposed synthetic dataset. The fact that SynthNN performs competitively with other state-of-the-art methods on the real-world T\\\"ubingen dataset provides strong evidence for the realism of the underlying exchangeable generative model.", "date": "2025-12-10", "categories": []}
{"id": "2603.24618", "title": "Causal AI For AMS Circuit Design: Interpretable Parameter Effects Analysis", "abstract": "Analog-mixed-signal (AMS) circuits are highly non-linear and operate on continuous real-world signals, making them far more difficult to model with data-driven AI than digital blocks. To close the gap between structured design data (device dimensions, bias voltages, etc.) and real-world performance, we propose a causal-inference framework that first discovers a directed-acyclic graph (DAG) from SPICE simulation data and then quantifies parameter impact through Average Treatment Effect (ATE) estimation. The approach yields human-interpretable rankings of design knobs and explicit 'what-if' predictions, enabling designers to understand trade-offs in sizing and topology. We evaluate the pipeline on three operational-amplifier families (OTA, telescopic, and folded-cascode) implemented in TSMC 65nm and benchmark it against a baseline neural-network (NN) regressor. Across all circuits the causal model reproduces simulation-based ATEs with an average absolute error of less than 25%, whereas the neural network deviates by more than 80% and frequently predicts the wrong sign. These results demonstrate that causal AI provides both higher accuracy and explainability, paving the way for more efficient, trustworthy AMS design automation.", "date": "2026-03-24", "categories": []}
{"id": "2603.25473", "title": "Causal-INSIGHT: Probing Temporal Models to Extract Causal Structure", "abstract": "Understanding directed temporal interactions in multivariate time series is essential for interpreting complex dynamical systems and the predictive models trained on them. We present Causal-INSIGHT, a model-agnostic, post-hoc interpretation framework for extracting model-implied (predictor-dependent), directed, time-lagged influence structure from trained temporal predictors. Rather than inferring causal structure at the level of the data-generating process, Causal-INSIGHT analyzes how a fixed, pre-trained predictor responds to systematic, intervention-inspired input clamping applied at inference time.\n  From these responses, we construct directed temporal influence signals that reflect the dependencies the predictor relies on for prediction, and introduce Qbic, a sparsity-aware graph selection criterion that balances predictive fidelity and structural complexity without requiring ground-truth graph labels. Experiments across synthetic, simulated, and realistic benchmarks show that Causal-INSIGHT generalizes across diverse backbone architectures, maintains competitive structural accuracy, and yields significant improvements in temporal delay localization when applied to existing predictors.", "date": "2026-03-26", "categories": []}
{"id": "2501.16562", "title": "C-HDNet: Hyperdimensional Computing for Causal Effect Estimation from Observational Data Under Network Interference", "abstract": "We address the problem of estimating causal effects from observational data in the presence of network confounding, a setting where both treatment assignment and observed outcomes of individuals may be influenced by their neighbors within a network structure, resulting in network interference. Traditional causal inference methods often fail to account for these dependencies, leading to biased estimates. To tackle this challenge, we introduce a novel matching-based approach that utilizes principles from hyperdimensional computing to effectively encode and incorporate structural network information. This enables more accurate identification of comparable individuals, thereby improving the reliability of causal effect estimates. Through extensive empirical evaluation on multiple benchmark datasets, we demonstrate that our method either outperforms or performs on par with existing state-of-the-art approaches, including several recent deep learning-based models that are significantly more computationally intensive. In addition to its strong empirical performance, our method offers substantial practical advantages, achieving nearly an order-of-magnitude reduction in runtime without compromising accuracy, making it particularly well-suited for large-scale or time-sensitive application", "date": "2025-01-27", "categories": []}
{"id": "2603.20295", "title": "MARLIN: Multi-Agent Reinforcement Learning for Incremental DAG Discovery", "abstract": "Uncovering causal structures from observational data is crucial for understanding complex systems and making informed decisions. While reinforcement learning (RL) has shown promise in identifying these structures in the form of a directed acyclic graph (DAG), existing methods often lack efficiency, making them unsuitable for online applications. In this paper, we propose MARLIN, an efficient multi agent RL based approach for incremental DAG learning. MARLIN uses a DAG generation policy that maps a continuous real valued space to the DAG space as an intra batch strategy, then incorporates two RL agents state specific and state invariant to uncover causal relationships and integrates these agents into an incremental learning framework. Furthermore, the framework leverages a factored action space to enhance parallelization efficiency. Extensive experiments on synthetic and real datasets demonstrate that MARLIN outperforms state of the art methods in terms of both efficiency and effectiveness.", "date": "2026-03-19", "categories": []}
{"id": "2603.20585", "title": "RECLAIM: Cyclic Causal Discovery Amid Measurement Noise", "abstract": "Uncovering causal relationships is a fundamental problem across science and engineering. However, most existing causal discovery methods assume acyclicity and direct access to the system variables -- assumptions that fail to hold in many real-world settings. For instance, in genomics, cyclic regulatory networks are common, and measurements are often corrupted by instrumental noise. To address these challenges, we propose RECLAIM, a causal discovery framework that natively handles both cycles and measurement noise. RECLAIM learns the causal graph structure by maximizing the likelihood of the observed measurements via expectation-maximization (EM), using residual normalizing flows for tractable likelihood computation. We consider two measurement models: (i) Gaussian additive noise, and (ii) a linear measurement system with additive Gaussian noise. We provide theoretical consistency guarantees for both the settings. Experiments on synthetic data and real-world protein signaling datasets demonstrate the efficacy of the proposed method.", "date": "2026-03-21", "categories": []}
{"id": "2603.20791", "title": "Neural Autoregressive Flows for Markov Boundary Learning", "abstract": "Recovering Markov boundary -- the minimal set of variables that maximizes predictive performance for a response variable -- is crucial in many applications. While recent advances improve upon traditional constraint-based techniques by scoring local causal structures, they still rely on nonparametric estimators and heuristic searches, lacking theoretical guarantees for reliability. This paper investigates a framework for efficient Markov boundary discovery by integrating conditional entropy from information theory as a scoring criterion. We design a novel masked autoregressive network to capture complex dependencies. A parallelizable greedy search strategy in polynomial time is proposed, supported by analytical evidence. We also discuss how initializing a graph with learned Markov boundaries accelerates the convergence of causal discovery. Comprehensive evaluations on real-world and synthetic datasets demonstrate the scalability and superior performance of our method in both Markov boundary discovery and causal discovery tasks.", "date": "2026-03-21", "categories": []}
{"id": "2603.20842", "title": "A Knowledge-Informed Pretrained Model for Causal Discovery", "abstract": "Causal discovery has been widely studied, yet many existing methods rely on strong assumptions or fall into two extremes: either depending on costly interventional signals or partial ground truth as strong priors, or adopting purely data driven paradigms with limited guidance, which hinders practical deployment. Motivated by real-world scenarios where only coarse domain knowledge is available, we propose a knowledge-informed pretrained model for causal discovery that integrates weak prior knowledge as a principled middle ground. Our model adopts a dual source encoder-decoder architecture to process observational data in a knowledge-informed way. We design a diverse pretraining dataset and a curriculum learning strategy that smoothly adapts the model to varying prior strengths across mechanisms, graph densities, and variable scales. Extensive experiments on in-distribution, out-of distribution, and real-world datasets demonstrate consistent improvements over existing baselines, with strong robustness and practical applicability.", "date": "2026-03-21", "categories": []}
{"id": "2603.21844", "title": "On the Number of Conditional Independence Tests in Constraint-based Causal Discovery", "abstract": "Learning causal relations from observational data is a fundamental problem with wide-ranging applications across many fields. Constraint-based methods infer the underlying causal structure by performing conditional independence tests. However, existing algorithms such as the prominent PC algorithm need to perform a large number of independence tests, which in the worst case is exponential in the maximum degree of the causal graph. Despite extensive research, it remains unclear if there exist algorithms with better complexity without additional assumptions. Here, we establish an algorithm that achieves a better complexity of $p^{\\mathcal{O}(s)}$ tests, where $p$ is the number of nodes in the graph and $s$ denotes the maximum undirected clique size of the underlying essential graph. Complementing this result, we prove that any constraint-based algorithm must perform at least $2^{\\Omega(s)}$ conditional independence tests, establishing that our proposed algorithm achieves exponent-optimality up to a logarithmic factor in terms of the number of conditional independence tests needed. Finally, we validate our theoretical findings through simulations, on semi-synthetic gene-expression data, and real-world data, demonstrating the efficiency of our algorithm compared to existing methods in terms of number of conditional independence tests needed.", "date": "2026-03-23", "categories": []}
{"id": "2406.15189", "title": "Causal Learning in Biomedical Applications: Krebs Cycle as a Benchmark", "abstract": "Learning causal relationships from time series data is an important but challenging problem. Existing synthetic datasets often contain hidden artifacts that can be exploited by causal discovery methods, reducing their usefulness for benchmarking. We present a new benchmark dataset based on simulations of the Krebs cycle, a key biochemical pathway. The data are generated using a particle-based simulator that models molecular interactions in a controlled environment. Four distinct scenarios are provided, varying in time series length, number of samples, and intervention settings. The benchmark includes ground-truth causal graphs for evaluation. It supports quantitative comparisons using metrics such as Structural Hamming Distance, Structural Intervention Distance, and F1-score. A comprehensive evaluation of 14 causal discovery methods from different modelling paradigms is presented. Performance is compared across datasets using multiple accuracy and efficiency measures. The dataset provides a reproducible, interpretable, and non-trivial benchmark for testing causal learning methods on time series data. It avoids common pitfalls such as residual structural patterns and supports interventions and evaluation with known causal ground truth. This makes it a useful tool for the development and comparison of causal discovery algorithms.", "date": "2024-06-21", "categories": []}
{"id": "2603.16313", "title": "Learning to Predict, Discover, and Reason in High-Dimensional Event Sequences", "abstract": "Electronic control units (ECUs) embedded within modern vehicles generate a large number of asynchronous events known as diagnostic trouble codes (DTCs). These discrete events form complex temporal sequences that reflect the evolving health of the vehicle's subsystems. In the automotive industry, domain experts manually group these codes into higher-level error patterns (EPs) using Boolean rules to characterize system faults and ensure safety. However, as vehicle complexity grows, this manual process becomes increasingly costly, error-prone, and difficult to scale. Notably, the number of unique DTCs in a modern vehicle is on the same order of magnitude as the vocabulary of a natural language, often numbering in the tens of thousands. This observation motivates a paradigm shift: treating diagnostic sequences as a language that can be modeled, predicted, and ultimately explained. Traditional statistical approaches fail to capture the rich dependencies and do not scale to high-dimensional datasets characterized by thousands of nodes, large sample sizes, and long sequence lengths. Specifically, the high cardinality of categorical event spaces in industrial logs poses a significant challenge, necessitating new machine learning architectures tailored to such event-driven systems. This thesis addresses automated fault diagnostics by unifying event sequence modeling, causal discovery, and large language models (LLMs) into a coherent framework for high-dimensional event streams. It is structured in three parts, reflecting a progressive transition from prediction to causal understanding and finally to reasoning for vehicle diagnostics. Consequently, we introduce several Transformer-based architectures for predictive maintenance, scalable sample- and population-level causal discovery frameworks and a multi-agent system that automates the synthesis of Boolean EP rules.", "date": "2026-03-17", "categories": []}
{"id": "2405.16924", "title": "Demystifying amortized causal discovery with transformers", "abstract": "Supervised learning for causal discovery from observational data often achieves competitive performance despite seemingly avoiding the explicit assumptions that traditional methods require for identifiability. In this work, we analyze CSIvA (Ke et al., 2023) on bivariate causal models, a transformer architecture for amortized inference promising to train on synthetic data and transfer to real ones. First, we bridge the gap with identifiability theory, showing that the training distribution implicitly defines a prior on the causal model of the test observations: consistent with classical approaches, good performance is achieved when we have a good prior on the test data, and the underlying model is identifiable. Second, we find that CSIvA can not generalize to classes of causal models unseen during training: to overcome this limitation, we theoretically and empirically analyze \\textit{when} training CSIvA on datasets generated by multiple identifiable causal models with different structural assumptions improves its generalization at test time. Overall, we find that amortized causal discovery with transformers still adheres to identifiability theory, violating the previous hypothesis from Lopez-Paz et al. (2015) that supervised learning methods could overcome its restrictions.", "date": "2024-05-27", "categories": []}
{"id": "2502.14719", "title": "How PC-based Methods Err: Towards Better Reporting of Assumption Violations and Small Sample Errors", "abstract": "Causal discovery methods based on the PC algorithm are proven to be sound if all structural assumptions are fulfilled and all conditional independence tests are correct. This idealized setting is rarely given in real data. In this work, we first analyze how local errors can propagate throughout the output graph of a PC-based method, highlighting how consequential seemingly innocuous errors can become. Next, we introduce coherency scores to find assumption violations and small sample errors in the absence of a ground truth. These scores do not require statistical tests beyond those already executed by the causal discovery algorithm. Errors detected by our approach extend the set of errors that can be detected by comparable existing methods. We place our computationally cheap global error detection and quantification scores as a bridge between computationally expensive global answer-set-programming-based methods and less expensive local error detection methods. The scores are analyzed on simulated and real-world datasets.", "date": "2025-02-20", "categories": []}
{"id": "2510.13417", "title": "Assessing LLM Reasoning Through Implicit Causal Chain Discovery in Climate Discourse", "abstract": "How does a cause lead to an effect, and which intermediate causal steps explain their connection? This work scrutinizes the mechanistic causal reasoning capabilities of large language models (LLMs) to answer these questions through the task of implicit causal chain discovery. In a diagnostic evaluation framework, we instruct nine LLMs to generate all possible intermediate causal steps linking given cause-effect pairs in causal chain structures. These pairs are drawn from recent resources in argumentation studies featuring polarized discussion on climate change. Our analysis reveals that LLMs vary in the number and granularity of causal steps they produce. Although they are generally self-consistent and confident about the intermediate causal connections in the generated chains, their judgments are mainly driven by associative pattern matching rather than genuine causal reasoning. Nonetheless, human evaluations confirmed the logical coherence and integrity of the generated chains. Our baseline causal chain discovery approach, insights from our diagnostic evaluation, and benchmark dataset with causal chains lay a solid foundation for advancing future work in implicit, mechanistic causal reasoning in argumentation settings.", "date": "2025-10-15", "categories": []}
{"id": "2603.15926", "title": "Evaluating Causal Discovery Algorithms for Path-Specific Fairness and Utility in Healthcare", "abstract": "Causal discovery in health data faces evaluation challenges when ground truth is unknown. We address this by collaborating with experts to construct proxy ground-truth graphs, establishing benchmarks for synthetic Alzheimer's disease and heart failure clinical records data. We evaluate the Peter-Clark, Greedy Equivalence Search, and Fast Causal Inference algorithms on structural recovery and path-specific fairness decomposition, going beyond composite fairness scores. On synthetic data, Peter-Clark achieved the best structural recovery. On heart failure data, Fast Causal Inference achieved the highest utility. For path-specific effects, ejection fraction contributed 3.37 percentage points to the indirect effect in the ground truth. These differences drove variations in the fairness-utility ratio across algorithms. Our results highlight the need for graph-aware fairness evaluation and fine-grained path-specific analysis when deploying causal discovery in clinical applications.", "date": "2026-03-16", "categories": []}
{"id": "2510.01112", "title": "The causal structure of galactic astrophysics", "abstract": "Data-driven astrophysics currently relies on the detection and characterisation of correlations between objects' properties, which are then used to test physical theories that make predictions for them. This process fails to utilise information in the data that forms a crucial part of the theories' predictions, namely which variables are directly correlated (as opposed to accidentally correlated through others), the directions of these determinations, and the presence or absence of confounders that correlate variables in the dataset but are themselves absent from it. We propose to recover this information through causal discovery, a well-developed methodology for inferring the causal structure of datasets that is however almost entirely unknown to astrophysics. We develop a causal discovery algorithm suitable for large astrophysical datasets and illustrate it on $\\sim$4.5$\\times10^5$ nearby galaxies from the Nasa Sloan Atlas, demonstrating its ability to distinguish physical mechanisms that are degenerate on the basis of correlations alone.", "date": "2025-10-01", "categories": []}
{"id": "2508.21742", "title": "Orientability of Causal Relations in Time Series using Summary Causal Graphs and Faithful Distributions", "abstract": "Understanding causal relations between temporal variables is a central challenge in time series analysis, particularly when the full causal structure is unknown. Even when the full causal structure cannot be fully specified, experts often succeed in providing a high-level abstraction of the causal graph, known as a summary causal graph, which captures the main causal relations between different time series while abstracting away micro-level details. In this work, we present conditions that guarantee the orientability of micro-level edges between temporal variables given the background knowledge encoded in a summary causal graph and assuming having access to a faithful and causally sufficient distribution with respect to the true unknown graph. Our results provide theoretical guarantees for edge orientation at the micro-level, even in the presence of cycles or bidirected edges at the macro-level. These findings offer practical guidance for leveraging SCGs to inform causal discovery in complex temporal systems and highlight the value of incorporating expert knowledge to improve causal inference from observational time series data.", "date": "2025-08-29", "categories": []}
{"id": "2601.15479", "title": "Benchmarking LLMs for Pairwise Causal Discovery in Biomedical and Multi-Domain Contexts", "abstract": "The safe deployment of large language models (LLMs) in high-stakes fields like biomedicine, requires them to be able to reason about cause and effect. We investigate this ability by testing 13 open-source LLMs on a fundamental task: pairwise causal discovery (PCD) from text. Our benchmark, using 12 diverse datasets, evaluates two core skills: 1) \\textbf{Causal Detection} (identifying if a text contains a causal link) and 2) \\textbf{Causal Extraction} (pulling out the exact cause and effect phrases). We tested various prompting methods, from simple instructions (zero-shot) to more complex strategies like Chain-of-Thought (CoT) and Few-shot In-Context Learning (FICL).\n  The results show major deficiencies in current models. The best model for detection, DeepSeek-R1-Distill-Llama-70B, only achieved a mean score of 49.57\\% ($C_{detect}$), while the best for extraction, Qwen2.5-Coder-32B-Instruct, reached just 47.12\\% ($C_{extract}$). Models performed best on simple, explicit, single-sentence relations. However, performance plummeted for more difficult (and realistic) cases, such as implicit relationships, links spanning multiple sentences, and texts containing multiple causal pairs. We provide a unified evaluation framework, built on a dataset validated with high inter-annotator agreement ($\\kappa \\ge 0.758$), and make all our data, code, and prompts publicly available to spur further research. \\href{https://github.com/sydneyanuyah/CausalDiscovery}{Code available here: https://github.com/sydneyanuyah/CausalDiscovery}", "date": "2026-01-21", "categories": []}
{"id": "2511.04361", "title": "Causal Regime Detection in Energy Markets With Augmented Time Series Structural Causal Models", "abstract": "Energy markets exhibit complex causal relationships between weather patterns, generation technologies, and price formation, with regime changes occurring continuously rather than at discrete break points. Current approaches model electricity prices without explicit causal interpretation or counterfactual reasoning capabilities. We introduce Augmented Time Series Causal Models (ATSCM) for energy markets, extending counterfactual reasoning frameworks to multivariate temporal data with learned causal structure. Our approach models energy systems through interpretable factors (weather, generation mix, demand patterns), rich grid dynamics, and observable market variables. We integrate neural causal discovery to learn time-varying causal graphs without requiring ground truth DAGs. Applied to real-world electricity price data, ATSCM enables novel counterfactual queries such as \"What would prices be under different renewable generation scenarios?\".", "date": "2025-11-06", "categories": []}
{"id": "2603.09563", "title": "Learning Bayesian and Markov Networks with an Unreliable Oracle", "abstract": "We study constraint-based structure learning of Markov networks and Bayesian networks in the presence of an unreliable conditional independence oracle that makes at most a bounded number of errors. For Markov networks, we observe that a low maximum number of vertex-wise disjoint paths implies that the structure is uniquely identifiable even if the number of errors is (moderately) exponential in the number of vertices. For Bayesian networks, however, we prove that one cannot tolerate any errors to always identify the structure even when many commonly used graph parameters like treewidth are bounded. Finally, we give algorithms for structure learning when the structure is uniquely identifiable.", "date": "2026-03-10", "categories": []}
{"id": "2309.12032", "title": "Expert-Aided Causal Discovery of Ancestral Graphs", "abstract": "Causal discovery (CD) is an important component of many scientific applications, yet most techniques produce unreliable point estimates that often contradict expert knowledge. To mitigate this, recent research has focused on ex-ante incorporation of background knowledge into the CD process, typically under an unrealistic causal sufficiency assumption. When probing experts is costly (e.g., hidden behind expensive LLM APIs), however, ex-post model refinement that maximizes query utility is preferable. Also, when independent experts provide conflicting but better-than-random feedback, a principled aggregation method is required. In this context, we introduce the first CD algorithm that enables (i) distributional inference over ancestral graphs (AGs), which represent causal systems under latent confounding, and (ii) integration of both ex-ante and uncertain ex-post expert knowledge. Briefly, our method is a diversity-seeking reinforcement learning algorithm, termed Ancestral GFlowNet (AGFN), whose policy we iteratively refine based on a Bayesian model of the noisy expert feedback. Importantly, we prove convergence to the true AG given sufficiently accurate responses. Through validation on synthetic and realistic datasets using simulated humans and LLMs, we show AGFN is competitive with or superior to strong baselines in terms of structural Hamming distance and Bayesian Information Criterion.", "date": "2023-09-21", "categories": []}
{"id": "2603.04473", "title": "Dictionary Based Pattern Entropy for Causal Direction Discovery", "abstract": "Discovering causal direction from temporal observational data is particularly challenging for symbolic sequences, where functional models and noise assumptions are often unavailable. We propose a novel \\emph{Dictionary Based Pattern Entropy ($DPE$)} framework that infers both the direction of causation and the specific subpatterns driving changes in the effect variable. The framework integrates \\emph{Algorithmic Information Theory} (AIT) and \\emph{Shannon Information Theory}. Causation is interpreted as the emergence of compact, rule based patterns in the candidate cause that systematically constrain the effect. $DPE$ constructs direction-specific dictionaries and quantifies their influence using entropy-based measures, enabling a principled link between deterministic pattern structure and stochastic variability. Causal direction is inferred via a minimum-uncertainty criterion, selecting the direction exhibiting stronger and more consistent pattern-driven organization. As summarized in Table 7, $DPE$ consistently achieves reliable performance across diverse synthetic systems, including delayed bit-flip perturbations, AR(1) coupling, 1D skew-tent maps, and sparse processes, outperforming or matching competing AIT-based methods ($ETC_E$, $ETC_P$, $LZ_P$). In biological and ecological datasets, performance is competitive, while alternative methods show advantages in specific genomic settings. Overall, the results demonstrate that minimizing pattern level uncertainty yields a robust, interpretable, and broadly applicable framework for causal discovery.", "date": "2026-03-04", "categories": []}
{"id": "2603.04534", "title": "Invariant Causal Routing for Governing Social Norms in Online Market Economies", "abstract": "Social norms are stable behavioral patterns that emerge endogenously within economic systems through repeated interactions among agents. In online market economies, such norms -- like fair exposure, sustained participation, and balanced reinvestment -- are critical for long-term stability. We aim to understand the causal mechanisms driving these emergent norms and to design principled interventions that can steer them toward desired outcomes. This is challenging because norms arise from countless micro-level interactions that aggregate into macro-level regularities, making causal attribution and policy transferability difficult. To address this, we propose \\textbf{Invariant Causal Routing (ICR)}, a causal governance framework that identifies policy-norm relations stable across heterogeneous environments. ICR integrates counterfactual reasoning with invariant causal discovery to separate genuine causal effects from spurious correlations and to construct interpretable, auditable policy rules that remain effective under distribution shift. In heterogeneous agent simulations calibrated with real data, ICR yields more stable norms, smaller generalization gaps, and more concise rules than correlation or coverage baselines, demonstrating that causal invariance offers a principled and interpretable foundation for governance.", "date": "2026-03-04", "categories": []}
{"id": "2603.04780", "title": "Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learning", "abstract": "Causal discovery with latent variables is a fundamental task. Yet most existing methods rely on strong structural assumptions, such as enforcing specific indicator patterns for latents or restricting how they can interact with others. We argue that a core obstacle to a general, structural-assumption-free approach is the lack of an equivalence characterization: without knowing what can be identified, one generally cannot design methods for how to identify it. In this work, we aim to close this gap for linear non-Gaussian models. We establish the graphical criterion for when two graphs with arbitrary latent structure and cycles are distributionally equivalent, that is, they induce the same observed distribution set. Key to our approach is a new tool, edge rank constraints, which fills a missing piece in the toolbox for latent-variable causal discovery in even broader settings. We further provide a procedure to traverse the whole equivalence class and develop an algorithm to recover models from data up to such equivalence. To our knowledge, this is the first equivalence characterization with latent variables in any parametric setting without structural assumptions, and hence the first structural-assumption-free discovery method. Code and an interactive demo are available at https://equiv.cc.", "date": "2026-03-05", "categories": []}
{"id": "2603.05149", "title": "Federated Causal Discovery Across Heterogeneous Datasets under Latent Confounding", "abstract": "Causal discovery across multiple datasets is often constrained by data privacy regulations and cross-site heterogeneity, limiting the use of conventional methods that require a single, centralized dataset. To address these challenges, we introduce fedCI, a federated conditional independence test that rigorously handles heterogeneous datasets with non-identical sets of variables, site-specific effects, and mixed variable types, including continuous, ordinal, binary, and categorical variables. At its core, fedCI uses a federated Iteratively Reweighted Least Squares (IRLS) procedure to estimate the parameters of generalized linear models underlying likelihood-ratio tests for conditional independence. Building on this, we develop fedCI-IOD, a federated extension of the Integration of Overlapping Datasets (IOD) algorithm, that replaces its meta-analysis strategy and enables, for the fist time, federated causal discovery under latent confounding across distributed and heterogeneous datasets. By aggregating evidence federatively, fedCI-IOD not only preserves privacy but also substantially enhances statistical power, achieving performance comparable to fully pooled analyses and mitigating artifacts from low local sample sizes. Our tools are publicly available as the fedCI Python package, a privacy-preserving R implementation of IOD, and a web application for the fedCI-IOD pipeline, providing versatile, user-friendly solutions for federated conditional independence testing and causal discovery.", "date": "2026-03-05", "categories": []}
{"id": "2603.05370", "title": "Learning Causal Structure of Time Series using Best Order Score Search", "abstract": "Causal structure learning from observational data is central to many scientific and policy domains, but the time series setting common to many disciplines poses several challenges due to temporal dependence. In this paper we focus on score-based causal discovery for multivariate time series and introduce TS-BOSS, a time series extension of the recently proposed Best Order Score Search (BOSS) (Andrews et al. 2023). TS-BOSS performs a permutation-based search over dynamic Bayesian network structures while leveraging grow-shrink trees to cache intermediate score computations, preserving the scalability and strong empirical performance of BOSS in the static setting. We provide theoretical guarantees establishing the soundness of TS-BOSS under suitable assumptions, and we present an intermediate result that extends classical subgraph minimality results for permutation-based methods to the dynamic (time series) setting. Our experiments on synthetic data show that TS-BOSS is especially effective in high auto-correlation regimes, where it consistently achieves higher adjacency recall at comparable precision than standard constraint-based methods. Overall, TS-BOSS offers a high-performing, scalable approach for time series causal discovery and our results provide a principled bridge for extending sparsity-based, permutation-driven causal learning theory to dynamic settings.", "date": "2026-03-05", "categories": []}
{"id": "2603.03411", "title": "Scalable Contrastive Causal Discovery under Unknown Soft Interventions", "abstract": "Observational causal discovery is only identifiable up to the Markov equivalence class. While interventions can reduce this ambiguity, in practice interventions are often soft with multiple unknown targets. In many realistic scenarios, only a single intervention regime is observed. We propose a scalable causal discovery model for paired observational and interventional settings with shared underlying causal structure and unknown soft interventions. The model aggregates subset-level PDAGs and applies contrastive cross-regime orientation rules to construct a globally consistent maximal PDAG under Meek closure, enabling generalization to both in-distribution and out-of-distribution settings. Theoretically, we prove that our model is sound with respect to a restricted $\\Psi$ equivalence class induced solely by the information available in the subset-restricted setting. We further show that the model asymptotically recovers the corresponding identifiable PDAG and can orient additional edges compared to non-contrastive subset-restricted methods. Experiments on synthetic data demonstrate improved causal structure recovery, generalization to unseen graphs with held-out causal mechanisms, and scalability to larger graphs, with ablations supporting the theoretical results.", "date": "2026-03-03", "categories": []}
{"id": "2603.04276", "title": "Causality Elicitation from Large Language Models", "abstract": "Large language models (LLMs) are trained on enormous amounts of data and encode knowledge in their parameters. We propose a pipeline to elicit causal relationships from LLMs. Specifically, (i) we sample many documents from LLMs on a given topic, (ii) we extract an event list from from each document, (iii) we group events that appear across documents into canonical events, (iv) we construct a binary indicator vector for each document over canonical events, and (v) we estimate candidate causal graphs using causal discovery methods. Our approach does not guarantee real-world causality. Rather, it provides a framework for presenting the set of causal hypotheses that LLMs can plausibly assume, as an inspectable set of variables and candidate graphs.", "date": "2026-03-04", "categories": []}
{"id": "2603.02902", "title": "Distributed Dynamic Invariant Causal Prediction in Environmental Time Series", "abstract": "The extraction of invariant causal relationships from time series data with environmental attributes is critical for robust decision-making in domains such as climate science and environmental monitoring. However, existing methods either emphasize dynamic causal analysis without leveraging environmental contexts or focus on static invariant causal inference, leaving a gap in distributed temporal settings. In this paper, we propose Distributed Dynamic Invariant Causal Prediction in Time-series (DisDy-ICPT), a novel framework that learns dynamic causal relationships over time while mitigating spatial confounding variables without requiring data communication. We theoretically prove that DisDy-ICPT recovers stable causal predictors within a bounded number of communication rounds under standard sampling assumptions. Empirical evaluations on synthetic benchmarks and environment-segmented real-world datasets show that DisDy-ICPT achieves superior predictive stability and accuracy compared to baseline methods A and B. Our approach offers promising applications in carbon monitoring and weather forecasting. Future work will extend DisDy-ICPT to online learning scenarios.", "date": "2026-03-03", "categories": []}
{"id": "2603.03207", "title": "I-CAM-UV: Integrating Causal Graphs over Non-Identical Variable Sets Using Causal Additive Models with Unobserved Variables", "abstract": "Causal discovery from observational data is a fundamental tool in various fields of science. While existing approaches are typically designed for a single dataset, we often need to handle multiple datasets with non-identical variable sets in practice. One straightforward approach is to estimate a causal graph from each dataset and construct a single causal graph by overlapping. However, this approach identifies limited causal relationships because unobserved variables in each dataset can be confounders, and some variable pairs may be unobserved in any dataset. To address this issue, we leverage Causal Additive Models with Unobserved Variables (CAM-UV) that provide causal graphs having information related to unobserved variables. We show that the ground truth causal graph has structural consistency with the information of CAM-UV on each dataset. As a result, we propose an approach named I-CAM-UV to integrate CAM-UV results by enumerating all consistent causal graphs. We also provide an efficient combinatorial search algorithm and demonstrate the usefulness of I-CAM-UV against existing methods.", "date": "2026-03-03", "categories": []}
{"id": "2508.11727", "title": "Causal Structure Learning in Hawkes Processes with Complex Latent Confounder Networks", "abstract": "Multivariate Hawkes process provides a powerful framework for modeling temporal dependencies and event-driven interactions in complex systems. While existing methods primarily focus on uncovering causal structures among observed subprocesses, real-world systems are often only partially observed, with latent subprocesses posing significant challenges. In this paper, we show that continuous-time event sequences can be represented by a discrete-time causal model as the time interval shrinks, and we leverage this insight to establish necessary and sufficient conditions for identifying latent subprocesses and the causal influences. Accordingly, we propose a two-phase iterative algorithm that alternates between inferring causal relationships among discovered subprocesses and uncovering new latent subprocesses, guided by path-based conditions that guarantee identifiability. Experiments on both synthetic and real-world datasets show that our method effectively recovers causal structures despite the presence of latent subprocesses.", "date": "2025-08-15", "categories": []}
{"id": "2603.01052", "title": "No More Maybe-Arrows: Resolving Causal Uncertainty by Breaking Symmetries", "abstract": "The recent works on causal discovery have followed a similar trend of learning partial ancestral graphs (PAGs) since observational data constrain the true causal directed acyclic graph (DAG) only up to a Markov equivalence class. This limits their application in the majority of downstream tasks, as uncertainty in causal relations remains unresolved. We propose a new refinement framework, CausalSAGE, for converting PAGs to DAGs while respecting the underlying causal relations. The framework expands discrete variables into state-level representations, constrains the search space using structural knowledge and soft priors, and applies a unified differentiable objective for joint optimization. The final DAG is obtained by aggregating the optimized structures and enforcing acyclicity when necessary. Our experimental evaluations show that the obtained DAGs preserve the underlying causal relations while also being efficient to obtain.", "date": "2026-03-01", "categories": []}
{"id": "2509.21021", "title": "Efficient Ensemble Conditional Independence Test Framework for Causal Discovery", "abstract": "Constraint-based causal discovery relies on numerous conditional independence tests (CITs), but its practical applicability is severely constrained by the prohibitive computational cost, especially as CITs themselves have high time complexity with respect to the sample size. To address this key bottleneck, we introduce the Ensemble Conditional Independence Test (E-CIT), a general-purpose and plug-and-play framework. E-CIT operates on an intuitive divide-and-aggregate strategy: it partitions the data into subsets, applies a given base CIT independently to each subset, and aggregates the resulting p-values using a novel method grounded in the properties of stable distributions. This framework reduces the computational complexity of a base CIT to linear in the sample size when the subset size is fixed. Moreover, our tailored p-value combination method offers theoretical consistency guarantees under mild conditions on the subtests. Experimental results demonstrate that E-CIT not only significantly reduces the computational burden of CITs and causal discovery but also achieves competitive performance. Notably, it exhibits an improvement in complex testing scenarios, particularly on real-world datasets.", "date": "2025-09-25", "categories": []}
{"id": "2510.04970", "title": "Embracing Discrete Search: A Reasonable Approach to Causal Structure Learning", "abstract": "We present FLOP (Fast Learning of Order and Parents), a score-based causal discovery algorithm for linear models. It pairs fast parent selection with iterative Cholesky-based score updates, cutting run-times over prior algorithms. This makes it feasible to fully embrace discrete search, enabling iterated local search with principled order initialization to find graphs with scores at or close to the global optimum. The resulting structures are highly accurate across benchmarks, with near-perfect recovery in standard settings. This performance calls for revisiting discrete search over graphs as a reasonable approach to causal discovery.", "date": "2025-10-06", "categories": []}
{"id": "2602.23800", "title": "Operationalizing Longitudinal Causal Discovery Under Real-World Workflow Constraints", "abstract": "Causal discovery has achieved substantial theoretical progress, yet its deployment in large-scale longitudinal systems remains limited. A key obstacle is that operational data are generated under institutional workflows whose induced partial orders are rarely formalized, enlarging the admissible graph space in ways inconsistent with the recording process. We characterize a workflow-induced constraint class for longitudinal causal discovery that restricts the admissible directed acyclic graph space through protocol-derived structural masks and timeline-aligned indexing. Rather than introducing a new optimization algorithm, we show that explicitly encoding workflow-consistent partial orders reduces structural ambiguity, especially in mixed discrete--continuous panels where within-time orientation is weakly identified. The framework combines workflow-derived admissible-edge constraints, measurement-aligned time indexing and block structure, bootstrap-based uncertainty quantification for lagged total effects, and a dynamic representation supporting intervention queries. In a nationwide annual health screening cohort in Japan with 107,261 individuals and 429,044 person-years, workflow-constrained longitudinal LiNGAM yields temporally consistent within-time substructures and interpretable lagged total effects with explicit uncertainty. Sensitivity analyses using alternative exposure and body-composition definitions preserve the main qualitative patterns. We argue that formalizing workflow-derived constraint classes improves structural interpretability without relying on domain-specific edge specification, providing a reproducible bridge between operational workflows and longitudinal causal discovery under standard identifiability assumptions.", "date": "2026-02-27", "categories": []}
{"id": "2505.08371", "title": "Density Ratio-based Causal Discovery from Bivariate Continuous-Discrete Data", "abstract": "We address the problem of inferring the causal direction between a continuous variable $X$ and a discrete variable $Y$ from observational data. For the model $X \\to Y$, we adopt the threshold model used in prior work. For the model $Y \\to X$, we consider two cases: (1) the conditional distributions of $X$ given different values of $Y$ form a location-shift family, and (2) they are mixtures of generalized normal distributions with independently parameterized components. We establish identifiability of the causal direction through three theoretical results. First, we prove that under $X \\to Y$, the density ratio of $X$ conditioned on different values of $Y$ is monotonic. Second, we establish that under $Y \\to X$ with non-location-shift conditionals, monotonicity of the density ratio holds only on a set of Lebesgue measure zero in the parameter space. Third, we show that under $X \\to Y$, the conditional distributions forming a location-shift family requires a precise coordination between the causal mechanism and input distribution, which is non-generic under the principle of independent mechanisms. Together, these results imply that monotonicity of the density ratio characterizes the direction $X \\to Y$, whereas non-monotonicity or location-shift conditionals characterizes $Y \\to X$. Based on this, we propose Density Ratio-based Causal Discovery (DRCD), a method that determines causal direction by testing for location-shift conditionals and monotonicity of the estimated density ratio. Experiments on synthetic and real-world datasets demonstrate that DRCD outperforms existing methods.", "date": "2025-05-13", "categories": []}
{"id": "2602.22254", "title": "Causal Direction from Convergence Time: Faster Training in the True Causal Direction", "abstract": "We introduce Causal Computational Asymmetry (CCA), a principle for causal direction identification based on optimization dynamics in which one neural network is trained to predict $Y$ from $X$ and another to predict $X$ from $Y$, and the direction that converges faster is inferred to be causal. Under the additive noise model $Y = f(X) + \\varepsilon$ with $\\varepsilon \\perp X$ and $f$ nonlinear and injective, we establish a formal asymmetry: in the reverse direction, residuals remain statistically dependent on the input regardless of approximation quality, inducing a strictly higher irreducible loss floor and non-separable gradient noise in the optimization dynamics, so that the reverse model requires strictly more gradient steps in expectation to reach any fixed loss threshold; consequently, the forward (causal) direction converges in fewer expected optimization steps. CCA operates in optimization-time space, distinguishing it from methods such as RESIT, IGCI, and SkewScore that rely on statistical independence or distributional asymmetries, and proper z-scoring of both variables is required for valid comparison of convergence rates. On synthetic benchmarks, CCA achieves 26/30 correct causal identifications across six neural architectures, including 30/30 on sine and exponential data-generating processes. We further embed CCA into a broader framework termed Causal Compression Learning (CCL), which integrates graph structure learning, causal information compression, and policy optimization, with all theoretical guarantees formally proved and empirically validated on synthetic datasets.", "date": "2026-02-24", "categories": []}
{"id": "2602.22532", "title": "Coarse-to-Fine Learning of Dynamic Causal Structures", "abstract": "Learning the dynamic causal structure of time series is a challenging problem. Most existing approaches rely on distributional or structural invariance to uncover underlying causal dynamics, assuming stationary or partially stationary causality. However, these assumptions often conflict with the complex, time-varying causal relationships observed in real-world systems. This motivates the need for methods that address fully dynamic causality, where both instantaneous and lagged dependencies evolve over time. Such a setting poses significant challenges for the efficiency and stability of causal discovery. To address these challenges, we introduce DyCausal, a dynamic causal structure learning framework. DyCausal leverages convolutional networks to capture causal patterns within coarse-grained time windows, and then applies linear interpolation to refine causal structures at each time step, thereby recovering fine-grained and time-varying causal graphs. In addition, we propose an acyclic constraint based on matrix norm scaling, which improves efficiency while effectively constraining loops in evolving causal structures. Comprehensive evaluations on both synthetic and real-world datasets demonstrate that DyCausal achieves superior performance compared to existing methods, offering a stable and efficient approach for identifying fully dynamic causal structures from coarse to fine.", "date": "2026-02-26", "categories": []}
{"id": "2509.25800", "title": "Characterization and Learning of Causal Graphs with Latent Confounders and Post-treatment Selection from Interventional Data", "abstract": "Interventional causal discovery seeks to identify causal relations by leveraging distributional changes introduced by interventions, even in the presence of latent confounders. Beyond the spurious dependencies induced by latent confounders, we highlight a common yet often overlooked challenge in the problem due to post-treatment selection, in which samples are selectively included in datasets after interventions. This fundamental challenge widely exists in biological studies; for example, in gene expression analysis, both observational and interventional samples are retained only if they meet quality control criteria (e.g., highly active cells). Neglecting post-treatment selection may introduce spurious dependencies and distributional changes under interventions, which can mimic causal responses, thereby distorting causal discovery results and challenging existing causal formulations. To address this, we introduce a novel causal formulation that explicitly models post-treatment selection and reveals how its differential reactions to interventions can distinguish causal relations from selection patterns, allowing us to go beyond traditional equivalence classes toward the underlying true causal structure. We then characterize its Markov properties and propose a Fine-grained Interventional equivalence class, named FI-Markov equivalence, represented by a new graphical diagram, F-PAG. Finally, we develop a provably sound and complete algorithm, F-FCI, to identify causal relations, latent confounders, and post-treatment selection up to $\\mathcal{FI}$-Markov equivalence, using both observational and interventional data. Experimental results on synthetic and real-world datasets demonstrate that our method recovers causal relations despite the presence of both selection and latent confounders.", "date": "2025-09-30", "categories": []}
{"id": "2602.20333", "title": "DMCD: Semantic-Statistical Framework for Causal Discovery", "abstract": "We present DMCD (DataMap Causal Discovery), a two-phase causal discovery framework that integrates LLM-based semantic drafting from variable metadata with statistical validation on observational data. In Phase I, a large language model proposes a sparse draft DAG, serving as a semantically informed prior over the space of possible causal structures. In Phase II, this draft is audited and refined via conditional independence testing, with detected discrepancies guiding targeted edge revisions.\n  We evaluate our approach on three metadata-rich real-world benchmarks spanning industrial engineering, environmental monitoring, and IT systems analysis. Across these datasets, DMCD achieves competitive or leading performance against diverse causal discovery baselines, with particularly large gains in recall and F1 score. Probing and ablation experiments suggest that these improvements arise from semantic reasoning over metadata rather than memorization of benchmark graphs. Overall, our results demonstrate that combining semantic priors with principled statistical verification yields a high-performing and practically effective approach to causal structure learning.", "date": "2026-02-23", "categories": []}
{"id": "2602.21036", "title": "Empirically Calibrated Conditional Independence Tests", "abstract": "Conditional independence tests (CIT) are widely used for causal discovery and feature selection. Even with false discovery rate (FDR) control procedures, they often fail to provide frequentist guarantees in practice. We highlight two common failure modes: (i) in small samples, asymptotic guarantees for many CITs can be inaccurate and even correctly specified models fail to estimate the noise levels and control the error, and (ii) when sample sizes are large but models are misspecified, unaccounted dependencies skew the test's behavior and fail to return uniform p-values under the null. We propose Empirically Calibrated Conditional Independence Tests (ECCIT), a method that measures and corrects for miscalibration. For a chosen base CIT (e.g., GCM, HRT), ECCIT optimizes an adversary that selects features and response functions to maximize a miscalibration metric. ECCIT then fits a monotone calibration map that adjusts the base-test p-values in proportion to the observed miscalibration. Across empirical benchmarks on synthetic and real data, ECCIT achieves valid FDR with higher power than existing calibration strategies while remaining test agnostic.", "date": "2026-02-24", "categories": []}
{"id": "2410.19412", "title": "Robust Time Series Causal Discovery for Agent-Based Model Validation", "abstract": "Agent-Based Model (ABM) validation is crucial as it helps ensuring the reliability of simulations, and causal discovery has become a powerful tool in this context. However, current causal discovery methods often face accuracy and robustness challenges when applied to complex and noisy time series data, which is typical in ABM scenarios. This study addresses these issues by proposing a Robust Cross-Validation (RCV) approach to enhance causal structure learning for ABM validation. We develop RCV-VarLiNGAM and RCV-PCMCI, novel extensions of two prominent causal discovery algorithms. These aim to reduce the impact of noise better and give more reliable causal relation results, even with high-dimensional, time-dependent data. The proposed approach is then integrated into an enhanced ABM validation framework, which is designed to handle diverse data and model structures.\n  The approach is evaluated using synthetic datasets and a complex simulated fMRI dataset. The results demonstrate greater reliability in causal structure identification. The study examines how various characteristics of datasets affect the performance of established causal discovery methods. These characteristics include linearity, noise distribution, stationarity, and causal structure density. This analysis is then extended to the RCV method to see how it compares in these different situations. This examination helps confirm whether the results are consistent with existing literature and also reveals the strengths and weaknesses of the novel approaches.\n  By tackling key methodological challenges, the study aims to enhance ABM validation with a more resilient valuation framework presented. These improvements increase the reliability of model-driven decision making processes in complex systems analysis.", "date": "2024-10-25", "categories": []}
{"id": "2602.18662", "title": "Large Causal Models for Temporal Causal Discovery", "abstract": "Causal discovery for both cross-sectional and temporal data has traditionally followed a dataset-specific paradigm, where a new model is fitted for each individual dataset. Such an approach limits the potential of multi-dataset pretraining. The concept of large causal models (LCMs) envisions a class of pre-trained neural architectures specifically designed for temporal causal discovery. Prior approaches are constrained to small variable counts, degrade with larger inputs, and rely heavily on synthetic data, limiting generalization. We propose a principled framework for LCMs, combining diverse synthetic generators with realistic time-series datasets, allowing learning at scale. Extensive experiments on synthetic, semi-synthetic and realistic benchmarks show that LCMs scale effectively to higher variable counts and deeper architectures while maintaining strong performance. Trained models achieve competitive or superior accuracy compared to classical and neural baselines, particularly in out-of-distribution settings, while enabling fast, single-pass inference. Results demonstrate LCMs as a promising foundation-model paradigm for temporal causal discovery. Experiments and model weights are available at https://github.com/kougioulis/LCM-paper/.", "date": "2026-02-20", "categories": []}
{"id": "2602.19131", "title": "Test-Time Learning of Causal Structure from Interventional Data", "abstract": "Supervised causal learning has shown promise in causal discovery, yet it often struggles with generalization across diverse interventional settings, particularly when intervention targets are unknown. To address this, we propose TICL (Test-time Interventional Causal Learning), a novel method that synergizes Test-Time Training with Joint Causal Inference. Specifically, we design a self-augmentation strategy to generate instance-specific training data at test time, effectively avoiding distribution shifts. Furthermore, by integrating joint causal inference, we developed a PC-inspired two-phase supervised learning scheme, which effectively leverages self-augmented training data while ensuring theoretical identifiability. Extensive experiments on bnlearn benchmarks demonstrate TICL's superiority in multiple aspects of causal discovery and intervention target detection.", "date": "2026-02-22", "categories": []}
{"id": "2602.19903", "title": "Rethinking Chronological Causal Discovery with Signal Processing", "abstract": "Causal discovery problems use a set of observations to deduce causality between variables in the real world, typically to answer questions about biological or physical systems. These observations are often recorded at regular time intervals, determined by a user or a machine, depending on the experiment design. There is generally no guarantee that the timing of these recordings matches the timing of the underlying biological or physical events. In this paper, we examine the sensitivity of causal discovery methods to this potential mismatch. We consider empirical and theoretical evidence to understand how causal discovery performance is impacted by changes of sampling rate and window length. We demonstrate that both classical and recent causal discovery methods exhibit sensitivity to these hyperparameters, and we discuss how ideas from signal processing may help us understand these phenomena.", "date": "2026-02-23", "categories": []}
{"id": "2602.20094", "title": "CausalFlip: A Benchmark for LLM Causal Judgment Beyond Semantic Matching", "abstract": "As large language models (LLMs) witness increasing deployment in complex, high-stakes decision-making scenarios, it becomes imperative to ground their reasoning in causality rather than spurious correlations. However, strong performance on traditional reasoning benchmarks does not guarantee true causal reasoning ability of LLMs, as high accuracy may still arise from memorizing semantic patterns instead of analyzing the underlying true causal structures. To bridge this critical gap, we propose a new causal reasoning benchmark, CausalFlip, designed to encourage the development of new LLM paradigm or training algorithms that ground LLM reasoning in causality rather than semantic correlation. CausalFlip consists of causal judgment questions built over event triples that could form different confounder, chain, and collider relations. Based on this, for each event triple, we construct pairs of semantically similar questions that reuse the same events but yield opposite causal answers, where models that rely heavily on semantic matching are systematically driven toward incorrect predictions. To further probe models' reliance on semantic patterns, we introduce a noisy-prefix evaluation that prepends causally irrelevant text before intermediate causal reasoning steps without altering the underlying causal relations or the logic of the reasoning process. We evaluate LLMs under multiple training paradigms, including answer-only training, explicit Chain-of-Thought (CoT) supervision, and a proposed internalized causal reasoning approach that aims to mitigate explicit reliance on correlation in the reasoning process. Our results show that explicit CoT can still be misled by spurious semantic correlations, where internalizing reasoning steps yields substantially improved causal grounding, suggesting that it is promising to better elicit the latent causal reasoning capabilities of base LLMs.", "date": "2026-02-23", "categories": []}
{"id": "2505.14825", "title": "Assimilative Causal Inference", "abstract": "Causal inference is fundamental across scientific disciplines, yet existing methods struggle to capture instantaneous, time-evolving causal relationships in complex, high-dimensional systems. In this paper, assimilative causal inference (ACI) is developed, which is a methodological framework that leverages Bayesian data assimilation to trace causes backward from observed effects. ACI solves the inverse problem rather than quantifying forward influence. It uniquely identifies dynamic causal interactions without requiring observations of candidate causes, accommodates short datasets, and, in principle, can be implemented in high-dimensional settings by employing efficient data assimilation algorithms. Crucially, it provides online tracking of causal roles that may reverse intermittently and facilitates a mathematically rigorous criterion for the causal influence range, revealing how far effects propagate. The effectiveness of ACI is demonstrated by complex dynamical systems showcasing intermittency and extreme events. ACI opens valuable pathways for studying complex systems, where transient causal structures are critical.", "date": "2025-05-20", "categories": []}
{"id": "2602.17829", "title": "Causality by Abstraction: Symbolic Rule Learning in Multivariate Timeseries with Large Language Models", "abstract": "Inferring causal relations in timeseries data with delayed effects is a fundamental challenge, especially when the underlying system exhibits complex dynamics that cannot be captured by simple functional mappings. Traditional approaches often fail to produce generalized and interpretable explanations, as multiple distinct input trajectories may yield nearly indistinguishable outputs. In this work, we present ruleXplain, a framework that leverages Large Language Models (LLMs) to extract formal explanations for input-output relations in simulation-driven dynamical systems. Our method introduces a constrained symbolic rule language with temporal operators and delay semantics, enabling LLMs to generate verifiable causal rules through structured prompting. ruleXplain relies on the availability of a principled model (e.g., a simulator) that maps multivariate input time series to output time series. Within ruleXplain, the simulator is used to generate diverse counterfactual input trajectories that yield similar target output, serving as candidate explanations. Such counterfactual inputs are clustered and provided as context to the LLM, which is tasked with the generation of symbolic rules encoding the joint temporal trends responsible for the patterns observable in the output times series. A closed-loop refinement process ensures rule consistency and semantic validity. We validate the framework using the PySIRTEM epidemic simulator, mapping testing rate inputs to daily infection counts; and the EnergyPlus building energy simulator, observing temperature and solar irradiance inputs to electricity needs. For validation, we perform three classes of experiments: (1) the efficacy of the ruleset through input reconstruction; (2) ablation studies evaluating the causal encoding of the ruleset; and (3) generalization tests of the extracted rules across unseen output trends with varying phase dynamics.", "date": "2026-02-19", "categories": []}
{"id": "2602.17217", "title": "Continual learning and refinement of causal models through dynamic predicate invention", "abstract": "Efficiently navigating complex environments requires agents to internalize the underlying logic of their world, yet standard world modelling methods often struggle with sample inefficiency, lack of transparency, and poor scalability. We propose a framework for constructing symbolic causal world models entirely online by integrating continuous model learning and repair into the agent's decision loop, by leveraging the power of Meta-Interpretive Learning and predicate invention to find semantically meaningful and reusable abstractions, allowing an agent to construct a hierarchy of disentangled, high-quality concepts from its observations. We demonstrate that our lifted inference approach scales to domains with complex relational dynamics, where propositional methods suffer from combinatorial explosion, while achieving sample-efficiency orders of magnitude higher than the established PPO neural-network-based baseline.", "date": "2026-02-19", "categories": []}
{"id": "2208.14153", "title": "Identifying Weight-Variant Latent Causal Models", "abstract": "The task of causal representation learning aims to uncover latent higher-level causal variables that affect lower-level observations. Identifying the true latent causal variables from observed data, while allowing instantaneous causal relations among latent variables, remains a challenge, however. To this end, we start with the analysis of three intrinsic indeterminacies in identifying latent variables from observations: transitivity, permutation indeterminacy, and scaling indeterminacy. We find that transitivity acts as a key role in impeding the identifiability of latent causal variables. To address the unidentifiable issue due to transitivity, we introduce a novel identifiability condition where the underlying latent causal model satisfies a linear-Gaussian model, in which the causal coefficients and the distribution of Gaussian noise are modulated by an additional observed variable. Under certain assumptions, including the existence of a reference condition under which latent causal influences vanish, we can show that the latent causal variables can be identified up to trivial permutation and scaling, and that partial identifiability results can still be obtained when this reference condition is violated for a subset of latent variables. Furthermore, based on these theoretical results, we propose a novel method, termed Structural caUsAl Variational autoEncoder (SuaVE), which directly learns causal representations and causal relationships among them, together with the mapping from the latent causal variables to the observed ones. Experimental results on synthetic and real data demonstrate the identifiability and consistency results and the efficacy of SuaVE in learning causal representations.", "date": "2022-08-30", "categories": []}
{"id": "2502.08963", "title": "Modeling Time-evolving Causality over Data Streams", "abstract": "Given an extensive, semi-infinite collection of multivariate coevolving data sequences (e.g., sensor/web activity streams) whose observations influence each other, how can we discover the time-changing cause-and-effect relationships in co-evolving data streams? How efficiently can we reveal dynamical patterns that allow us to forecast future values? In this paper, we present a novel streaming method, ModePlait, which is designed for modeling such causal relationships (i.e., time-evolving causality) in multivariate co-evolving data streams and forecasting their future values. The solution relies on characteristics of the causal relationships that evolve over time in accordance with the dynamic changes of exogenous variables. ModePlait has the following properties: (a) Effective: it discovers the time-evolving causality in multivariate co-evolving data streams by detecting the transitions of distinct dynamical patterns adaptively. (b) Accurate: it enables both the discovery of time-evolving causality and the forecasting of future values in a streaming fashion. (c) Scalable: our algorithm does not depend on data stream length and thus is applicable to very large sequences. Extensive experiments on both synthetic and real-world datasets demonstrate that our proposed model outperforms state-of-the-art methods in terms of discovering the time-evolving causality as well as forecasting.", "date": "2025-02-13", "categories": []}
{"id": "2602.16481", "title": "Leveraging Large Language Models for Causal Discovery: a Constraint-based, Argumentation-driven Approach", "abstract": "Causal discovery seeks to uncover causal relations from data, typically represented as causal graphs, and is essential for predicting the effects of interventions. While expert knowledge is required to construct principled causal graphs, many statistical methods have been proposed to leverage observational data with varying formal guarantees. Causal Assumption-based Argumentation (ABA) is a framework that uses symbolic reasoning to ensure correspondence between input constraints and output graphs, while offering a principled way to combine data and expertise. We explore the use of large language models (LLMs) as imperfect experts for Causal ABA, eliciting semantic structural priors from variable names and descriptions and integrating them with conditional-independence evidence. Experiments on standard benchmarks and semantically grounded synthetic graphs demonstrate state-of-the-art performance, and we additionally introduce an evaluation protocol to mitigate memorisation bias when assessing LLMs for causal discovery.", "date": "2026-02-18", "categories": []}
{"id": "2602.15306", "title": "Sparse Additive Model Pruning for Order-Based Causal Structure Learning", "abstract": "Causal structure learning, also known as causal discovery, aims to estimate causal relationships between variables as a form of a causal directed acyclic graph (DAG) from observational data. One of the major frameworks is the order-based approach that first estimates a topological order of the underlying DAG and then prunes spurious edges from the fully-connected DAG induced by the estimated topological order. Previous studies often focus on the former ordering step because it can dramatically reduce the search space of DAGs. In practice, the latter pruning step is equally crucial for ensuring both computational efficiency and estimation accuracy. Most existing methods employ a pruning technique based on generalized additive models and hypothesis testing, commonly known as CAM-pruning. However, this approach can be a computational bottleneck as it requires repeatedly fitting additive models for all variables. Furthermore, it may harm estimation quality due to multiple testing. To address these issues, we introduce a new pruning method based on sparse additive models, which enables direct pruning of redundant edges without relying on hypothesis testing. We propose an efficient algorithm for learning sparse additive models by combining the randomized tree embedding technique with group-wise sparse regression. Experimental results on both synthetic and real datasets demonstrated that our method is significantly faster than existing pruning methods while maintaining comparable or superior accuracy.", "date": "2026-02-17", "categories": []}
{"id": "2402.02644", "title": "Permutation-based Inference for Variational Learning of Directed Acyclic Graphs", "abstract": "Estimating the structure of Bayesian networks as directed acyclic graphs (DAGs) from observational data is a fundamental challenge, particularly in causal discovery. Bayesian approaches excel by quantifying uncertainty and addressing identifiability, but key obstacles remain: (i) representing distributions over DAGs and (ii) estimating a posterior in the underlying combinatorial space. We introduce PIVID, a method that jointly infers a distribution over permutations and DAGs using variational inference and continuous relaxations of discrete distributions. Through experiments on synthetic and real-world datasets, we show that PIVID can outperform deterministic and Bayesian approaches, achieving superior accuracy-uncertainty trade-offs while scaling efficiently with the number of variables.", "date": "2024-02-04", "categories": []}
{"id": "2406.04955", "title": "Experimental Evaluation of ROS-Causal in Real-World Human-Robot Spatial Interaction Scenarios", "abstract": "Deploying robots in human-shared environments requires a deep understanding of how nearby agents and objects interact. Employing causal inference to model cause-and-effect relationships facilitates the prediction of human behaviours and enables the anticipation of robot interventions. However, a significant challenge arises due to the absence of implementation of existing causal discovery methods within the ROS ecosystem, the standard de-facto framework in robotics, hindering effective utilisation on real robots. To bridge this gap, in our previous work we proposed ROS-Causal, a ROS-based framework designed for onboard data collection and causal discovery in human-robot spatial interactions. In this work, we present an experimental evaluation of ROS-Causal both in simulation and on a new dataset of human-robot spatial interactions in a lab scenario, to assess its performance and effectiveness. Our analysis demonstrates the efficacy of this approach, showcasing how causal models can be extracted directly onboard by robots during data collection. The online causal models generated from the simulation are consistent with those from lab experiments. These findings can help researchers to enhance the performance of robotic systems in shared environments, firstly by studying the causal relations between variables in simulation without real people, and then facilitating the actual robot deployment in real human environments. ROS-Causal: https://lcastri.github.io/roscausal", "date": "2024-06-07", "categories": []}
{"id": "2601.00097", "title": "The Agentic Leash: Extracting Causal Feedback Fuzzy Cognitive Maps with LLMs", "abstract": "We design a large-language-model (LLM) agent system that extracts causal feedback fuzzy cognitive maps (FCMs) from raw text. The causal learning or extraction process is agentic both because of the LLM's semi-autonomy and because ultimately the FCM dynamical system's equilibria drive the LLM agents to fetch and process causal text. The fetched text can in principle modify the adaptive FCM causal structure and so modify the source of its quasi-autonomy$-$its equilibrium limit cycles and fixed-point attractors. This bidirectional process endows the evolving FCM dynamical system with a degree of autonomy while the system still stays on its agentic leash. We show in particular that a sequence of three system-instruction sets guide an LLM agent as it systematically extracts key nouns and noun phrases from text, as it extracts FCM concept nodes from among those nouns and noun phrases, and then as it extracts or infers partial or fuzzy causal edges between those FCM nodes. We test this FCM generation on a recent essay about the promise of AI from the late diplomat and political theorist Henry Kissinger and his colleagues. This three-step process produced FCM dynamical systems that converged to the same equilibrium limit cycles as did the human-generated FCMs even though the human-generated FCM differed in the number of nodes and edges. A final FCM mixed generated FCMs from separate Gemini and ChatGPT LLM agents. The mixed FCM absorbed the equilibria of its dominant mixture component but also created new equilibria of its own to better approximate the underlying causal dynamical system.", "date": "2025-12-31", "categories": []}
{"id": "2602.14456", "title": "Traceable Latent Variable Discovery Based on Multi-Agent Collaboration", "abstract": "Revealing the underlying causal mechanisms in the real world is crucial for scientific and technological progress. Despite notable advances in recent decades, the lack of high-quality data and the reliance of traditional causal discovery algorithms (TCDA) on the assumption of no latent confounders, as well as their tendency to overlook the precise semantics of latent variables, have long been major obstacles to the broader application of causal discovery. To address this issue, we propose a novel causal modeling framework, TLVD, which integrates the metadata-based reasoning capabilities of large language models (LLMs) with the data-driven modeling capabilities of TCDA for inferring latent variables and their semantics. Specifically, we first employ a data-driven approach to construct a causal graph that incorporates latent variables. Then, we employ multi-LLM collaboration for latent variable inference, modeling this process as a game with incomplete information and seeking its Bayesian Nash Equilibrium (BNE) to infer the possible specific latent variables. Finally, to validate the inferred latent variables across multiple real-world web-based data sources, we leverage LLMs for evidence exploration to ensure traceability. We comprehensively evaluate TLVD on three de-identified real patient datasets provided by a hospital and two benchmark datasets. Extensive experimental results confirm the effectiveness and reliability of TLVD, with average improvements of 32.67% in Acc, 62.21% in CAcc, and 26.72% in ECit across the five datasets.", "date": "2026-02-16", "categories": []}
{"id": "2602.14972", "title": "Use What You Know: Causal Foundation Models with Partial Graphs", "abstract": "Estimating causal quantities traditionally relies on bespoke estimators tailored to specific assumptions. Recently proposed Causal Foundation Models (CFMs) promise a more unified approach by amortising causal discovery and inference in a single step. However, in their current state, they do not allow for the incorporation of any domain knowledge, which can lead to suboptimal predictions. We bridge this gap by introducing methods to condition CFMs on causal information, such as the causal graph or more readily available ancestral information. When access to complete causal graph information is too strict a requirement, our approach also effectively leverages partial causal information. We systematically evaluate conditioning strategies and find that injecting learnable biases into the attention mechanism is the most effective method to utilise full and partial causal information. Our experiments show that this conditioning allows a general-purpose CFM to match the performance of specialised models trained on specific causal structures. Overall, our approach addresses a central hurdle on the path towards all-in-one causal foundation models: the capability to answer causal queries in a data-driven manner while effectively leveraging any amount of domain expertise.", "date": "2026-02-16", "categories": []}
{"id": "2511.21537", "title": "Context-Specific Causal Graph Discovery with Unobserved Contexts: Non-Stationarity, Regimes and Spatio-Temporal Patterns", "abstract": "Real-world problems, for example in climate applications, often require causal reasoning on spatially gridded time series data or data with comparable structure. While the underlying system is often believed to behave similarly at different Points in space and time, those variations that do exist are relevant twofold: They often encode important information in and of themselves. And they may negatively affect the stability and validity of results if not accounted for. We study the information encoded in changes of the causal graph, with stability in mind. Two core challenges arise, related to the complexity of encoding system-states and to statistical convergence properties in the presence of imperfectly recoverable non-stationary structure. We provide a framework realizing principles conceptually suitable to overcome these challenges - an interpretation supported by numerical experiments. Primarily, we modify constraint-based causal discovery approaches on the level of independence testing. This leads to a framework which is additionally highly modular, easily extensible and widely applicable. For example, it allows to leverage existing constraint-based causal discovery methods (demonstrated on PC, PC-stable, FCI, PCMCI, PCMCI+ and LPCMCI), and to systematically divide the problem into simpler subproblems that are easier to analyze and understand and relate more clearly to well-studied problems like change-point-detection, clustering, independence-testing and more. Code is available at https://github.com/martin-rabel/Causal_GLDF.", "date": "2025-11-26", "categories": []}
{"id": "2602.12961", "title": "Ca-MCF: Category-level Multi-label Causal Feature selection", "abstract": "Multi-label causal feature selection has attracted extensive attention in recent years. However, current methods primarily operate at the label level, treating each label variable as a monolithic entity and overlooking the fine-grained causal mechanisms unique to individual categories. To address this, we propose a Category-level Multi-label Causal Feature selection method named Ca-MCF. Ca-MCF utilizes label category flattening to decompose label variables into specific category nodes, enabling precise modeling of causal structures within the label space. Furthermore, we introduce an explanatory competition-based category-aware recovery mechanism that leverages the proposed Specific Category-Specific Mutual Information (SCSMI) and Distinct Category-Specific Mutual Information (DCSMI) to salvage causal features obscured by label correlations. The method also incorporates structural symmetry checks and cross-dimensional redundancy removal to ensure the robustness and compactness of the identified Markov Blankets. Extensive experiments across seven real-world datasets demonstrate that Ca-MCF significantly outperforms state-of-the-art benchmarks, achieving superior predictive accuracy with reduced feature dimensionality.", "date": "2026-02-13", "categories": []}
{"id": "2601.21014", "title": "Efficient Causal Structure Learning via Modular Subgraph Integration", "abstract": "Learning causal structures from observational data remains a fundamental yet computationally intensive task, particularly in high-dimensional settings where existing methods face challenges such as the super-exponential growth of the search space and increasing computational demands. To address this, we introduce VISTA (Voting-based Integration of Subgraph Topologies for Acyclicity), a modular framework that decomposes the global causal structure learning problem into local subgraphs based on Markov Blankets. The global integration is achieved through a weighted voting mechanism that penalizes low-support edges via exponential decay, filters unreliable ones with an adaptive threshold, and ensures acyclicity using a Feedback Arc Set (FAS) algorithm. The framework is model-agnostic, imposing no assumptions on the inductive biases of base learners, is compatible with arbitrary data settings without requiring specific structural forms, and fully supports parallelization. We also theoretically establish finite-sample error bounds for VISTA, and prove its asymptotic consistency under mild conditions. Extensive experiments on both synthetic and real datasets consistently demonstrate the effectiveness of VISTA, yielding notable improvements in both accuracy and efficiency over a wide range of base learners.", "date": "2026-01-28", "categories": []}
{"id": "2507.05526", "title": "Estimating Interventional Distributions with Uncertain Causal Graphs through Meta-Learning", "abstract": "In scientific domains -- from biology to the social sciences -- many questions boil down to \\textit{What effect will we observe if we intervene on a particular variable?} If the causal relationships (e.g.~a causal graph) are known, it is possible to estimate the intervention distributions. In the absence of this domain knowledge, the causal structure must be discovered from the available observational data. However, observational data are often compatible with multiple causal graphs, making methods that commit to a single structure prone to overconfidence. A principled way to manage this structural uncertainty is via Bayesian inference, which averages over a posterior distribution on possible causal structures and functional mechanisms. Unfortunately, the number of causal structures grows super-exponentially with the number of nodes in the graph, making computations intractable. We propose to circumvent these challenges by using meta-learning to create an end-to-end model: the Model-Averaged Causal Estimation Transformer Neural Process (MACE-TNP). The model is trained to predict the Bayesian model-averaged interventional posterior distribution, and its end-to-end nature bypasses the need for expensive calculations. Empirically, we demonstrate that MACE-TNP outperforms strong Bayesian baselines. Our work establishes meta-learning as a flexible and scalable paradigm for approximating complex Bayesian causal inference, that can be scaled to increasingly challenging settings in the future.", "date": "2025-07-07", "categories": []}
{"id": "2602.07233", "title": "Extracting Root-Causal Brain Activity Driving Psychopathology from Resting State fMRI", "abstract": "Neuroimaging studies of psychiatric disorders often correlate imaging patterns with diagnostic labels or composite symptom scores, yielding diffuse associations that obscure underlying mechanisms. We instead seek to identify root-causal maps -- localized BOLD disturbances that initiate pathological cascades -- and to link them selectively to symptom dimensions. We introduce a bilevel structural causal model that connects between-subject symptom structure to within-subject resting-state fMRI via independent latent sources with localized direct effects. Based on this model, we develop SOURCE (Symptom-Oriented Uncovering of Root-Causal Elements), a procedure that links interpretable symptom axes to a parsimonious set of localized drivers. Experiments show that SOURCE recovers localized maps consistent with root-causal BOLD drivers and increases interpretability and anatomical specificity relative to existing comparators.", "date": "2026-02-06", "categories": []}
{"id": "2602.08315", "title": "Fast Flow Matching based Conditional Independence Tests for Causal Discovery", "abstract": "Constraint-based causal discovery methods require a large number of conditional independence (CI) tests, which severely limits their practical applicability due to high computational complexity. Therefore, it is crucial to design an algorithm that accelerates each individual test. To this end, we propose the Flow Matching-based Conditional Independence Test (FMCIT). The proposed test leverages the high computational efficiency of flow matching and requires the model to be trained only once throughout the entire causal discovery procedure, substantially accelerating causal discovery. According to numerical experiments, FMCIT effectively controls type-I error and maintains high testing power under the alternative hypothesis, even in the presence of high-dimensional conditioning sets. In addition, we further integrate FMCIT into a two-stage guided PC skeleton learning framework, termed GPC-FMCIT, which combines fast screening with guided, budgeted refinement using FMCIT. This design yields explicit bounds on the number of CI queries while maintaining high statistical power. Experiments on synthetic and real-world causal discovery tasks demonstrate favorable accuracy-efficiency trade-offs over existing CI testing methods and PC variants.", "date": "2026-02-09", "categories": []}
{"id": "2602.08340", "title": "Effect-Level Validation for Causal Discovery", "abstract": "Causal discovery is increasingly applied to large-scale telemetry data to estimate the effects of user-facing interventions, yet its reliability for decision-making in feedback-driven systems with strong self-selection remains unclear. In this paper, we propose an effect-centric, admissibility-first framework that treats discovered graphs as structural hypotheses and evaluates them by identifiability, stability, and falsification rather than by graph recovery accuracy alone. Empirically, we study the effect of early exposure to competitive gameplay on short-term retention using real-world game telemetry. We find that many statistically plausible discovery outputs do not admit point-identified causal queries once minimal temporal and semantic constraints are enforced, highlighting identifiability as a critical bottleneck for decision support. When identification is possible, several algorithm families converge to similar, decision-consistent effect estimates despite producing substantially different graph structures, including cases where the direct treatment-outcome edge is absent and the effect is preserved through indirect causal pathways. These converging estimates survive placebo, subsampling, and sensitivity refutation. In contrast, other methods exhibit sporadic admissibility and threshold-sensitive or attenuated effects due to endpoint ambiguity. These results suggest that graph-level metrics alone are inadequate proxies for causal reliability for a given target query. Therefore, trustworthy causal conclusions in telemetry-driven systems require prioritizing admissibility and effect-level validation over causal structural recovery alone.", "date": "2026-02-09", "categories": []}
{"id": "2602.08629", "title": "CauScale: Neural Causal Discovery at Scale", "abstract": "Causal discovery is essential for advancing data-driven fields such as scientific AI and data analysis, yet existing approaches face significant time- and space-efficiency bottlenecks when scaling to large graphs. To address this challenge, we present CauScale, a neural architecture designed for efficient causal discovery that scales inference to graphs with up to 1000 nodes. CauScale improves time efficiency via a reduction unit that compresses data embeddings and improves space efficiency by adopting tied attention weights to avoid maintaining axis-specific attention maps. To keep high causal discovery accuracy, CauScale adopts a two-stream design: a data stream extracts relational evidence from high-dimensional observations, while a graph stream integrates statistical graph priors and preserves key structural signals. CauScale successfully scales to 500-node graphs during training, where prior work fails due to space limitations. Across testing data with varying graph scales and causal mechanisms, CauScale achieves 99.6% mAP on in-distribution data and 84.4% on out-of-distribution data, while delivering 4-13,000 times inference speedups over prior methods. Our project page is at https://github.com/OpenCausaLab/CauScale.", "date": "2026-02-09", "categories": []}
{"id": "2405.15167", "title": "ProDAG: Projected Variational Inference for Directed Acyclic Graphs", "abstract": "Directed acyclic graph (DAG) learning is a central task in structure discovery and causal inference. Although the field has witnessed remarkable advances over the past few years, it remains statistically and computationally challenging to learn a single (point estimate) DAG from data, let alone provide uncertainty quantification. We address the difficult task of quantifying graph uncertainty by developing a Bayesian variational inference framework based on novel, provably valid distributions that have support directly on the space of sparse DAGs. These distributions, which we use to define our prior and variational posterior, are induced by a projection operation that maps an arbitrary continuous distribution onto the space of sparse weighted acyclic adjacency matrices. While this projection is combinatorial, it can be solved efficiently using recent continuous reformulations of acyclicity constraints. We empirically demonstrate that our method, ProDAG, can outperform state-of-the-art alternatives in both accuracy and uncertainty quantification.", "date": "2024-05-24", "categories": []}
{"id": "2602.06899", "title": "Sample Complexity of Causal Identification with Temporal Heterogeneity", "abstract": "Recovering a unique causal graph from observational data is an ill-posed problem because multiple generating mechanisms can lead to the same observational distribution. This problem becomes solvable only by exploiting specific structural or distributional assumptions. While recent work has separately utilized time-series dynamics or multi-environment heterogeneity to constrain this problem, we integrate both as complementary sources of heterogeneity. This integration yields unified necessary identifiability conditions and enables a rigorous analysis of the statistical limits of recovery under thin versus heavy-tailed noise. In particular, temporal structure is shown to effectively substitute for missing environmental diversity, possibly achieving identifiability even under insufficient heterogeneity. Extending this analysis to heavy-tailed (Student's t) distributions, we demonstrate that while geometric identifiability conditions remain invariant, the sample complexity diverges significantly from the Gaussian baseline. Explicit information-theoretic bounds quantify this cost of robustness, establishing the fundamental limits of covariance-based causal graph recovery methods in realistic non-stationary systems. This work shifts the focus from whether causal structure is identifiable to whether it is statistically recoverable in practice.", "date": "2026-02-06", "categories": []}
{"id": "2510.22031", "title": "Differentiable Constraint-Based Causal Discovery", "abstract": "Causal discovery from observational data is a fundamental task in artificial intelligence, with far-reaching implications for decision-making, predictions, and interventions. Despite significant advances, existing methods can be broadly categorized as constraint-based or score-based approaches. Constraint-based methods offer rigorous causal discovery but are often hindered by small sample sizes, while score-based methods provide flexible optimization but typically forgo explicit conditional independence testing. This work explores a third avenue: developing differentiable $d$-separation scores, obtained through a percolation theory using soft logic. This enables the implementation of a new type of causal discovery method: gradient-based optimization of conditional independence constraints. Empirical evaluations demonstrate the robust performance of our approach in low-sample regimes, surpassing traditional constraint-based and score-based baselines on a real-world dataset. Code and data of the proposed method are publicly available at https://github$.$com/PurdueMINDS/DAGPA.", "date": "2025-10-24", "categories": []}
{"id": "2602.03914", "title": "Causal Discovery for Cross-Sectional Data Based on Super-Structure and Divide-and-Conquer", "abstract": "This paper tackles a critical bottleneck in Super-Structure-based divide-and-conquer causal discovery: the high computational cost of constructing accurate Super-Structures--particularly when conditional independence (CI) tests are expensive and domain knowledge is unavailable. We propose a novel, lightweight framework that relaxes the strict requirements on Super-Structure construction while preserving the algorithmic benefits of divide-and-conquer. By integrating weakly constrained Super-Structures with efficient graph partitioning and merging strategies, our approach substantially lowers CI test overhead without sacrificing accuracy. We instantiate the framework in a concrete causal discovery algorithm and rigorously evaluate its components on synthetic data. Comprehensive experiments on Gaussian Bayesian networks, including magic-NIAB, ECOLI70, and magic-IRRI, demonstrate that our method matches or closely approximates the structural accuracy of PC and FCI while drastically reducing the number of CI tests. Further validation on the real-world China Health and Retirement Longitudinal Study (CHARLS) dataset confirms its practical applicability. Our results establish that accurate, scalable causal discovery is achievable even under minimal assumptions about the initial Super-Structure, opening new avenues for applying divide-and-conquer methods to large-scale, knowledge-scarce domains such as biomedical and social science research.", "date": "2026-02-03", "categories": []}
{"id": "2602.01155", "title": "Multi-Agent Causal Reasoning System for Error Pattern Rule Automation in Vehicles", "abstract": "Modern vehicles generate thousands of different discrete events known as Diagnostic Trouble Codes (DTCs). Automotive manufacturers use Boolean combinations of these codes, called error patterns (EPs), to characterize system faults and ensure vehicle safety. Yet, EP rules are still manually handcrafted by domain experts, a process that is expensive and prone to errors as vehicle complexity grows. This paper introduces CAREP (Causal Automated Reasoning for Error Patterns), a multi-agent system that automatizes the generation of EP rules from high-dimensional event sequences of DTCs. CAREP combines a causal discovery agent that identifies potential DTC-EP relations, a contextual information agent that integrates metadata and descriptions, and an orchestrator agent that synthesizes candidate boolean rules together with interpretable reasoning traces. Evaluation on a large-scale automotive dataset with over 29,100 unique DTCs and 474 error patterns demonstrates that CAREP can automatically and accurately discover the unknown EP rules, outperforming LLM-only baselines while providing transparent causal explanations. By uniting practical causal discovery and agent-based reasoning, CAREP represents a step toward fully automated fault diagnostics, enabling scalable, interpretable, and cost-efficient vehicle maintenance.", "date": "2026-02-01", "categories": []}
{"id": "2602.02601", "title": "CaST: Causal Discovery via Spatio-Temporal Graphs in Disaster Tweets", "abstract": "Understanding causality between real-world events from social media is essential for situational awareness, yet existing causal discovery methods often overlook the interplay between semantic, spatial, and temporal contexts. We propose CaST: Causal Discovery via Spatio-Temporal Graphs, a unified framework for causal discovery in disaster domain that integrates semantic similarity and spatio-temporal proximity using Large Language Models (LLMs) pretrained on disaster datasets. CaST constructs an event graph for each window of tweets. Each event extracted from tweets is represented as a node embedding enriched with its contextual semantics, geographic coordinates, and temporal features. These event nodes are then connected to form a spatio-temporal event graph, which is processed using a multi-head Graph Attention Network (GAT) \\cite{gat} to learn directed causal relationships. We construct an in-house dataset of approximately 167K disaster-related tweets collected during Hurricane Harvey and annotated following the MAVEN-ERE schema. Experimental results show that CaST achieves superior performance over both traditional and state-of-the-art methods. Ablation studies further confirm that incorporating spatial and temporal signals substantially improves both recall and stability during training. Overall, CaST demonstrates that integrating spatio-temporal reasoning into event graphs enables more robust and interpretable causal discovery in disaster-related social media text.", "date": "2026-02-01", "categories": []}
{"id": "2602.03353", "title": "Causal Graph Learning via Distributional Invariance of Cause-Effect Relationship", "abstract": "This paper introduces a new framework for recovering causal graphs from observational data, leveraging the observation that the distribution of an effect, conditioned on its causes, remains invariant to changes in the prior distribution of those causes. This insight enables a direct test for potential causal relationships by checking the variance of their corresponding effect-cause conditional distributions across multiple downsampled subsets of the data. These subsets are selected to reflect different prior cause distributions, while preserving the effect-cause conditional relationships. Using this invariance test and exploiting an (empirical) sparsity of most causal graphs, we develop an algorithm that efficiently uncovers causal relationships with quadratic complexity in the number of observational variables, reducing the processing time by up to 25x compared to state-of-the-art methods. Our empirical experiments on a varied benchmark of large-scale datasets show superior or equivalent performance compared to existing works, while achieving enhanced scalability.", "date": "2026-02-03", "categories": []}
{"id": "2505.12801", "title": "Transportability without Graphs: A Bayesian Approach to Identifying s-Admissible Backdoor Sets", "abstract": "Transporting causal information across populations is a critical challenge in clinical decision-making. Causal modeling provides criteria for identifiability and transportability, but these require knowledge of the causal graph, which rarely holds in practice. We propose a Bayesian method that combines observational data from the target domain with experimental data from a different domain to identify s-admissible backdoor sets, which enable unbiased estimation of causal effects across populations, without requiring the causal graph. We prove that if such a set exists, we can always find one within the Markov boundary of the outcome, narrowing the search space, and we establish asymptotic convergence guarantees for our method. We develop a greedy algorithm that reframes transportability as a feature selection problem, selecting conditioning sets that maximize the marginal likelihood of experimental data given observational data. In simulated and semi-synthetic data, our method correctly identifies transportability bias, improves causal effect estimation, and performs favorably against alternatives.", "date": "2025-05-19", "categories": []}
{"id": "2505.18410", "title": "On Theoretical Identifiability of Discrete Latent Causal Graphical Models", "abstract": "This paper considers a challenging problem of identifying a causal graphical model under the presence of latent variables. While various identifiability conditions have been proposed in the literature, they often require multiple pure children per latent variable or restrictions on the latent causal graph. Furthermore, it is common for all observed variables to exhibit the same modality. Consequently, the existing identifiability conditions are often too stringent for complex real-world data. We consider a general nonparametric measurement model with arbitrary observed variable types and binary latent variables, and propose a double triangular graphical condition that guarantees identifiability of the entire causal graphical model. The proposed condition significantly relaxes the popular pure children condition. We also establish necessary conditions for identifiability and provide valuable insights into fundamental limits of identifiability. Simulation studies verify that latent structures satisfying our conditions can be accurately estimated from data.", "date": "2025-05-23", "categories": []}
{"id": "2602.00427", "title": "Topological Residual Asymmetry for Bivariate Causal Direction", "abstract": "Inferring causal direction from purely observational bivariate data is fragile: many methods commit to a direction even in ambiguous or near non-identifiable regimes. We propose Topological Residual Asymmetry (TRA), a geometry-based criterion for additive-noise models. TRA compares the shapes of two cross-fitted regressor-residual clouds after rank-based copula standardization: in the correct direction, residuals are approximately independent, producing a two-dimensional bulk, while in the reverse direction -- especially under low noise -- the cloud concentrates near a one-dimensional tube. We quantify this bulk-tube contrast using a 0D persistent-homology functional, computed efficiently from Euclidean MST edge-length profiles. We prove consistency in a triangular-array small-noise regime, extend the method to fixed noise via a binned variant (TRA-s), and introduce TRA-C, a confounding-aware abstention rule calibrated by a Gaussian-copula plug-in bootstrap. Extensive experiments across many challenging synthetic and real-data scenarios demonstrate the method's superiority.", "date": "2026-01-31", "categories": []}
{"id": "2602.02451", "title": "Active Causal Experimentalist (ACE): Learning Intervention Strategies via Direct Preference Optimization", "abstract": "Discovering causal relationships requires controlled experiments, but experimentalists face a sequential decision problem: each intervention reveals information that should inform what to try next. Traditional approaches such as random sampling, greedy information maximization, and round-robin coverage treat each decision in isolation, unable to learn adaptive strategies from experience. We propose Active Causal Experimentalist (ACE), which learns experimental design as a sequential policy. Our key insight is that while absolute information gains diminish as knowledge accumulates (making value-based RL unstable), relative comparisons between candidate interventions remain meaningful throughout. ACE exploits this via Direct Preference Optimization, learning from pairwise intervention comparisons rather than non-stationary reward magnitudes. Across synthetic benchmarks, physics simulations, and economic data, ACE achieves 70-71% improvement over baselines at equal intervention budgets (p < 0.001, Cohen's d ~ 2). Notably, the learned policy autonomously discovers that collider mechanisms require concentrated interventions on parent variables, a theoretically-grounded strategy that emerges purely from experience. This suggests preference-based learning can recover principled experimental strategies, complementing theory with learned domain adaptation.", "date": "2026-02-02", "categories": []}
{"id": "2601.16249", "title": "Ordering-based Causal Discovery via Generalized Score Matching", "abstract": "Learning DAG structures from purely observational data remains a long-standing challenge across scientific domains. An emerging line of research leverages the score of the data distribution to initially identify a topological order of the underlying DAG via leaf node detection and subsequently performs edge pruning for graph recovery. This paper extends the score matching framework for causal discovery, which is originally designated for continuous data, and introduces a novel leaf discriminant criterion based on the discrete score function. Through simulated and real-world experiments, we demonstrate that our theory enables accurate inference of true causal orders from observed discrete data and the identified ordering can significantly boost the accuracy of existing causal discovery baselines on nearly all of the settings.", "date": "2026-01-22", "categories": []}
{"id": "2601.18189", "title": "Smooth, Sparse, and Stable: Finite-Time Exact Skeleton Recovery via Smoothed Proximal Gradients", "abstract": "Continuous optimization has significantly advanced causal discovery, yet existing methods (e.g., NOTEARS) generally guarantee only asymptotic convergence to a stationary point. This often yields dense weighted matrices that require arbitrary post-hoc thresholding to recover a DAG. This gap between continuous optimization and discrete graph structures remains a fundamental challenge. In this paper, we bridge this gap by proposing the Hybrid-Order Acyclicity Constraint (AHOC) and optimizing it via the Smoothed Proximal Gradient (SPG-AHOC). Leveraging the Manifold Identification Property of proximal algorithms, we provide a rigorous theoretical guarantee: the Finite-Time Oracle Property. We prove that under standard identifiability assumptions, SPG-AHOC recovers the exact DAG support (structure) in finite iterations, even when optimizing a smoothed approximation. This result eliminates structural ambiguity, as our algorithm returns graphs with exact zero entries without heuristic truncation. Empirically, SPG-AHOC achieves state-of-the-art accuracy and strongly corroborates the finite-time identification theory.", "date": "2026-01-26", "categories": []}
{"id": "2408.08023", "title": "Causal Discovery from Time-Series Data with Short-Term Invariance-Based Convolutional Neural Networks", "abstract": "Causal discovery from time-series data aims to capture both intra-slice (contemporaneous) and inter-slice (time-lagged) causality between variables within the temporal chain, which is crucial for various scientific disciplines. Compared to causal discovery from non-time-series data, causal discovery from time-series data necessitates more serialized samples with a larger amount of observed time steps. To address the challenges, we propose a novel gradient-based causal discovery approach STIC, which focuses on \\textbf{S}hort-\\textbf{T}erm \\textbf{I}nvariance using \\textbf{C}onvolutional neural networks to uncover the causal relationships from time-series data. Specifically, STIC leverages both the short-term time and mechanism invariance of causality within each window observation, which possesses the property of independence, to enhance sample efficiency. Furthermore, we construct two causal convolution kernels, which correspond to the short-term time and mechanism invariance respectively, to estimate the window causal graph. To demonstrate the necessity of convolutional neural networks for causal discovery from time-series data, we theoretically derive the equivalence between convolution and the underlying generative principle of time-series data under the assumption that the additive noise model is identifiable. Experimental evaluations conducted on both synthetic and FMRI benchmark datasets demonstrate that our STIC outperforms baselines significantly and achieves the state-of-the-art performance, particularly when the datasets contain a limited number of observed time steps. Code is available at \\url{https://github.com/HITshenrj/STIC}.", "date": "2024-08-15", "categories": []}
{"id": "2508.08450", "title": "Differentiable Cyclic Causal Discovery Under Unmeasured Confounders", "abstract": "Understanding causal relationships between variables is fundamental across scientific disciplines. Most causal discovery algorithms rely on two key assumptions: (i) all variables are observed, and (ii) the underlying causal graph is acyclic. While these assumptions simplify theoretical analysis, they are often violated in real-world systems, such as biological networks. Existing methods that account for confounders either assume linearity or struggle with scalability. To address these limitations, we propose DCCD-CONF, a novel framework for differentiable learning of nonlinear cyclic causal graphs in the presence of unmeasured confounders using interventional data. Our approach alternates between optimizing the graph structure and estimating the confounder distribution by maximizing the log-likelihood of the data. Through experiments on synthetic data and real-world gene perturbation datasets, we show that DCCD-CONF outperforms state-of-the-art methods in both causal graph recovery and confounder identification. Additionally, we also provide consistency guarantees for our framework, reinforcing its theoretical soundness.", "date": "2025-08-11", "categories": []}
{"id": "2405.15325", "title": "On the Identification of Temporally Causal Representation with Instantaneous Dependence", "abstract": "Temporally causal representation learning aims to identify the latent causal process from time series observations, but most methods require the assumption that the latent causal processes do not have instantaneous relations. Although some recent methods achieve identifiability in the instantaneous causality case, they require either interventions on the latent variables or grouping of the observations, which are in general difficult to obtain in real-world scenarios. To fill this gap, we propose an \\textbf{ID}entification framework for instantane\\textbf{O}us \\textbf{L}atent dynamics (\\textbf{IDOL}) by imposing a sparse influence constraint that the latent causal processes have sparse time-delayed and instantaneous relations. Specifically, we establish identifiability results of the latent causal process based on sufficient variability and the sparse influence constraint by employing contextual information of time series data. Based on these theories, we incorporate a temporally variational inference architecture to estimate the latent variables and a gradient-based sparsity regularization to identify the latent causal process. Experimental results on simulation datasets illustrate that our method can identify the latent causal process. Furthermore, evaluations on multiple human motion forecasting benchmarks with instantaneous dependencies indicate the effectiveness of our method in real-world settings.", "date": "2024-05-24", "categories": []}
{"id": "2512.10032", "title": "Cluster-Dags as Powerful Background Knowledge For Causal Discovery", "abstract": "Finding cause-effect relationships is of key importance in science. Causal discovery aims to recover a graph from data that succinctly describes these cause-effect relationships. However, current methods face several challenges, especially when dealing with high-dimensional data and complex dependencies. Incorporating prior knowledge about the system can aid causal discovery. In this work, we leverage Cluster-DAGs as a prior knowledge framework to warm-start causal discovery. We show that Cluster-DAGs offer greater flexibility than existing approaches based on tiered background knowledge and introduce two modified constraint-based algorithms, Cluster-PC and Cluster-FCI, for causal discovery in the fully and partially observed setting, respectively. Empirical evaluation on simulated data demonstrates that Cluster-PC and Cluster-FCI outperform their respective baselines without prior knowledge.", "date": "2025-12-10", "categories": []}
{"id": "2601.13365", "title": "CausationEntropy: Pythonic Optimal Causation Entropy", "abstract": "Optimal Causation Entropy (oCSE) is a robust causal network modeling technique that reveals causal networks from dynamical systems and coupled oscillators, distinguishing direct from indirect paths. CausationEntropy is a Python package that implements oCSE and several of its significant optimizations and methodological extensions. In this paper, we introduce the version 1.1 release of CausationEntropy, which includes new synthetic data generators, plotting tools, and several advanced information-theoretical causal network discovery algorithms with criteria for estimating Gaussian, k-nearest neighbors (kNN), geometric k-nearest neighbors (geometric-kNN), kernel density (KDE) and Poisson entropic estimators. The package is easy to install from the PyPi software repository, is thoroughly documented, supplemented with extensive code examples, and is modularly structured to support future additions. The entire codebase is released under the MIT license and is available on GitHub and through PyPi Repository. We expect this package to serve as a benchmark tool for causal discovery in complex dynamical systems.", "date": "2026-01-19", "categories": []}
{"id": "2601.13614", "title": "CauScientist: Teaching LLMs to Respect Data for Causal Discovery", "abstract": "Causal discovery is fundamental to scientific understanding and reliable decision-making. Existing approaches face critical limitations: purely data-driven methods suffer from statistical indistinguishability and modeling assumptions, while recent LLM-based methods either ignore statistical evidence or incorporate unverified priors that can mislead result. To this end, we propose CauScientist, a collaborative framework that synergizes LLMs as hypothesis-generating \"data scientists\" with probabilistic statistics as rigorous \"verifiers\". CauScientist employs hybrid initialization to select superior starting graphs, iteratively refines structures through LLM-proposed modifications validated by statistical criteria, and maintains error memory to guide efficient search space. Experiments demonstrate that CauScientist substantially outperforms purely data-driven baselines, achieving up to 53.8% F1 score improvement and enhancing recall from 35.0% to 100.0%. Notably, while standalone LLM performance degrades with graph complexity, CauScientist reduces structural hamming distance (SHD) by 44.0% compared to Qwen3-32B on 37-node graphs. Our project page is at https://github.com/OpenCausaLab/CauScientist.", "date": "2026-01-20", "categories": []}
{"id": "2601.10137", "title": "Step-by-Step Causality: Transparent Causal Discovery with Multi-Agent Tree-Query and Adversarial Confidence Estimation", "abstract": "Causal discovery aims to recover ``what causes what'', but classical constraint-based methods (e.g., PC, FCI) suffer from error propagation, and recent LLM-based causal oracles often behave as opaque, confidence-free black boxes. This paper introduces Tree-Query, a tree-structured, multi-expert LLM framework that reduces pairwise causal discovery to a short sequence of queries about backdoor paths, (in)dependence, latent confounding, and causal direction, yielding interpretable judgments with robustness-aware confidence scores. Theoretical guarantees are provided for asymptotic identifiability of four pairwise relations. On data-free benchmarks derived from Mooij et al. and UCI causal graphs, Tree-Query improves structural metrics over direct LLM baselines, and a diet--weight case study illustrates confounder screening and stable, high-confidence causal conclusions. Tree-Query thus offers a principled way to obtain data-free causal priors from LLMs that can complement downstream data-driven causal discovery. Code is available at https://anonymous.4open.science/r/Repo-9B3E-4F96.", "date": "2026-01-15", "categories": []}
{"id": "2601.09579", "title": "Constraint- and Score-Based Nonlinear Granger Causality Discovery with Kernels", "abstract": "Kernel-based methods are used in the context of Granger Causality to enable the identification of nonlinear causal relationships between time series variables. In this paper, we show that two state of the art kernel-based Granger Causality (GC) approaches can be theoretically unified under the framework of Kernel Principal Component Regression (KPCR), and introduce a method based on this unification, demonstrating that this approach can improve causal identification. Additionally, we introduce a Gaussian Process score-based model with Smooth Information Criterion penalisation on the marginal likelihood, and demonstrate improved performance over existing state of the art time-series nonlinear causal discovery methods. Furthermore, we propose a contemporaneous causal identification algorithm, fully based on GC, using the proposed score-based $GP_{SIC}$ method, and compare its performance to a state of the art contemporaneous time series causal discovery algorithm.", "date": "2026-01-14", "categories": []}
{"id": "2601.05474", "title": "Efficient Differentiable Causal Discovery via Reliable Super-Structure Learning", "abstract": "Recently, differentiable causal discovery has emerged as a promising approach to improve the accuracy and efficiency of existing methods. However, when applied to high-dimensional data or data with latent confounders, these methods, often based on off-the-shelf continuous optimization algorithms, struggle with the vast search space, the complexity of the objective function, and the nontrivial nature of graph-theoretical constraints. As a result, there has been a surge of interest in leveraging super-structures to guide the optimization process. Nonetheless, learning an appropriate super-structure at the right level of granularity, and doing so efficiently across various settings, presents significant challenges.\n  In this paper, we propose ALVGL, a novel and general enhancement to the differentiable causal discovery pipeline. ALVGL employs a sparse and low-rank decomposition to learn the precision matrix of the data. We design an ADMM procedure to optimize this decomposition, identifying components in the precision matrix that are most relevant to the underlying causal structure. These components are then combined to construct a super-structure that is provably a superset of the true causal graph. This super-structure is used to initialize a standard differentiable causal discovery method with a more focused search space, thereby improving both optimization efficiency and accuracy.\n  We demonstrate the versatility of ALVGL by instantiating it across a range of structural causal models, including both Gaussian and non-Gaussian settings, with and without unmeasured confounders. Extensive experiments on synthetic and real-world datasets show that ALVGL not only achieves state-of-the-art accuracy but also significantly improves optimization efficiency, making it a reliable and effective solution for differentiable causal discovery.", "date": "2026-01-09", "categories": []}
{"id": "2601.05647", "title": "Transformer Is Inherently a Causal Learner", "abstract": "We reveal that transformers trained in an autoregressive manner naturally encode time-delayed causal structures in their learned representations. When predicting future values in multivariate time series, the gradient sensitivities of transformer outputs with respect to past inputs directly recover the underlying causal graph, without any explicit causal objectives or structural constraints. We prove this connection theoretically under standard identifiability conditions and develop a practical extraction method using aggregated gradient attributions. On challenging cases such as nonlinear dynamics, long-term dependencies, and non-stationary systems, this approach greatly surpasses the performance of state-of-the-art discovery algorithms, especially as data heterogeneity increases, exhibiting scaling potential where causal accuracy improves with data volume and heterogeneity, a property traditional methods lack. This unifying view lays the groundwork for a future paradigm where causal discovery operates through the lens of foundation models, and foundation models gain interpretability and enhancement through the lens of causality.", "date": "2026-01-09", "categories": []}
{"id": "2412.11850", "title": "Causal Invariance Learning via Efficient Nonconvex Optimization", "abstract": "Identifying the causal relationship among variables from observational data is an important yet challenging task. This work focuses on identifying the direct causes of an outcome and estimating their magnitude, i.e., learning the causal outcome model. Data from multiple environments provide valuable opportunities to uncover causality by exploiting the invariance principle that the causal outcome model holds across heterogeneous environments. Based on the invariance principle, we propose the Negative Weighted Distributionally Robust Optimization (NegDRO) framework to learn an invariant prediction model. NegDRO minimizes the worst-case combination of risks across multiple environments and enforces invariance by allowing potential negative weights. Under the additive interventions regime, we establish three major contributions: (i) On the statistical side, we provide sufficient and nearly necessary identification conditions under which the invariant prediction model coincides with the causal outcome model; (ii) On the optimization side, despite the nonconvexity of NegDRO, we establish its benign optimization landscape, where all stationary points lie close to the true causal outcome model; (iii) On the computational side, we develop a gradient-based algorithm that provably converges to the causal outcome model, with non-asymptotic convergence rates in both sample size and gradient-descent iterations. In particular, our method avoids exhaustive combinatorial searches over exponentially many subsets of covariates found in the literature, ensuring scalability even when the dimension of the covariates is large. To our knowledge, this is the first causal invariance learning method that finds the approximate global optimality for a nonconvex optimization problem efficiently.", "date": "2024-12-16", "categories": []}
{"id": "2506.12227", "title": "Uncovering Bias Paths with LLM-guided Causal Discovery: An Active Learning and Dynamic Scoring Approach", "abstract": "Ensuring fairness in machine learning requires understanding how sensitive attributes like race or gender causally influence outcomes. Existing causal discovery (CD) methods often struggle to recover fairness-relevant pathways in the presence of noise, confounding, or data corruption. Large language models (LLMs) offer a complementary signal by leveraging semantic priors from variable metadata. We propose a hybrid LLM-guided CD framework that extends a breadth-first search strategy with active learning and dynamic scoring. Variable pairs are prioritized for querying using a composite score combining mutual information, partial correlation, and LLM confidence, enabling more efficient and robust structure discovery. To evaluate fairness sensitivity, we introduce a semi-synthetic benchmark based on the UCI Adult dataset, embedding domain-informed bias pathways alongside noise and latent confounders. We assess how well CD methods recover both global graph structure and fairness-critical paths (e.g., sex-->education-->income). Our results demonstrate that LLM-guided methods, including our active, dynamically scored variant, outperform baselines in recovering fairness-relevant structure under noisy conditions. We analyze when LLM-driven insights complement statistical dependencies and discuss implications for fairness auditing in high-stakes domains.", "date": "2025-06-13", "categories": []}
{"id": "2510.14073", "title": "Exploratory Causal Inference in SAEnce", "abstract": "Randomized Controlled Trials are one of the pillars of science; nevertheless, they rely on hand-crafted hypotheses and expensive analysis. Such constraints prevent causal effect estimation at scale, potentially anchoring on popular yet incomplete hypotheses. We propose to discover the unknown effects of a treatment directly from data. For this, we turn unstructured data from a trial into meaningful representations via pretrained foundation models and interpret them via a sparse autoencoder. However, discovering significant causal effects at the neural level is not trivial due to multiple-testing issues and effects entanglement. To address these challenges, we introduce Neural Effect Search, a novel recursive procedure solving both issues by progressive stratification. After assessing the robustness of our algorithm on semi-synthetic experiments, we showcase, in the context of experimental ecology, the first successful unsupervised causal effect identification on a real-world scientific trial.", "date": "2025-10-15", "categories": []}
{"id": "2410.16100", "title": "ExDBN: Learning Dynamic Bayesian Networks using Extended Mixed-Integer Programming Formulations", "abstract": "Causal learning from data has received much attention recently. Bayesian networks can be used to capture causal relationships. There, one recovers a weighted directed acyclic graph in which random variables are represented by vertices, and the weights associated with each edge represent the strengths of the causal relationships between them. This concept is extended to capture dynamic effects by introducing a dependency on past data, which may be captured by the structural equation model. This formalism is utilized in the present contribution to propose a score-based learning algorithm. A mixed-integer quadratic program is formulated and an algorithmic solution proposed, in which the pre-generation of exponentially many acyclicity constraints is avoided by utilizing the so-called branch-and-cut (``lazy constraint'') method. Comparing the novel approach to the state-of-the-art, we show that the proposed approach turns out to produce more accurate results when applied to small and medium-sized synthetic instances containing up to 80 time series. Lastly, two interesting applications in bioscience and finance, to which the method is directly applied, further stress the importance of developing highly accurate, globally convergent solvers that can handle instances of modest size.", "date": "2024-10-21", "categories": []}
{"id": "2510.24639", "title": "Causal Ordering for Structure Learning from Time Series", "abstract": "Predicting causal structure from time series data is crucial for understanding complex phenomena in physiology, brain connectivity, climate dynamics, and socio-economic behaviour. Causal discovery in time series is hindered by the combinatorial complexity of identifying true causal relationships, especially as the number of variables and time points grow. A common approach to simplify the task is the so-called ordering-based methods. Traditional ordering methods inherently limit the representational capacity of the resulting model. In this work, we fix this issue by leveraging multiple valid causal orderings, instead of a single one as standard practice. We propose DOTS (Diffusion Ordered Temporal Structure), using diffusion-based causal discovery for temporal data. By integrating multiple orderings, DOTS effectively recovers the transitive closure of the underlying directed acyclic graph, mitigating spurious artifacts inherent in single-ordering approaches. We formalise the problem under standard assumptions such as stationarity and the additive noise model, and leverage score matching with diffusion processes to enable efficient Hessian estimation. Extensive experiments validate the approach. Empirical evaluations on synthetic and real-world datasets demonstrate that DOTS outperforms state-of-the-art baselines, offering a scalable and robust approach to temporal causal discovery. On synthetic benchmarks ($d{=}\\!3-\\!6$ variables, $T{=}200\\!-\\!5{,}000$ samples), DOTS improves mean window-graph $F1$ from $0.63$ (best baseline) to $0.81$. On the CausalTime real-world benchmark ($d{=}20\\!-\\!36$), while baselines remain the best on individual datasets, DOTS attains the highest average summary-graph $F1$ while halving runtime relative to graph-optimisation methods. These results establish DOTS as a scalable and accurate solution for temporal causal discovery.", "date": "2025-10-28", "categories": []}
{"id": "2512.24478", "title": "HOLOGRAPH: Active Causal Discovery via Sheaf-Theoretic Alignment of Large Language Model Priors", "abstract": "Causal discovery from observational data remains fundamentally limited by identifiability constraints. Recent work has explored leveraging Large Language Models (LLMs) as sources of prior causal knowledge, but existing approaches rely on heuristic integration that lacks theoretical grounding. We introduce HOLOGRAPH, a framework that formalizes LLM-guided causal discovery through sheaf theory--representing local causal beliefs as sections of a presheaf over variable subsets. Our key insight is that coherent global causal structure corresponds to the existence of a global section, while topological obstructions manifest as non-vanishing sheaf cohomology. We propose the Algebraic Latent Projection to handle hidden confounders and Natural Gradient Descent on the belief manifold for principled optimization. Experiments on synthetic and real-world benchmarks demonstrate that HOLOGRAPH provides rigorous mathematical foundations while achieving competitive performance on causal discovery tasks with 50-100 variables. Our sheaf-theoretic analysis reveals that while Identity, Transitivity, and Gluing axioms are satisfied to numerical precision (<10^{-6}), the Locality axiom fails for larger graphs, suggesting fundamental non-local coupling in latent variable projections. Code is available at [https://github.com/hyunjun1121/holograph](https://github.com/hyunjun1121/holograph).", "date": "2025-12-30", "categories": []}
{"id": "2601.01368", "title": "Causal discovery for linear causal model with correlated noise: an Adversarial Learning Approach", "abstract": "Causal discovery from data with unmeasured confounding factors is a challenging problem. This paper proposes an approach based on the f-GAN framework, learning the binary causal structure independent of specific weight values. We reformulate the structure learning problem as minimizing Bayesian free energy and prove that this problem is equivalent to minimizing the f-divergence between the true data distribution and the model-generated distribution. Using the f-GAN framework, we transform this objective into a min-max adversarial optimization problem. We implement the gradient search in the discrete graph space using Gumbel-Softmax relaxation.", "date": "2026-01-04", "categories": []}
{"id": "2512.24696", "title": "Causal Discovery with Mixed Latent Confounding via Precision Decomposition", "abstract": "We study causal discovery from observational data in linear Gaussian systems affected by \\emph{mixed latent confounding}, where some unobserved factors act broadly across many variables while others influence only small subsets. This setting is common in practice and poses a challenge for existing methods: differentiable and score-based DAG learners can misinterpret global latent effects as causal edges, while latent-variable graphical models recover only undirected structure.\n  We propose \\textsc{DCL-DECOR}, a modular, precision-led pipeline that separates these roles. The method first isolates pervasive latent effects by decomposing the observed precision matrix into a structured component and a low-rank component. The structured component corresponds to the conditional distribution after accounting for pervasive confounders and retains only local dependence induced by the causal graph and localized confounding. A correlated-noise DAG learner is then applied to this deconfounded representation to recover directed edges while modeling remaining structured error correlations, followed by a simple reconciliation step to enforce bow-freeness.\n  We provide identifiability results that characterize the recoverable causal target under mixed confounding and show how the overall problem reduces to well-studied subproblems with modular guarantees. Synthetic experiments that vary the strength and dimensionality of pervasive confounding demonstrate consistent improvements in directed edge recovery over applying correlated-noise DAG learning directly to the confounded data.", "date": "2025-12-31", "categories": []}
{"id": "2512.19746", "title": "Robust Causal Directionality Inference in Quantum Inference under MNAR Observation and High-Dimensional Noise", "abstract": "In quantum mechanics, observation actively shapes the system, paralleling the statistical notion of Missing Not At Random (MNAR). This study introduces a unified framework for \\textbf{robust causal directionality inference} in quantum engineering, determining whether relations are system$\\to$observation, observation$\\to$system, or bidirectional.\n  The method integrates CVAE-based latent constraints, MNAR-aware selection models, GEE-stabilized regression, penalized empirical likelihood, and Bayesian optimization. It jointly addresses quantum and classical noise while uncovering causal directionality, with theoretical guarantees for double robustness, perturbation stability, and oracle inequalities.\n  Simulation and real-data analyses (TCGA gene expression, proteomics) show that the proposed MNAR-stabilized CVAE+GEE+AIPW+PEL framework achieves lower bias and variance, near-nominal coverage, and superior quantum-specific diagnostics. This establishes robust causal directionality inference as a key methodological advance for reliable quantum engineering.", "date": "2025-12-18", "categories": []}
{"id": "2503.21526", "title": "Constraint-based causal discovery with tiered background knowledge and latent variables in single or overlapping datasets", "abstract": "In this paper we consider the use of tiered background knowledge within constraint based causal discovery. Our focus is on settings relaxing causal sufficiency, i.e. allowing for latent variables which may arise because relevant information could not be measured at all, or not jointly, as in the case of multiple overlapping datasets. We first present novel insights into the properties of the 'tiered FCI' (tFCI) algorithm. Building on this, we introduce a new extension of the IOD (integrating overlapping datasets) algorithm incorporating tiered background knowledge, the 'tiered IOD' (tIOD) algorithm. We show that under full usage of the tiered background knowledge tFCI and tIOD are sound, while simple versions of the tIOD and tFCI are sound and complete. We further show that the tIOD algorithm can often be expected to be considerably more efficient and informative than the IOD algorithm even beyond the obvious restriction of the Markov equivalence classes. We provide a formal result on the conditions for this gain in efficiency and informativeness. Our results are accompanied by a series of examples illustrating the exact role and usefulness of tiered background knowledge.", "date": "2025-03-27", "categories": []}
{"id": "2512.16233", "title": "DAG Learning from Zero-Inflated Count Data Using Continuous Optimization", "abstract": "We address network structure learning from zero-inflated count data by casting each node as a zero-inflated generalized linear model and optimizing a smooth, score-based objective under a directed acyclic graph constraint. Our Zero-Inflated Continuous Optimization (ZICO) approach uses node-wise likelihoods with canonical links and enforces acyclicity through a differentiable surrogate constraint combined with sparsity regularization. ZICO achieves superior performance with faster runtimes on simulated data. It also performs comparably to or better than common algorithms for reverse engineering gene regulatory networks. ZICO is fully vectorized and mini-batched, enabling learning on larger variable sets with practical runtimes in a wide range of domains.", "date": "2025-12-18", "categories": []}
{"id": "2503.17037", "title": "Unitless Unrestricted Markov-Consistent SCM Generation: Better Benchmark Datasets for Causal Discovery", "abstract": "Causal discovery aims to extract qualitative causal knowledge in the form of causal graphs from data. Because causal ground truth is rarely known in the real world, simulated data plays a vital role in evaluating the performance of the various causal discovery algorithms proposed in the literature. But recent work highlighted certain artifacts of commonly used data generation techniques for a standard class of structural causal models (SCM) that may be nonphysical, including var- and R2-sortability, where the variables' variance and coefficients of determination (R2) after regressing on all other variables, respectively, increase along the causal order. Some causal methods exploit such artifacts, leading to unrealistic expectations for their performance on real-world data. Some modifications have been proposed to remove these artifacts; notably, the internally-standardized structural causal model (iSCM) avoids varsortability and largely alleviates R2-sortability on sparse causal graphs, but exhibits a reversed R2-sortability pattern for denser graphs not featured in their work. We analyze which sortability patterns we expect to see in real data, and propose a method for drawing coefficients that we argue more effectively samples the space of SCMs. Finally, we propose a novel extension of our SCM generation method to the time series setting.", "date": "2025-03-21", "categories": []}
{"id": "2512.14361", "title": "Causal Structure Learning for Dynamical Systems with Theoretical Score Analysis", "abstract": "Real world systems evolve in continuous-time according to their underlying causal relationships, yet their dynamics are often unknown. Existing approaches to learning such dynamics typically either discretize time -- leading to poor performance on irregularly sampled data -- or ignore the underlying causality. We propose CaDyT, a novel method for causal discovery on dynamical systems addressing both these challenges. In contrast to state-of-the-art causal discovery methods that model the problem using discrete-time Dynamic Bayesian networks, our formulation is grounded in Difference-based causal models, which allow milder assumptions for modeling the continuous nature of the system. CaDyT leverages exact Gaussian Process inference for modeling the continuous-time dynamics which is more aligned with the underlying dynamical process. We propose a practical instantiation that identifies the causal structure via a greedy search guided by the Algorithmic Markov Condition and Minimum Description Length principle. Our experiments show that CaDyT outperforms state-of-the-art methods on both regularly and irregularly-sampled data, discovering causal networks closer to the true underlying dynamics.", "date": "2025-12-16", "categories": []}
{"id": "2512.11840", "title": "Amortized Causal Discovery with Prior-Fitted Networks", "abstract": "In recent years, differentiable penalized likelihood methods have gained popularity, optimizing the causal structure by maximizing its likelihood with respect to the data. However, recent research has shown that errors in likelihood estimation, even on relatively large sample sizes, disallow the discovery of proper structures. We propose a new approach to amortized causal discovery that addresses the limitations of likelihood estimator accuracy. Our method leverages Prior-Fitted Networks (PFNs) to amortize data-dependent likelihood estimation, yielding more reliable scores for structure learning. Experiments on synthetic, simulated, and real-world datasets show significant gains in structure recovery compared to standard baselines. Furthermore, we demonstrate directly that PFNs provide more accurate likelihood estimates than conventional neural network-based approaches.", "date": "2025-12-03", "categories": []}
{"id": "2509.19112", "title": "Towards Practical Multi-label Causal Discovery in High-Dimensional Event Sequences via One-Shot Graph Aggregation", "abstract": "Understanding causality in event sequences where outcome labels such as diseases or system failures arise from preceding events like symptoms or error codes is critical. Yet remains an unsolved challenge across domains like healthcare or vehicle diagnostics. We introduce CARGO, a scalable multi-label causal discovery method for sparse, high-dimensional event sequences comprising of thousands of unique event types. Using two pretrained causal Transformers as domain-specific foundation models for event sequences. CARGO infers in parallel, per sequence one-shot causal graphs and aggregates them using an adaptive frequency fusion to reconstruct the global Markov boundaries of labels. This two-stage approach enables efficient probabilistic reasoning at scale while bypassing the intractable cost of full-dataset conditional independence testing. Our results on a challenging real-world automotive fault prediction dataset with over 29,100 unique event types and 474 imbalanced labels demonstrate CARGO's ability to perform structured reasoning.", "date": "2025-09-23", "categories": []}
{"id": "2512.11219", "title": "Latent Variable Causal Discovery under Selection Bias", "abstract": "Addressing selection bias in latent variable causal discovery is important yet underexplored, largely due to a lack of suitable statistical tools: While various tools beyond basic conditional independencies have been developed to handle latent variables, none have been adapted for selection bias. We make an attempt by studying rank constraints, which, as a generalization to conditional independence constraints, exploits the ranks of covariance submatrices in linear Gaussian models. We show that although selection can significantly complicate the joint distribution, interestingly, the ranks in the biased covariance matrices still preserve meaningful information about both causal structures and selection mechanisms. We provide a graph-theoretic characterization of such rank constraints. Using this tool, we demonstrate that the one-factor model, a classical latent variable model, can be identified under selection bias. Simulations and real-world experiments confirm the effectiveness of using our rank constraints.", "date": "2025-12-12", "categories": []}
{"id": "2506.20347", "title": "Emergent Granger Causality in Neural Networks: Can Prediction Alone Reveal Structure?", "abstract": "Granger Causality (GC) offers an elegant statistical framework to study the association between multivariate time series data. Vector autoregressive models (VAR) are simple and easy to fit, but have limited application because of their inherent inability to capture more complex (e.g., non-linear) associations. Numerous attempts have already been made in the literature that exploit the functional approximation power of deep neural networks (DNNs) for GC. However, these methods treat GC as a variable selection problem. We present a novel paradigm for investigating the learned GC from a single neural network used for joint modeling of all components of multivariate time series data, which is essentially linked with prediction and assessing the distribution shift in residuals. A deep learning model, with proper regularization, may learn the true GC structure when jointly used for all components of the time series when there is sufficient training data. We propose to uncover the learned GC structure by comparing the model uncertainty or distribution of the residuals when the past of everything is used as compared to the one where a specific time series component is dropped from the model. We also compare the effect of input layer dropout on the ability of a neural network to learn GC. We show that a well-regularized model can learn the true GC structure from the data without explicitly adding terms in the loss function that guide the model to select variables or perform sparse regression under specific settings. We also provide a comparison of deep learning architectures such as CNN, LSTM and transformer models on their ability to discover Granger Causality. The numerical experiments demonstrate that, compared to sparse regression models, a simple joint model is a strong baseline for learning the true GC which has the advantage that it does not require tuning of many extra hyper-parameters.", "date": "2025-06-25", "categories": []}
{"id": "2512.07267", "title": "Non-negative DAG Learning from Time-Series Data", "abstract": "This work aims to learn the directed acyclic graph (DAG) that captures the instantaneous dependencies underlying a multivariate time series. The observed data follow a linear structural vector autoregressive model (SVARM) with both instantaneous and time-lagged dependencies, where the instantaneous structure is modeled by a DAG to reflect potential causal relationships. While recent continuous relaxation approaches impose acyclicity through smooth constraint functions involving powers of the adjacency matrix, they lead to non-convex optimization problems that are challenging to solve. In contrast, we assume that the underlying DAG has only non-negative edge weights, and leverage this additional structure to impose acyclicity via a convex constraint. This enables us to cast the problem of non-negative DAG recovery from multivariate time-series data as a convex optimization problem in abstract form, which we solve using the method of multipliers. Crucially, the convex formulation guarantees global optimality of the solution. Finally, we assess the performance of the proposed method on synthetic time-series data, where it outperforms existing alternatives.", "date": "2025-12-08", "categories": []}
{"id": "2512.07796", "title": "Large Causal Models from Large Language Models", "abstract": "We introduce a new paradigm for building large causal models (LCMs) that exploits the enormous potential latent in today's large language models (LLMs). We describe our ongoing experiments with an implemented system called DEMOCRITUS (Decentralized Extraction of Manifold Ontologies of Causal Relations Integrating Topos Universal Slices) aimed at building, organizing, and visualizing LCMs that span disparate domains extracted from carefully targeted textual queries to LLMs. DEMOCRITUS is methodologically distinct from traditional narrow domain and hypothesis centered causal inference that builds causal models from experiments that produce numerical data. A high-quality LLM is used to propose topics, generate causal questions, and extract plausible causal statements from a diverse range of domains. The technical challenge is then to take these isolated, fragmented, potentially ambiguous and possibly conflicting causal claims, and weave them into a coherent whole, converting them into relational causal triples and embedding them into a LCM. Addressing this technical challenge required inventing new categorical machine learning methods, which we can only briefly summarize in this paper, as it is focused more on the systems side of building DEMOCRITUS. We describe the implementation pipeline for DEMOCRITUS comprising of six modules, examine its computational cost profile to determine where the current bottlenecks in scaling the system to larger models. We describe the results of using DEMOCRITUS over a wide range of domains, spanning archaeology, biology, climate change, economics, medicine and technology. We discuss the limitations of the current DEMOCRITUS system, and outline directions for extending its capabilities.", "date": "2025-12-08", "categories": []}
{"id": "2505.11085", "title": "A Fast Kernel-based Conditional Independence test with Application to Causal Discovery", "abstract": "Kernel-based conditional independence (KCI) testing is a powerful nonparametric method commonly employed in causal discovery tasks. Despite its flexibility and statistical reliability, cubic computational complexity limits its application to large datasets. To address this computational bottleneck, we propose \\textit{FastKCI}, a scalable and parallelizable kernel-based conditional independence test that utilizes a mixture-of-experts approach inspired by embarrassingly parallel inference techniques for Gaussian processes. By partitioning the dataset based on a Gaussian mixture model over the conditioning variables, FastKCI conducts local KCI tests in parallel, aggregating the results using an importance-weighted sampling scheme. Experiments on synthetic datasets and benchmarks on real-world production data validate that FastKCI maintains the statistical power of the original KCI test while achieving substantial computational speedups. FastKCI thus represents a practical and efficient solution for conditional independence testing in causal inference on large-scale data.", "date": "2025-05-16", "categories": []}
{"id": "2509.21423", "title": "Near-Optimal Experiment Design in Linear non-Gaussian Cyclic Models", "abstract": "We study the problem of causal structure learning from a combination of observational and interventional data generated by a linear non-Gaussian structural equation model that might contain cycles. Recent results show that using mere observational data identifies the causal graph only up to a permutation-equivalence class. We obtain a combinatorial characterization of this class by showing that each graph in an equivalence class corresponds to a perfect matching in a bipartite graph. This bipartite representation allows us to analyze how interventions modify or constrain the matchings. Specifically, we show that each atomic intervention reveals one edge of the true matching and eliminates all incompatible causal graphs. Consequently, we formalize the optimal experiment design task as an adaptive stochastic optimization problem over the set of equivalence classes with a natural reward function that quantifies how many graphs are eliminated from the equivalence class by an intervention. We show that this reward function is adaptive submodular and provide a greedy policy with a provable near-optimal performance guarantee. A key technical challenge is to efficiently estimate the reward function without having to explicitly enumerate all the graphs in the equivalence class. We propose a sampling-based estimator using random matchings and analyze its bias and concentration behavior. Our simulation results show that performing a small number of interventions guided by our stochastic optimization framework recovers the true underlying causal structure.", "date": "2025-09-25", "categories": []}
{"id": "2512.03428", "title": "GaussDetect-LiNGAM:Causal Direction Identification without Gaussianity test", "abstract": "We propose GaussDetect-LiNGAM, a novel approach for bivariate causal discovery that eliminates the need for explicit Gaussianity tests by leveraging a fundamental equivalence between noise Gaussianity and residual independence in the reverse regression. Under the standard LiNGAM assumptions of linearity, acyclicity, and exogeneity, we prove that the Gaussianity of the forward-model noise is equivalent to the independence between the regressor and residual in the reverse model. This theoretical insight allows us to replace fragile and sample-sensitive Gaussianity tests with robust kernel-based independence tests. Experimental results validate the equivalence and demonstrate that GaussDetect-LiNGAM maintains high consistency across diverse noise types and sample sizes, while reducing the number of tests per decision (TPD). Our method enhances both the efficiency and practical applicability of causal inference, making LiNGAM more accessible and reliable in real-world scenarios.", "date": "2025-12-03", "categories": []}
{"id": "2512.00839", "title": "ARCADIA: Scalable Causal Discovery for Corporate Bankruptcy Analysis Using Agentic AI", "abstract": "This paper introduces ARCADIA, an agentic AI framework for causal discovery that integrates large-language-model reasoning with statistical diagnostics to construct valid, temporally coherent causal structures. Unlike traditional algorithms, ARCADIA iteratively refines candidate DAGs through constraint-guided prompting and causal-validity feedback, leading to stable and interpretable models for real-world high-stakes domains. Experiments on corporate bankruptcy data show that ARCADIA produces more reliable causal graphs than NOTEARS, GOLEM, and DirectLiNGAM while offering a fully explainable, intervention-ready pipeline. The framework advances AI by demonstrating how agentic LLMs can participate in autonomous scientific modeling and structured causal inference.", "date": "2025-11-30", "categories": []}
{"id": "2512.01827", "title": "CauSight: Learning to Supersense for Visual Causal Discovery", "abstract": "Causal thinking enables humans to understand not just what is seen, but why it happens. To replicate this capability in modern AI systems, we introduce the task of visual causal discovery. It requires models to infer cause-and-effect relations among visual entities across diverse scenarios instead of merely perceiving their presence. To this end, we first construct the Visual Causal Graph dataset (VCG-32K), a large-scale collection of over 32,000 images annotated with entity-level causal graphs, and further develop CauSight, a novel vision-language model to perform visual causal discovery through causally aware reasoning. Our training recipe integrates three components: (1) training data curation from VCG-32K, (2) Tree-of-Causal-Thought (ToCT) for synthesizing reasoning trajectories, and (3) reinforcement learning with a designed causal reward to refine the reasoning policy. Experiments show that CauSight outperforms GPT-4.1 on visual causal discovery, achieving over a threefold performance boost (21% absolute gain). Our code, model, and dataset are fully open-sourced at project page: https://github.com/OpenCausaLab/CauSight.", "date": "2025-12-01", "categories": []}
{"id": "2511.19273", "title": "Scalable Bayesian Network Structure Learning Using Tsetlin Machine to Constrain the Search Space", "abstract": "The PC algorithm is a widely used method in causal inference for learning the structure of Bayesian networks. Despite its popularity, the PC algorithm suffers from significant time complexity, particularly as the size of the dataset increases, which limits its applicability in large-scale real-world problems. In this study, we propose a novel approach that utilises the Tsetlin Machine (TM) to construct Bayesian structures more efficiently. Our method leverages the most significant literals extracted from the TM and performs conditional independence (CI) tests on these selected literals instead of the full set of variables, resulting in a considerable reduction in computational time. We implemented our approach and compared it with various state-of-the-art methods. Our evaluation includes categorical datasets from the bnlearn repository, such as Munin1, Hepar2. The findings indicate that the proposed TM-based method not only reduces computational complexity but also maintains competitive accuracy in causal discovery, making it a viable alternative to traditional PC algorithm implementations by offering improved efficiency without compromising performance.", "date": "2025-11-24", "categories": []}
{"id": "2511.16016", "title": "CARE: Turning LLMs Into Causal Reasoning Expert", "abstract": "Large language models (LLMs) have recently demonstrated impressive capabilities across a range of reasoning and generation tasks. However, research studies have shown that LLMs lack the ability to identify causal relationships, a fundamental cornerstone of human intelligence. We first conduct an exploratory investigation of LLMs' behavior when asked to perform a causal-discovery task and find that they mostly rely on the semantic meaning of variable names, ignoring the observation data. This is unsurprising, given that LLMs were never trained to process structural datasets. To first tackle this challenge, we prompt the LLMs with the outputs of established causal discovery algorithms designed for observational datasets. These algorithm outputs effectively serve as the sufficient statistics of the observation data. However, quite surprisingly, we find that prompting the LLMs with these sufficient statistics decreases the LLMs' performance in causal discovery. To address this current limitation, we propose CARE, a framework that enhances LLMs' causal-reasoning ability by teaching them to effectively utilize the outputs of established causal-discovery algorithms through supervised fine-tuning. Experimental results show that a finetuned Qwen2.5-1.5B model produced by CARE significantly outperforms both traditional causal-discovery algorithms and state-of-the-art LLMs with over a thousand times more parameters, demonstrating effective utilization of its own knowledge and the external algorithmic clues.", "date": "2025-11-20", "categories": []}
{"id": "2406.15229", "title": "ExDAG: an MIQP Algorithm for Learning DAGs", "abstract": "There has been a growing interest in causal learning in recent years. Commonly used representations of causal structures, including Bayesian networks and structural equation models (SEM), take the form of directed acyclic graphs (DAGs). We provide a novel mixed-integer quadratic programming formulation and an associated algorithm that identifies DAGs with a low structural Hamming distance between the identified DAG and the ground truth, under identifiability assumptions. The eventual exact learning is guaranteed by the global convergence of the branch-and-bound-and-cut algorithm, which is utilized. In addition to this, integer programming techniques give us access to the dual bound, which allows for a real time assessment of the quality of solution. Previously, integer programming techniques have been shown to lead to limited scaling in the case of DAG identification due to the super exponential number of constraints, which prevent the formation of cycles. The algorithm proposed circumvents this by selectively generating only the violated constraints using the so-called \"lazy\" constraints methodology. Our empirical results show that ExDAG outperforms state-of-the-art solvers in terms of structural Hamming distance and $F_1$ score when considering Gaussian noise on medium-sized graphs.", "date": "2024-06-21", "categories": []}
{"id": "2511.14001", "title": "How to Marginalize in Causal Structure Learning?", "abstract": "Bayesian networks (BNs) are a widely used class of probabilistic graphical models employed in numerous application domains. However, inferring the network's graphical structure from data remains challenging. Bayesian structure learners approach this problem by inferring a posterior distribution over the possible directed acyclic graphs underlying the BN. The inference process often requires marginalizing over probability distributions, which is typically done using dynamic programming methods that restrict the set of possible parents for each node. Instead, we present a novel method that utilizes tractable probabilistic circuits to circumvent this restriction. This method utilizes a new learning routine that trains these circuits on both the original distribution and marginal queries. The architecture of probabilistic circuits then inherently allows for fast and exact marginalization on the learned distribution. We then show empirically that utilizing our method to answer marginals allows Bayesian structure learners to improve their performance compared to current methods.", "date": "2025-11-18", "categories": []}
{"id": "2511.14206", "title": "Causal Discovery on Higher-Order Interactions", "abstract": "Causal discovery combines data with knowledge provided by experts to learn the DAG representing the causal relationships between a given set of variables. When data are scarce, bagging is used to measure our confidence in an average DAG obtained by aggregating bootstrapped DAGs. However, the aggregation step has received little attention from the specialized literature: the average DAG is constructed using only the confidence in the individual edges of the bootstrapped DAGs, thus disregarding complex higher-order edge structures. In this paper, we introduce a novel theoretical framework based on higher-order structures and describe a new DAG aggregation algorithm. We perform a simulation study, discussing the advantages and limitations of the proposed approach. Our proposal is both computationally efficient and effective, outperforming state-of-the-art solutions, especially in low sample size regimes and under high dimensionality settings.", "date": "2025-11-18", "categories": []}
{"id": "2511.14441", "title": "Skewness-Robust Causal Discovery in Location-Scale Noise Models", "abstract": "To distinguish Markov equivalent graphs in causal discovery, it is necessary to restrict the structural causal model. Crucially, we need to be able to distinguish cause $X$ from effect $Y$ in bivariate models, that is, distinguish the two graphs $X \\to Y$ and $Y \\to X$. Location-scale noise models (LSNMs), in which the effect $Y$ is modeled based on the cause $X$ as $Y = f(X) + g(X)N$, form a flexible class of models that is general and identifiable in most cases. Estimating these models for arbitrary noise terms $N$, however, is challenging. Therefore, practical estimators are typically restricted to symmetric distributions, such as the normal distribution. As we showcase in this paper, when $N$ is a skewed random variable, which is likely in real-world domains, the reliability of these approaches decreases. To approach this limitation, we propose SkewD, a likelihood-based algorithm for bivariate causal discovery under LSNMs with skewed noise distributions. SkewD extends the usual normal-distribution framework to the skew-normal setting, enabling reliable inference under symmetric and skewed noise. For parameter estimation, we employ a combination of a heuristic search and an expectation conditional maximization algorithm. We evaluate SkewD on novel synthetically generated datasets with skewed noise as well as established benchmark datasets. Throughout our experiments, SkewD exhibits a strong performance and, in comparison to prior work, remains robust under high skewness.", "date": "2025-11-18", "categories": []}
{"id": "2405.04715", "title": "Causality Pursuit from Heterogeneous Environments via Neural Adversarial Invariance Learning", "abstract": "Pursuing causality from data is a fundamental problem in scientific discovery, treatment intervention, and transfer learning. This paper introduces a novel algorithmic method for addressing nonparametric invariance and causality learning in regression models across multiple environments, where the joint distribution of response variables and covariates varies, but the conditional expectations of outcome given an unknown set of quasi-causal variables are invariant. The challenge of finding such an unknown set of quasi-causal or invariant variables is compounded by the presence of endogenous variables that have heterogeneous effects across different environments. The proposed Focused Adversarial Invariant Regularization (FAIR) framework utilizes an innovative minimax optimization approach that drives regression models toward prediction-invariant solutions through adversarial testing. Leveraging the representation power of neural networks, FAIR neural networks (FAIR-NN) are introduced for causality pursuit. It is shown that FAIR-NN can find the invariant variables and quasi-causal variables under a minimal identification condition and that the resulting procedure is adaptive to low-dimensional composition structures in a non-asymptotic analysis. Under a structural causal model, variables identified by FAIR-NN represent pragmatic causality and provably align with exact causal mechanisms under conditions of sufficient heterogeneity. Computationally, FAIR-NN employs a novel Gumbel approximation with decreased temperature and a stochastic gradient descent ascent algorithm. The procedures are demonstrated using simulated and real-data examples.", "date": "2024-05-07", "categories": []}
{"id": "2511.13295", "title": "Causal Inference, Biomarker Discovery, Graph Neural Network, Feature Selection", "abstract": "Biomarker discovery from high-throughput transcriptomic data is crucial for advancing precision medicine. However, existing methods often neglect gene-gene regulatory relationships and lack stability across datasets, leading to conflation of spurious correlations with genuine causal effects. To address these issues, we develop a causal graph neural network (Causal-GNN) method that integrates causal inference with multi-layer graph neural networks (GNNs). The key innovation is the incorporation of causal effect estimation for identifying stable biomarkers, coupled with a GNN-based propensity scoring mechanism that leverages cross-gene regulatory networks. Experimental results demonstrate that our method achieves consistently high predictive accuracy across four distinct datasets and four independent classifiers. Moreover, it enables the identification of more stable biomarkers compared to traditional methods. Our work provides a robust, efficient, and biologically interpretable tool for biomarker discovery, demonstrating strong potential for broad application across medical disciplines.", "date": "2025-11-17", "categories": []}
{"id": "2511.13389", "title": "Uncovering Causal Drivers of Energy Efficiency for Industrial Process in Foundry via Time-Series Causal Inference", "abstract": "Improving energy efficiency in industrial foundry processes is a critical challenge, as these operations are highly energy-intensive and marked by complex interdependencies among process variables. Correlation-based analyses often fail to distinguish true causal drivers from spurious associations, limiting their usefulness for decision-making. This paper applies a time-series causal inference framework to identify the operational factors that directly affect energy efficiency in induction furnace melting. Using production data from a Danish foundry, the study integrates time-series clustering to segment melting cycles into distinct operational modes with the PCMCI+ algorithm, a state-of-the-art causal discovery method, to uncover cause-effect relationships within each mode. Across clusters, robust causal relations among energy consumption, furnace temperature, and material weight define the core drivers of efficiency, while voltage consistently influences cooling water temperature with a delayed response. Cluster-specific differences further distinguish operational regimes: efficient clusters are characterized by stable causal structures, whereas inefficient ones exhibit reinforcing feedback loops and atypical dependencies. The contributions of this study are twofold. First, it introduces an integrated clustering-causal inference pipeline as a methodological innovation for analyzing energy-intensive processes. Second, it provides actionable insights that enable foundry operators to optimize performance, reduce energy consumption, and lower emissions.", "date": "2025-11-17", "categories": []}
{"id": "2509.23213", "title": "One-Shot Multi-Label Causal Discovery in High-Dimensional Event Sequences", "abstract": "Understanding causality in event sequences with thousands of sparse event types is critical in domains such as healthcare, cybersecurity, or vehicle diagnostics, yet current methods fail to scale. We present OSCAR, a one-shot causal autoregressive method that infers per-sequence Markov Boundaries using two pretrained Transformers as density estimators. This enables efficient, parallel causal discovery without costly global CI testing. On a real-world automotive dataset with 29,100 events and 474 labels, OSCAR recovers interpretable causal structures in minutes, while classical methods fail to scale, enabling practical scientific diagnostics at production scale.", "date": "2025-09-27", "categories": []}
{"id": "2511.10031", "title": "Temporal Latent Variable Structural Causal Model for Causal Discovery under External Interferences", "abstract": "Inferring causal relationships from observed data is an important task, yet it becomes challenging when the data is subject to various external interferences. Most of these interferences are the additional effects of external factors on observed variables. Since these external factors are often unknown, we introduce latent variables to represent these unobserved factors that affect the observed data. Specifically, to capture the causal strength and adjacency information, we propose a new temporal latent variable structural causal model, incorporating causal strength and adjacency coefficients that represent the causal relationships between variables. Considering that expert knowledge can provide information about unknown interferences in certain scenarios, we develop a method that facilitates the incorporation of prior knowledge into parameter learning based on Variational Inference, to guide the model estimation. Experimental results demonstrate the stability and accuracy of our proposed method.", "date": "2025-11-13", "categories": []}
{"id": "2506.03163", "title": "Causal Discovery in Dynamic Fading Wireless Networks", "abstract": "Dynamic causal discovery in wireless networks is essential due to evolving interference, fading, and mobility, which complicate traditional static causal models. This paper addresses causal inference challenges in dynamic fading wireless environments by proposing a sequential regression-based algorithm with a novel application of the NOTEARS acyclicity constraint, enabling efficient online updates. We derive theoretical lower and upper bounds on the detection delay required to identify structural changes, explicitly quantifying their dependence on network size, noise variance, and fading severity. Monte Carlo simulations validate these theoretical results, demonstrating linear increases in detection delay with network size, quadratic growth with noise variance, and inverse-square dependence on the magnitude of structural changes. Our findings provide rigorous theoretical insights and practical guidelines for designing robust online causal inference mechanisms to maintain network reliability under nonstationary wireless conditions.", "date": "2025-05-24", "categories": []}
{"id": "2511.06790", "title": "Robust Causal Discovery under Imperfect Structural Constraints", "abstract": "Robust causal discovery from observational data under imperfect prior knowledge remains a significant and largely unresolved challenge. Existing methods typically presuppose perfect priors or can only handle specific, pre-identified error types. And their performance degrades substantially when confronted with flawed constraints of unknown location and type. This decline arises because most of them rely on inflexible and biased thresholding strategies that may conflict with the data distribution. To overcome these limitations, we propose to harmonizes knowledge and data through prior alignment and conflict resolution. First, we assess the credibility of imperfect structural constraints through a surrogate model, which then guides a sparse penalization term measuring the loss between the learned and constrained adjacency matrices. We theoretically prove that, under ideal assumption, the knowledge-driven objective aligns with the data-driven objective. Furthermore, to resolve conflicts when this assumption is violated, we introduce a multi-task learning framework optimized via multi-gradient descent, jointly minimizing both objectives. Our proposed method is robust to both linear and nonlinear settings. Extensive experiments, conducted under diverse noise conditions and structural equation model types, demonstrate the effectiveness and efficiency of our method under imperfect structural constraints.", "date": "2025-11-10", "categories": []}
{"id": "2511.07236", "title": "Does TabPFN Understand Causal Structures?", "abstract": "Causal discovery is fundamental for multiple scientific domains, yet extracting causal information from real world data remains a significant challenge. Given the recent success on real data, we investigate whether TabPFN, a transformer-based tabular foundation model pre-trained on synthetic datasets generated from structural causal models, encodes causal information in its internal representations. We develop an adapter framework using a learnable decoder and causal tokens that extract causal signals from TabPFN's frozen embeddings and decode them into adjacency matrices for causal discovery. Our evaluations demonstrate that TabPFN's embeddings contain causal information, outperforming several traditional causal discovery algorithms, with such causal information being concentrated in mid-range layers. These findings establish a new direction for interpretable and adaptable foundation models and demonstrate the potential for leveraging pre-trained tabular models for causal discovery.", "date": "2025-11-10", "categories": []}
{"id": "2506.22331", "title": "Less Greedy Equivalence Search", "abstract": "Greedy Equivalence Search (GES) is a classic score-based algorithm for causal discovery from observational data. In the sample limit, it recovers the Markov equivalence class of graphs that describe the data. Still, it faces two challenges in practice: computational cost and finite-sample accuracy. In this paper, we develop Less Greedy Equivalence Search (LGES), a variant of GES that retains its theoretical guarantees while partially addressing these limitations. LGES modifies the greedy step; rather than always applying the highest-scoring insertion, it avoids edge insertions between variables for which the score implies some conditional independence. This more targeted search yields up to a \\(10\\)-fold speed-up and a substantial reduction in structural error relative to GES. Moreover, LGES can guide the search using prior knowledge, and can correct this knowledge when contradicted by data. Finally, LGES can use interventional data to refine the learned observational equivalence class. We prove that LGES recovers the true equivalence class in the sample limit, even with misspecified knowledge. Experiments demonstrate that LGES outperforms GES and other baselines in speed, accuracy, and robustness to misspecified knowledge. Our code is available at https://github.com/CausalAILab/lges.", "date": "2025-06-27", "categories": []}
{"id": "2511.04790", "title": "Causal Structure and Representation Learning with Biomedical Applications", "abstract": "Massive data collection holds the promise of a better understanding of complex phenomena and, ultimately, better decisions. Representation learning has become a key driver of deep learning applications, as it allows learning latent spaces that capture important properties of the data without requiring any supervised annotations. Although representation learning has been hugely successful in predictive tasks, it can fail miserably in causal tasks including predicting the effect of a perturbation/intervention. This calls for a marriage between representation learning and causal inference. An exciting opportunity in this regard stems from the growing availability of multi-modal data (observational and perturbational, imaging-based and sequencing-based, at the single-cell level, tissue-level, and organism-level). We outline a statistical and computational framework for causal structure and representation learning motivated by fundamental biomedical questions: how to effectively use observational and perturbational data to perform causal discovery on observed causal variables; how to use multi-modal views of the system to learn causal variables; and how to design optimal perturbations.", "date": "2025-11-06", "categories": []}
{"id": "2511.03831", "title": "Higher-Order Causal Structure Learning with Additive Models", "abstract": "Causal structure learning has long been the central task of inferring causal insights from data. Despite the abundance of real-world processes exhibiting higher-order mechanisms, however, an explicit treatment of interactions in causal discovery has received little attention. In this work, we focus on extending the causal additive model (CAM) to additive models with higher-order interactions. This second level of modularity we introduce to the structure learning problem is most easily represented by a directed acyclic hypergraph which extends the DAG. We introduce the necessary definitions and theoretical tools to handle the novel structure we introduce and then provide identifiability results for the hyper DAG, extending the typical Markov equivalence classes. We next provide insights into why learning the more complex hypergraph structure may actually lead to better empirical results. In particular, more restrictive assumptions like CAM correspond to easier-to-learn hyper DAGs and better finite sample complexity. We finally develop an extension of the greedy CAM algorithm which can handle the more complex hyper DAG search space and demonstrate its empirical usefulness in synthetic experiments.", "date": "2025-11-05", "categories": []}
{"id": "2511.04619", "title": "Dynamic causal discovery in Alzheimer's disease through latent pseudotime modelling", "abstract": "The application of causal discovery to diseases like Alzheimer's (AD) is limited by the static graph assumptions of most methods; such models cannot account for an evolving pathophysiology, modulated by a latent disease pseudotime. We propose to apply an existing latent variable model to real-world AD data, inferring a pseudotime that orders patients along a data-driven disease trajectory independent of chronological age, then learning how causal relationships evolve. Pseudotime outperformed age in predicting diagnosis (AUC 0.82 vs 0.59). Incorporating minimal, disease-agnostic background knowledge substantially improved graph accuracy and orientation. Our framework reveals dynamic interactions between novel (NfL, GFAP) and established AD markers, enabling practical causal discovery despite violated assumptions.", "date": "2025-11-06", "categories": []}
{"id": "2510.04263", "title": "Efficient Latent Variable Causal Discovery: Combining Score Search and Targeted Testing", "abstract": "Learning causal structure from observational data is especially challenging when latent variables or selection bias are present. The Fast Causal Inference (FCI) algorithm addresses this setting but performs exhaustive conditional independence tests across many subsets, often leading to spurious independences, missing or extra edges, and unreliable orientations. We present a family of score-guided mixed-strategy causal search algorithms that extend this framework. First, we introduce BOSS-FCI and GRaSP-FCI, variants of GFCI (Greedy Fast Causal Inference) that substitute BOSS (Best Order Score Search) or GRaSP (Greedy Relaxations of Sparsest Permutation) for FGES (Fast Greedy Equivalence Search), preserving correctness while trading off scalability and conservativeness. Second, we develop FCI Targeted-Testing (FCIT), a novel hybrid method that replaces exhaustive testing with targeted, score-informed tests guided by BOSS. FCIT guarantees well-formed PAGs and achieves higher precision and efficiency across sample sizes. Finally, we propose a lightweight heuristic, LV-Dumb (Latent Variable \"Dumb\"), which returns the PAG of the BOSS DAG (Directed Acyclic Graph). Though not strictly sound for latent confounding, LV-Dumb often matches FCIT's accuracy while running substantially faster. Simulations and real-data analyses show that BOSS-FCI and GRaSP-FCI provide robust baselines, FCIT yields the best balance of precision and reliability, and LV-Dumb offers a fast, near-equivalent alternative. Together, these methods demonstrate that targeted and score-guided strategies can dramatically improve the efficiency and correctness of latent-variable causal discovery.", "date": "2025-10-05", "categories": []}
{"id": "2511.03168", "title": "UnCLe: Towards Scalable Dynamic Causal Discovery in Non-linear Temporal Systems", "abstract": "Uncovering cause-effect relationships from observational time series is fundamental to understanding complex systems. While many methods infer static causal graphs, real-world systems often exhibit dynamic causality-where relationships evolve over time. Accurately capturing these temporal dynamics requires time-resolved causal graphs. We propose UnCLe, a novel deep learning method for scalable dynamic causal discovery. UnCLe employs a pair of Uncoupler and Recoupler networks to disentangle input time series into semantic representations and learns inter-variable dependencies via auto-regressive Dependency Matrices. It estimates dynamic causal influences by analyzing datapoint-wise prediction errors induced by temporal perturbations. Extensive experiments demonstrate that UnCLe not only outperforms state-of-the-art baselines on static causal discovery benchmarks but, more importantly, exhibits a unique capability to accurately capture and represent evolving temporal causality in both synthetic and real-world dynamic systems (e.g., human motion). UnCLe offers a promising approach for revealing the underlying, time-varying mechanisms of complex phenomena.", "date": "2025-11-05", "categories": []}
{"id": "2501.10124", "title": "Gene Regulatory Network Inference in the Presence of Selection Bias and Latent Confounders", "abstract": "Gene regulatory network inference (GRNI) aims to discover how genes causally regulate each other from gene expression data. It is well-known that statistical dependencies in observed data do not necessarily imply causation, as spurious dependencies may arise from latent confounders, such as non-coding RNAs. Numerous GRNI methods have thus been proposed to address this confounding issue. However, dependencies may also result from selection--only cells satisfying certain survival or inclusion criteria are observed--while these selection-induced spurious dependencies are frequently overlooked in gene expression data analyses. In this work, we show that such selection is ubiquitous and, when ignored or conflated with true regulations, can lead to flawed causal interpretation and misguided intervention recommendations. To address this challenge, a fundamental question arises: can we distinguish dependencies due to regulation, confounding, and crucially, selection? We show that gene perturbations offer a simple yet effective answer: selection-induced dependencies are symmetric under perturbation, while those from regulation or confounding are not. Building on this motivation, we propose GISL (Gene regulatory network Inference in the presence of Selection bias and Latent confounders), a principled algorithm that leverages perturbation data to uncover both true gene regulatory relations and non-regulatory mechanisms of selection and confounding up to the equivalence class. Experiments on synthetic and real-world gene expression data demonstrate the effectiveness of our method.", "date": "2025-01-17", "categories": []}
{"id": "2507.01700", "title": "Relational Causal Discovery with Latent Confounders", "abstract": "Estimating causal effects from real-world relational data can be challenging when the underlying causal model and potential confounders are unknown. While several causal discovery algorithms exist for learning causal models with latent confounders from data, they assume that the data is independent and identically distributed (i.i.d.) and are not well-suited for learning from relational data. Similarly, existing relational causal discovery algorithms assume causal sufficiency, which is unrealistic for many real-world datasets. To address this gap, we propose RelFCI, a sound and complete causal discovery algorithm for relational data with latent confounders. Our work builds upon the Fast Causal Inference (FCI) and Relational Causal Discovery (RCD) algorithms and it defines new graphical models, necessary to support causal discovery in relational domains. We also establish soundness and completeness guarantees for relational d-separation with latent confounders. We present experimental results demonstrating the effectiveness of RelFCI in identifying the correct causal structure in relational causal models with latent confounders.", "date": "2025-07-02", "categories": []}
{"id": "2510.04276", "title": "Scalable Causal Discovery from Recursive Nonlinear Data via Truncated Basis Function Scores and Tests", "abstract": "Learning graphical conditional independence structures from nonlinear, continuous or mixed data is a central challenge in machine learning and the sciences, and many existing methods struggle to scale to thousands of samples or hundreds of variables. We introduce two basis-expansion tools for scalable causal discovery. First, the Basis Function BIC (BF-BIC) score uses truncated additive expansions to approximate nonlinear dependencies. BF-BIC is theoretically consistent under additive models and extends to post-nonlinear (PNL) models via an invertible reparameterization. It remains robust under moderate interactions and supports mixed data through a degenerate-Gaussian embedding for discrete variables. In simulations with fully nonlinear neural causal models (NCMs), BF-BIC outperforms kernel- and constraint-based methods (e.g., KCI, RFCI) in both accuracy and runtime. Second, the Basis Function Likelihood Ratio Test (BF-LRT) provides an approximate conditional independence test that is substantially faster than kernel tests while retaining competitive accuracy. Extensive simulations and a real-data application to Canadian wildfire risk show that, when integrated into hybrid searches, BF-based methods enable interpretable and scalable causal discovery. Implementations are available in Python, R, and Java.", "date": "2025-10-05", "categories": []}
{"id": "2511.02536", "title": "Theoretical Guarantees for Causal Discovery on Large Random Graphs", "abstract": "We investigate theoretical guarantees for the false-negative rate (FNR) -- the fraction of true causal edges whose orientation is not recovered, under single-variable random interventions and an $\\epsilon$-interventional faithfulness assumption that accommodates latent confounding. For sparse Erd\\H{o}s--R\\'enyi directed acyclic graphs, where the edge probability scales as $p_e = \\Theta(1/d)$, we show that the FNR concentrates around its mean at rate $O(\\frac{\\log d}{\\sqrt d})$, implying that large deviations above the expected error become exponentially unlikely as dimensionality increases. This concentration ensures that derived upper bounds hold with high probability in large-scale settings. Extending the analysis to generalized Barab\\'asi--Albert graphs reveals an even stronger phenomenon: when the degree exponent satisfies $\\gamma > 3$, the deviation width scales as $O(d^{\\beta - \\frac{1}{2}})$ with $\\beta = 1/(\\gamma - 1) < \\frac{1}{2}$, and hence vanishes in the limit. This demonstrates that realistic scale-free topologies intrinsically regularize causal discovery, reducing variability in orientation error. These finite-dimension results provide the first dimension-adaptive, faithfulness-robust guarantees for causal structure recovery, and challenge the intuition that high dimensionality and network heterogeneity necessarily hinder accurate discovery. Our simulation results corroborate these theoretical predictions, showing that the FNR indeed concentrates and often vanishes in practice as dimensionality grows.", "date": "2025-11-04", "categories": []}
{"id": "2505.01037", "title": "Characterization and Learning of Causal Graphs from Hard Interventions", "abstract": "A fundamental challenge in the empirical sciences involves uncovering causal structure through observation and experimentation. Causal discovery entails linking the conditional independence (CI) invariances in observational data to their corresponding graphical constraints via d-separation. In this paper, we consider a general setting where we have access to data from multiple experimental distributions resulting from hard interventions, as well as potentially from an observational distribution. By comparing different interventional distributions, we propose a set of graphical constraints that are fundamentally linked to Pearl's do-calculus within the framework of hard interventions. These graphical constraints associate each graphical structure with a set of interventional distributions that are consistent with the rules of do-calculus. We characterize the interventional equivalence class of causal graphs with latent variables and introduce a graphical representation that can be used to determine whether two causal graphs are interventionally equivalent, i.e., whether they are associated with the same family of hard interventional distributions, where the elements of the family are indistinguishable using the invariances from do-calculus. We also propose a learning algorithm to integrate multiple datasets from hard interventions, introducing new orientation rules. The learning objective is a tuple of augmented graphs which entails a set of causal graphs. We also prove the soundness of the proposed algorithm.", "date": "2025-05-02", "categories": []}
{"id": "2510.16026", "title": "A tutorial on discovering and quantifying the effect of latent causal sources of multimodal EHR data", "abstract": "We provide an accessible description of a peer-reviewed generalizable causal machine learning pipeline to (i) discover latent causal sources of large-scale electronic health records observations, and (ii) quantify the source causal effects on clinical outcomes. We illustrate how imperfect multimodal clinical data can be processed, decomposed into probabilistic independent latent sources, and used to train taskspecific causal models from which individual causal effects can be estimated. We summarize the findings of the two real-world applications of the approach to date as a demonstration of its versatility and utility for medical discovery at scale.", "date": "2025-10-15", "categories": []}
{"id": "2509.17784", "title": "Revealing Multimodal Causality with Large Language Models", "abstract": "Uncovering cause-and-effect mechanisms from data is fundamental to scientific progress. While large language models (LLMs) show promise for enhancing causal discovery (CD) from unstructured data, their application to the increasingly prevalent multimodal setting remains a critical challenge. Even with the advent of multimodal LLMs (MLLMs), their efficacy in multimodal CD is hindered by two primary limitations: (1) difficulty in exploring intra- and inter-modal interactions for comprehensive causal variable identification; and (2) insufficiency to handle structural ambiguities with purely observational data. To address these challenges, we propose MLLM-CD, a novel framework for multimodal causal discovery from unstructured data. It consists of three key components: (1) a novel contrastive factor discovery module to identify genuine multimodal factors based on the interactions explored from contrastive sample pairs; (2) a statistical causal structure discovery module to infer causal relationships among discovered factors; and (3) an iterative multimodal counterfactual reasoning module to refine the discovery outcomes iteratively by incorporating the world knowledge and reasoning capabilities of MLLMs. Extensive experiments on both synthetic and real-world datasets demonstrate the effectiveness of the proposed MLLM-CD in revealing genuine factors and causal relationships among them from multimodal unstructured data.", "date": "2025-09-22", "categories": []}
{"id": "2510.26342", "title": "Linear Causal Discovery with Interventional Constraints", "abstract": "Incorporating causal knowledge and mechanisms is essential for refining causal models and improving downstream tasks such as designing new treatments. In this paper, we introduce a novel concept in causal discovery, termed interventional constraints, which differs fundamentally from interventional data. While interventional data require direct perturbations of variables, interventional constraints encode high-level causal knowledge in the form of inequality constraints on causal effects. For instance, in the Sachs dataset (Sachs et al.\\ 2005), Akt has been shown to be activated by PIP3, meaning PIP3 exerts a positive causal effect on Akt. Existing causal discovery methods allow enforcing structural constraints (for example, requiring a causal path from PIP3 to Akt), but they may still produce incorrect causal conclusions such as learning that \"PIP3 inhibits Akt\". Interventional constraints bridge this gap by explicitly constraining the total causal effect between variable pairs, ensuring learned models respect known causal influences. To formalize interventional constraints, we propose a metric to quantify total causal effects for linear causal models and formulate the problem as a constrained optimization task, solved using a two-stage constrained optimization method. We evaluate our approach on real-world datasets and demonstrate that integrating interventional constraints not only improves model accuracy and ensures consistency with established findings, making models more explainable, but also facilitates the discovery of new causal relationships that would otherwise be costly to identify.", "date": "2025-10-30", "categories": []}
{"id": "2510.23906", "title": "Group Interventions on Deep Networks for Causal Discovery in Subsystems", "abstract": "Causal discovery uncovers complex relationships between variables, enhancing predictions, decision-making, and insights into real-world systems, especially in nonlinear multivariate time series. However, most existing methods primarily focus on pairwise cause-effect relationships, overlooking interactions among groups of variables, i.e., subsystems and their collective causal influence. In this study, we introduce gCDMI, a novel multi-group causal discovery method that leverages group-level interventions on trained deep neural networks and employs model invariance testing to infer causal relationships. Our approach involves three key steps. First, we use deep learning to jointly model the structural relationships among groups of all time series. Second, we apply group-wise interventions to the trained model. Finally, we conduct model invariance testing to determine the presence of causal links among variable groups. We evaluate our method on simulated datasets, demonstrating its superior performance in identifying group-level causal relationships compared to existing methods. Additionally, we validate our approach on real-world datasets, including brain networks and climate ecosystems. Our results highlight that applying group-level interventions to deep learning models, combined with invariance testing, can effectively reveal complex causal structures, offering valuable insights for domains such as neuroscience and climate science.", "date": "2025-10-27", "categories": []}
{"id": "2510.25037", "title": "Graph Distance Based on Cause-Effect Estimands with Latents", "abstract": "Causal discovery aims to recover graphs that represent causal relations among given variables from observations, and new methods are constantly being proposed. Increasingly, the community raises questions about how much progress is made, because properly evaluating discovered graphs remains notoriously difficult, particularly under latent confounding. We propose a graph distance measure for acyclic directed mixed graphs (ADMGs) based on the downstream task of cause-effect estimation under unobserved confounding. Our approach uses identification via fixing and a symbolic verifier to quantify how graph differences distort cause-effect estimands for different treatment-outcome pairs. We analyze the behavior of the measure under different graph perturbations and compare it against existing distance metrics.", "date": "2025-10-28", "categories": []}
{"id": "2509.04415", "title": "Interpretable Clustering with Adaptive Heterogeneous Causal Structure Learning in Mixed Observational Data", "abstract": "Understanding causal heterogeneity is essential for scientific discovery in domains such as biology and medicine. However, existing methods lack causal awareness, with insufficient modeling of heterogeneity, confounding, and observational constraints, leading to poor interpretability and difficulty distinguishing true causal heterogeneity from spurious associations. We propose an unsupervised framework, HCL (Interpretable Causal Mechanism-Aware Clustering with Adaptive Heterogeneous Causal Structure Learning), that jointly infers latent clusters and their associated causal structures from mixed-type observational data without requiring temporal ordering, environment labels, interventions or other prior knowledge. HCL relaxes the homogeneity and sufficiency assumptions by introducing an equivalent representation that encodes both structural heterogeneity and confounding. It further develops a bi-directional iterative strategy to alternately refine causal clustering and structure learning, along with a self-supervised regularization that balance cross-cluster universality and specificity. Together, these components enable convergence toward interpretable, heterogeneous causal patterns. Theoretically, we show identifiability of heterogeneous causal structures under mild conditions. Empirically, HCL achieves superior performance in both clustering and structure learning tasks, and recovers biologically meaningful mechanisms in real-world single-cell perturbation data, demonstrating its utility for discovering interpretable, mechanism-level causal heterogeneity.", "date": "2025-09-04", "categories": []}
{"id": "2510.23942", "title": "Decentralized Causal Discovery using Judo Calculus", "abstract": "We describe a theory and implementation of an intuitionistic decentralized framework for causal discovery using judo calculus, which is formally defined as j-stable causal inference using j-do-calculus in a topos of sheaves. In real-world applications -- from biology to medicine and social science -- causal effects depend on regime (age, country, dose, genotype, or lab protocol). Our proposed judo calculus formalizes this context dependence formally as local truth: a causal claim is proven true on a cover of regimes, not everywhere at once. The Lawvere-Tierney modal operator j chooses which regimes are relevant; j-stability means the claim holds constructively and consistently across that family. We describe an algorithmic and implementation framework for judo calculus, combining it with standard score-based, constraint-based, and gradient-based causal discovery methods. We describe experimental results on a range of domains, from synthetic to real-world datasets from biology and economics. Our experimental results show the computational efficiency gained by the decentralized nature of sheaf-theoretic causal discovery, as well as improved performance over classical causal discovery methods.", "date": "2025-10-27", "categories": []}
{"id": "2411.16315", "title": "Local Learning for Covariate Selection in Nonparametric Causal Effect Estimation with Latent Variables", "abstract": "Estimating causal effects from nonexperimental data is a fundamental problem in many fields of science. A key component of this task is selecting an appropriate set of covariates for confounding adjustment to avoid bias. Most existing methods for covariate selection often assume the absence of latent variables and rely on learning the global network structure among variables. However, identifying the global structure can be unnecessary and inefficient, especially when our primary interest lies in estimating the effect of a treatment variable on an outcome variable. To address this limitation, we propose a novel local learning approach for covariate selection in nonparametric causal effect estimation, which accounts for the presence of latent variables. Our approach leverages testable independence and dependence relationships among observed variables to identify a valid adjustment set for a target causal relationship, ensuring both soundness and completeness under standard assumptions. We validate the effectiveness of our algorithm through extensive experiments on both synthetic and real-world data.", "date": "2024-11-25", "categories": []}
{"id": "2501.07227", "title": "MECD+: Unlocking Event-Level Causal Graph Discovery for Video Reasoning", "abstract": "Video causal reasoning aims to achieve a high-level understanding of videos from a causal perspective. However, it exhibits limitations in its scope, primarily executed in a question-answering paradigm and focusing on brief video segments containing isolated events and basic causal relations, lacking comprehensive and structured causality analysis for videos with multiple interconnected events. To fill this gap, we introduce a new task and dataset, Multi-Event Causal Discovery (MECD). It aims to uncover the causal relations between events distributed chronologically across long videos. Given visual segments and textual descriptions of events, MECD identifies the causal associations between these events to derive a comprehensive and structured event-level video causal graph explaining why and how the result event occurred. To address the challenges of MECD, we devise a novel framework inspired by the Granger Causality method, incorporating an efficient mask-based event prediction model to perform an Event Granger Test. It estimates causality by comparing the predicted result event when premise events are masked versus unmasked. Furthermore, we integrate causal inference techniques such as front-door adjustment and counterfactual inference to mitigate challenges in MECD like causality confounding and illusory causality. Additionally, context chain reasoning is introduced to conduct more robust and generalized reasoning. Experiments validate the effectiveness of our framework in reasoning complete causal relations, outperforming GPT-4o and VideoChat2 by 5.77% and 2.70%, respectively. Further experiments demonstrate that causal relation graphs can also contribute to downstream video understanding tasks such as video question answering and video event prediction.", "date": "2025-01-13", "categories": []}
{"id": "2506.23068", "title": "Curious Causality-Seeking Agents Learn Meta Causal World", "abstract": "When building a world model, a common assumption is that the environment has a single, unchanging underlying causal rule, like applying Newton's laws to every situation. In reality, what appears as a drifting causal mechanism is often the manifestation of a fixed underlying mechanism seen through a narrow observational window. This brings about a problem that, when building a world model, even subtle shifts in policy or environment states can alter the very observed causal mechanisms. In this work, we introduce the \\textbf{Meta-Causal Graph} as world models, a minimal unified representation that efficiently encodes the transformation rules governing how causal structures shift across different latent world states. A single Meta-Causal Graph is composed of multiple causal subgraphs, each triggered by meta state, which is in the latent state space. Building on this representation, we introduce a \\textbf{Causality-Seeking Agent} whose objectives are to (1) identify the meta states that trigger each subgraph, (2) discover the corresponding causal relationships by agent curiosity-driven intervention policy, and (3) iteratively refine the Meta-Causal Graph through ongoing curiosity-driven exploration and agent experiences. Experiments on both synthetic tasks and a challenging robot arm manipulation task demonstrate that our method robustly captures shifts in causal dynamics and generalizes effectively to previously unseen contexts.", "date": "2025-06-29", "categories": []}
{"id": "2508.12650", "title": "Score-informed Neural Operator for Enhancing Ordering-based Causal Discovery", "abstract": "Ordering-based approaches to causal discovery identify topological orders of causal graphs, providing scalable alternatives to combinatorial search methods. Under the Additive Noise Model (ANM) assumption, recent causal ordering methods based on score matching require an accurate estimation of the Hessian diagonal of the log-densities. In this paper, we aim to improve the approximation of the Hessian diagonal of the log-densities, thereby enhancing the performance of ordering-based causal discovery algorithms. Existing approaches that rely on Stein gradient estimators are computationally expensive and memory-intensive, while diffusion-model-based methods remain unstable due to the second-order derivatives of score models. To alleviate these problems, we propose Score-informed Neural Operator (SciNO), a probabilistic generative model in smooth function spaces designed to stably approximate the Hessian diagonal and to preserve structural information during the score modeling. Empirical results show that SciNO reduces order divergence by 42.7% on synthetic graphs and by 31.5% on real-world datasets on average compared to DiffAN, while maintaining memory efficiency and scalability. Furthermore, we propose a probabilistic control algorithm for causal reasoning with autoregressive models that integrates SciNO's probability estimates with autoregressive model priors, enabling reliable data-driven causal ordering informed by semantic information. Consequently, the proposed method enhances causal reasoning abilities of LLMs without additional fine-tuning or prompt engineering.", "date": "2025-08-18", "categories": []}
{"id": "2509.21658", "title": "Differentiable Structure Learning and Causal Discovery for General Binary Data", "abstract": "Existing methods for differentiable structure learning in discrete data typically assume that the data are generated from specific structural equation models. However, these assumptions may not align with the true data-generating process, which limits the general applicability of such methods. Furthermore, current approaches often ignore the complex dependence structure inherent in discrete data and consider only linear effects. We propose a differentiable structure learning framework that is capable of capturing arbitrary dependencies among discrete variables. We show that although general discrete models are unidentifiable from purely observational data, it is possible to characterize the complete set of compatible parameters and structures. Additionally, we establish identifiability up to Markov equivalence under mild assumptions. We formulate the learning problem as a single differentiable optimization task in the most general form, thereby avoiding the unrealistic simplifications adopted by previous methods. Empirical results demonstrate that our approach effectively captures complex relationships in discrete data.", "date": "2025-09-25", "categories": []}
{"id": "2510.21889", "title": "Bridging Prediction and Attribution: Identifying Forward and Backward Causal Influence Ranges Using Assimilative Causal Inference", "abstract": "Causal inference identifies cause-and-effect relationships between variables. While traditional approaches rely on data to reveal causal links, a recently developed method, assimilative causal inference (ACI), integrates observations with dynamical models. It utilizes Bayesian data assimilation to trace causes back from observed effects by quantifying the reduction in uncertainty. ACI advances the detection of instantaneous causal relationships and the intermittent reversal of causal roles over time. Beyond identifying causal connections, an equally important challenge is determining the associated causal influence range (CIR), indicating when causal influences emerged and for how long they persist. In this paper, ACI is employed to develop mathematically rigorous formulations of both forward and backward CIRs at each time. The forward CIR quantifies the temporal impact of a cause, while the backward CIR traces the onset of triggers for an observed effect, thus characterizing causal predictability and attribution of outcomes at each transient phase, respectively. Objective and robust metrics for both CIRs are introduced, eliminating the need for empirical thresholds. Computationally efficient approximation algorithms to compute CIRs are developed, which facilitate the use of closed-form expressions for a broad class of nonlinear dynamical systems. Numerical simulations demonstrate how this forward and backward CIR framework provides new possibilities for probing complex dynamical systems. It advances the study of bifurcation-driven and noise-induced tipping points in Earth systems, investigates the impact from resolving the interfering variables when determining the influence ranges, and elucidates atmospheric blocking mechanisms in the equatorial region. These results have direct implications for science, policy, and decision-making.", "date": "2025-10-24", "categories": []}
{"id": "2510.22298", "title": "MetaCaDI: A Meta-Learning Framework for Scalable Causal Discovery with Unknown Interventions", "abstract": "Uncovering the underlying causal mechanisms of complex real-world systems remains a significant challenge, as these systems often entail high data collection costs and involve unknown interventions. We introduce MetaCaDI, the first framework to cast the joint discovery of a causal graph and unknown interventions as a meta-learning problem. MetaCaDI is a Bayesian framework that learns a shared causal graph structure across multiple experiments and is optimized to rapidly adapt to new, few-shot intervention target prediction tasks. A key innovation is our model's analytical adaptation, which uses a closed-form solution to bypass expensive and potentially unstable gradient-based bilevel optimization. Extensive experiments on synthetic and complex gene expression data demonstrate that MetaCaDI significantly outperforms state-of-the-art methods. It excels at both causal graph recovery and identifying intervention targets from as few as 10 data instances, proving its robustness in data-scarce scenarios.", "date": "2025-10-25", "categories": []}
{"id": "2510.22711", "title": "Identification of Causal Direction under an Arbitrary Number of Latent Confounders", "abstract": "Recovering causal structure in the presence of latent variables is an important but challenging task. While many methods have been proposed to handle it, most of them require strict and/or untestable assumptions on the causal structure. In real-world scenarios, observed variables may be affected by multiple latent variables simultaneously, which, generally speaking, cannot be handled by these methods. In this paper, we consider the linear, non-Gaussian case, and make use of the joint higher-order cumulant matrix of the observed variables constructed in a specific way. We show that, surprisingly, causal asymmetry between two observed variables can be directly seen from the rank deficiency properties of such higher-order cumulant matrices, even in the presence of an arbitrary number of latent confounders. Identifiability results are established, and the corresponding identification methods do not even involve iterative procedures. Experimental results demonstrate the effectiveness and asymptotic correctness of our proposed method.", "date": "2025-10-26", "categories": []}
{"id": "2509.07036", "title": "Methodological Insights into Structural Causal Modelling and Uncertainty-Aware Forecasting for Economic Indicators", "abstract": "This paper presents a methodological approach to financial time series analysis by combining causal discovery and uncertainty-aware forecasting. As a case study, we focus on four key U.S. macroeconomic indicators -- GDP, economic growth, inflation, and unemployment -- and we apply the LPCMCI framework with Gaussian Process Distance Correlation (GPDC) to uncover dynamic causal relationships in quarterly data from 1970 to 2021. Our results reveal a robust unidirectional causal link from economic growth to GDP and highlight the limited connectivity of inflation, suggesting the influence of latent factors. Unemployment exhibits strong autoregressive dependence, motivating its use as a case study for probabilistic forecasting. Leveraging the Chronos framework, a large language model trained for time series, we perform zero-shot predictions on unemployment. This approach delivers accurate forecasts one and two quarters ahead, without requiring task-specific training. Crucially, the model's uncertainty-aware predictions yield 90\\% confidence intervals, enabling effective anomaly detection through statistically principled deviation analysis. This study demonstrates the value of combining causal structure learning with probabilistic language models to inform economic policy and enhance forecasting robustness.", "date": "2025-09-08", "categories": []}
{"id": "2510.21181", "title": "Shylock: Causal Discovery in Multivariate Time Series based on Hybrid Constraints", "abstract": "Causal relationship discovery has been drawing increasing attention due to its prevalent application. Existing methods rely on human experience, statistical methods, or graphical criteria methods which are error-prone, stuck at the idealized assumption, and rely on a huge amount of data. And there is also a serious data gap in accessing Multivariate time series(MTS) in many areas, adding difficulty in finding their causal relationship. Existing methods are easy to be over-fitting on them. To fill the gap we mentioned above, in this paper, we propose Shylock, a novel method that can work well in both few-shot and normal MTS to find the causal relationship. Shylock can reduce the number of parameters exponentially by using group dilated convolution and a sharing kernel, but still learn a better representation of variables with time delay. By combing the global constraint and the local constraint, Shylock achieves information sharing among networks to help improve the accuracy. To evaluate the performance of Shylock, we also design a data generation method to generate MTS with time delay. We evaluate it on commonly used benchmarks and generated datasets. Extensive experiments show that Shylock outperforms two existing state-of-art methods on both few-shot and normal MTS. We also developed Tcausal, a library for easy use and deployed it on the EarthDataMiner platform", "date": "2025-10-24", "categories": []}
{"id": "2506.17065", "title": "Flow based approach for Dynamic Temporal Causal models with non-Gaussian or Heteroscedastic Noises", "abstract": "Understanding causal relationships in multivariate time series is crucial in many scenarios, such as those dealing with financial or neurological data. Many such time series exhibit multiple regimes, i.e., consecutive temporal segments with a priori unknown boundaries, with each regime having its own causal structure. Inferring causal dependencies and regime shifts is critical for analyzing the underlying processes. However, causal structure learning in this setting is challenging due to (1) non-stationarity, i.e., each regime can have its own causal graph and mixing function, and (2) complex noise distributions, which may be nonGaussian or heteroscedastic. Existing causal discovery approaches cannot address these challenges, since generally assume stationarity or Gaussian noise with constant variance. Hence, we introduce FANTOM, a unified framework for causal discovery that handles non-stationary processes along with non-Gaussian and heteroscedastic noises. FANTOM simultaneously infers the number of regimes and their corresponding indices and learns each regime's Directed Acyclic Graph. It uses a Bayesian Expectation Maximization algorithm that maximizes the evidence lower bound of the data log-likelihood. On the theoretical side, we prove, under mild assumptions, that temporal heteroscedastic causal models, introduced in FANTOM's formulation, are identifiable in both stationary and non-stationary settings. In addition, extensive experiments on synthetic and real data show that FANTOM outperforms existing methods.", "date": "2025-06-20", "categories": []}
{"id": "2510.20106", "title": "Competition is the key: A Game Theoretic Causal Discovery Approach", "abstract": "Causal discovery remains a central challenge in machine learning, yet existing methods face a fundamental gap: algorithms like GES and GraN-DAG achieve strong empirical performance but lack finite-sample guarantees, while theoretically principled approaches fail to scale. We close this gap by introducing a game-theoretic reinforcement learning framework for causal discovery, where a DDQN agent directly competes against a strong baseline (GES or GraN-DAG), always warm-starting from the opponent's solution. This design yields three provable guarantees: the learned graph is never worse than the opponent, warm-starting strictly accelerates convergence, and most importantly, with high probability the algorithm selects the true best candidate graph. To the best of our knowledge, our result makes a first-of-its-kind progress in explaining such finite-sample guarantees in causal discovery: on synthetic SEMs (30 nodes), the observed error probability decays with n, tightly matching theory. On real-world benchmarks including Sachs, Asia, Alarm, Child, Hepar2, Dream, and Andes, our method consistently improves upon GES and GraN-DAG while remaining theoretically safe. Remarkably, it scales to large graphs such as Hepar2 (70 nodes), Dream (100 nodes), and Andes (220 nodes). Together, these results establish a new class of RL-based causal discovery algorithms that are simultaneously provably consistent, sample-efficient, and practically scalable, marking a decisive step toward unifying empirical performance with rigorous finite-sample theory.", "date": "2025-10-23", "categories": []}
{"id": "2510.20221", "title": "FinCARE: Financial Causal Analysis with Reasoning and Evidence", "abstract": "Portfolio managers rely on correlation-based analysis and heuristic methods that fail to capture true causal relationships driving performance. We present a hybrid framework that integrates statistical causal discovery algorithms with domain knowledge from two complementary sources: a financial knowledge graph extracted from SEC 10-K filings and large language model reasoning. Our approach systematically enhances three representative causal discovery paradigms, constraint-based (PC), score-based (GES), and continuous optimization (NOTEARS), by encoding knowledge graph constraints algorithmically and leveraging LLM conceptual reasoning for hypothesis generation. Evaluated on a synthetic financial dataset of 500 firms across 18 variables, our KG+LLM-enhanced methods demonstrate consistent improvements across all three algorithms: PC (F1: 0.622 vs. 0.459 baseline, +36%), GES (F1: 0.735 vs. 0.367, +100%), and NOTEARS (F1: 0.759 vs. 0.163, +366%). The framework enables reliable scenario analysis with mean absolute error of 0.003610 for counterfactual predictions and perfect directional accuracy for intervention effects. It also addresses critical limitations of existing methods by grounding statistical discoveries in financial domain expertise while maintaining empirical validation, providing portfolio managers with the causal foundation necessary for proactive risk management and strategic decision-making in dynamic market environments.", "date": "2025-10-23", "categories": []}
{"id": "2510.19138", "title": "InvarGC: Invariant Granger Causality for Heterogeneous Interventional Time Series under Latent Confounding", "abstract": "Granger causality is widely used for causal structure discovery in complex systems from multivariate time series data. Traditional Granger causality tests based on linear models often fail to detect even mild non-linear causal relationships. Therefore, numerous recent studies have investigated non-linear Granger causality methods, achieving improved performance. However, these methods often rely on two key assumptions: causal sufficiency and known interventional targets. Causal sufficiency assumes the absence of latent confounders, yet their presence can introduce spurious correlations. Moreover, real-world time series data usually come from heterogeneous environments, without prior knowledge of interventions. Therefore, in practice, it is difficult to distinguish intervened environments from non-intervened ones, and even harder to identify which variables or timesteps are affected. To address these challenges, we propose Invariant Granger Causality (InvarGC), which leverages cross-environment heterogeneity to mitigate the effects of latent confounding and to distinguish intervened from non-intervened environments with edge-level granularity, thereby recovering invariant causal relations. In addition, we establish the identifiability under these conditions. Extensive experiments on both synthetic and real-world datasets demonstrate the competitive performance of our approach compared to state-of-the-art methods.", "date": "2025-10-22", "categories": []}
{"id": "2306.07032", "title": "Mitigating Prior Errors in Causal Structure Learning: A Resilient Approach via Bayesian Networks", "abstract": "Causal structure learning (CSL), a prominent technique for encoding cause-and-effect relationships among variables, through Bayesian Networks (BNs). Although recovering causal structure solely from data is a challenge, the integration of prior knowledge, revealing partial structural truth, can markedly enhance learning quality. However, current methods based on prior knowledge exhibit limited resilience to errors in the prior, with hard constraint methods disregarding priors entirely, and soft constraints accepting priors based on a predetermined confidence level, which may require expert intervention. To address this issue, we propose a strategy resilient to edge-level prior errors for CSL, thereby minimizing human intervention. We classify prior errors into different types and provide their theoretical impact on the Structural Hamming Distance (SHD) under the presumption of sufficient data. Intriguingly, we discover and prove that the strong hazard of prior errors is associated with a unique acyclic closed structure, defined as ``quasi-circle''. Leveraging this insight, a post-hoc strategy is employed to identify the prior errors by its impact on the increment of ``quasi-circles''. Through empirical evaluation on both real and synthetic datasets, we demonstrate our strategy's robustness against prior errors. Specifically, we highlight its substantial ability to resist order-reversed errors while maintaining the majority of correct prior.", "date": "2023-06-12", "categories": []}
{"id": "2311.06928", "title": "Attention for Causal Relationship Discovery from Biological Neural Dynamics", "abstract": "This paper explores the potential of the transformer models for learning Granger causality in networks with complex nonlinear dynamics at every node, as in neurobiological and biophysical networks. Our study primarily focuses on a proof-of-concept investigation based on simulated neural dynamics, for which the ground-truth causality is known through the underlying connectivity matrix. For transformer models trained to forecast neuronal population dynamics, we show that the cross attention module effectively captures the causal relationship among neurons, with an accuracy equal or superior to that for the most popular Granger causality analysis method. While we acknowledge that real-world neurobiology data will bring further challenges, including dynamic connectivity and unobserved variability, this research offers an encouraging preliminary glimpse into the utility of the transformer model for causal representation learning in neuroscience.", "date": "2023-11-12", "categories": []}
{"id": "2510.16530", "title": "Realizing LLMs' Causal Potential Requires Science-Grounded, Novel Benchmarks", "abstract": "Recent claims of strong performance by Large Language Models (LLMs) on causal discovery are undermined by a key flaw: many evaluations rely on benchmarks likely included in pretraining corpora. Thus, apparent success suggests that LLM-only methods, which ignore observational data, outperform classical statistical approaches. We challenge this narrative by asking: Do LLMs truly reason about causal structure, and how can we measure it without memorization concerns? Can they be trusted for real-world scientific discovery? We argue that realizing LLMs' potential for causal analysis requires two shifts: (P.1) developing robust evaluation protocols based on recent scientific studies to guard against dataset leakage, and (P.2) designing hybrid methods that combine LLM-derived knowledge with data-driven statistics. To address P.1, we encourage evaluating discovery methods on novel, real-world scientific studies. We outline a practical recipe for extracting causal graphs from recent publications released after an LLM's training cutoff, ensuring relevance and preventing memorization while capturing both established and novel relations. Compared to benchmarks like BNLearn, where LLMs achieve near-perfect accuracy, they perform far worse on our curated graphs, underscoring the need for statistical grounding. Supporting P.2, we show that using LLM predictions as priors for the classical PC algorithm significantly improves accuracy over both LLM-only and purely statistical methods. We call on the community to adopt science-grounded, leakage-resistant benchmarks and invest in hybrid causal discovery methods suited to real-world inquiry.", "date": "2025-10-18", "categories": []}
{"id": "2510.16656", "title": "Simulation-free Structure Learning for Stochastic Dynamics", "abstract": "Modeling dynamical systems and unraveling their underlying causal relationships is central to many domains in the natural sciences. Various physical systems, such as those arising in cell biology, are inherently high-dimensional and stochastic in nature, and admit only partial, noisy state measurements. This poses a significant challenge for addressing the problems of modeling the underlying dynamics and inferring the network structure of these systems. Existing methods are typically tailored either for structure learning or modeling dynamics at the population level, but are limited in their ability to address both problems together. In this work, we address both problems simultaneously: we present StructureFlow, a novel and principled simulation-free approach for jointly learning the structure and stochastic population dynamics of physical systems. We showcase the utility of StructureFlow for the tasks of structure learning from interventions and dynamical (trajectory) inference of conditional population dynamics. We empirically evaluate our approach on high-dimensional synthetic systems, a set of biologically plausible simulated systems, and an experimental single-cell dataset. We show that StructureFlow can learn the structure of underlying systems while simultaneously modeling their conditional population dynamics -- a key step toward the mechanistic understanding of systems behavior.", "date": "2025-10-18", "categories": []}
{"id": "2501.12706", "title": "REX: Causal discovery based on machine learning and explainability techniques", "abstract": "Explainable Artificial Intelligence (XAI) techniques hold significant potential for enhancing the causal discovery process, which is crucial for understanding complex systems in areas like healthcare, economics, and artificial intelligence. However, no causal discovery methods currently incorporate explainability into their models to derive the causal graphs. Thus, in this paper we explore this innovative approach, as it offers substantial potential and represents a promising new direction worth investigating. Specifically, we introduce ReX, a causal discovery method that leverages machine learning (ML) models coupled with explainability techniques, specifically Shapley values, to identify and interpret significant causal relationships among variables. Comparative evaluations on synthetic datasets comprising continuous tabular data reveal that ReX outperforms state-of-the-art causal discovery methods across diverse data generation processes, including non-linear and additive noise models. Moreover, ReX was tested on the Sachs single-cell protein-signaling dataset, achieving a precision of 0.952 and recovering key causal relationships with no incorrect edges. Taking together, these results showcase ReX's effectiveness in accurately recovering true causal structures while minimizing false positive predictions, its robustness across diverse datasets, and its applicability to real-world problems. By combining ML and explainability techniques with causal discovery, ReX bridges the gap between predictive modeling and causal inference, offering an effective tool for understanding complex causal structures.", "date": "2025-01-22", "categories": []}
{"id": "2510.15265", "title": "Causal Time Series Modeling of Supraglacial Lake Evolution in Greenland under Distribution Shift", "abstract": "Causal modeling offers a principled foundation for uncovering stable, invariant relationships in time-series data, thereby improving robustness and generalization under distribution shifts. Yet its potential is underutilized in spatiotemporal Earth observation, where models often depend on purely correlational features that fail to transfer across heterogeneous domains. We propose RIC-TSC, a regionally-informed causal time-series classification framework that embeds lag-aware causal discovery directly into sequence modeling, enabling both predictive accuracy and scientific interpretability. Using multi-modal satellite and reanalysis data-including Sentinel-1 microwave backscatter, Sentinel-2 and Landsat-8 optical reflectance, and CARRA meteorological variables-we leverage Joint PCMCI+ (J-PCMCI+) to identify region-specific and invariant predictors of supraglacial lake evolution in Greenland. Causal graphs are estimated globally and per basin, with validated predictors and their time lags supplied to lightweight classifiers. On a balanced benchmark of 1000 manually labeled lakes from two contrasting melt seasons (2018-2019), causal models achieve up to 12.59% higher accuracy than correlation-based baselines under out-of-distribution evaluation. These results show that causal discovery is not only a means of feature selection but also a pathway to generalizable and mechanistically grounded models of dynamic Earth surface processes.", "date": "2025-10-17", "categories": []}
{"id": "2510.14488", "title": "From Guess2Graph: When and How Can Unreliable Experts Safely Boost Causal Discovery in Finite Samples?", "abstract": "Causal discovery algorithms often perform poorly with limited samples. While integrating expert knowledge (including from LLMs) as constraints promises to improve performance, guarantees for existing methods require perfect predictions or uncertainty estimates, making them unreliable for practical use. We propose the Guess2Graph (G2G) framework, which uses expert guesses to guide the sequence of statistical tests rather than replacing them. This maintains statistical consistency while enabling performance improvements. We develop two instantiations of G2G: PC-Guess, which augments the PC algorithm, and gPC-Guess, a learning-augmented variant designed to better leverage high-quality expert input. Theoretically, both preserve correctness regardless of expert error, with gPC-Guess provably outperforming its non-augmented counterpart in finite samples when experts are \"better than random.\" Empirically, both show monotonic improvement with expert accuracy, with gPC-Guess achieving significantly stronger gains.", "date": "2025-10-16", "categories": []}
{"id": "2510.14780", "title": "Causal Discovery for Linear DAGs with Dependent Latent Variables via Higher-order Cumulants", "abstract": "This paper addresses the problem of estimating causal directed acyclic graphs in linear non-Gaussian acyclic models with latent confounders (LvLiNGAM). Existing methods assume mutually independent latent confounders or cannot properly handle models with causal relationships among observed variables.\n  We propose a novel algorithm that identifies causal DAGs in LvLiNGAM, allowing causal structures among latent variables, among observed variables, and between the two. The proposed method leverages higher-order cumulants of observed data to identify the causal structure. Extensive simulations and experiments with real-world data demonstrate the validity and practical utility of the proposed algorithm.", "date": "2025-10-16", "categories": []}
{"id": "2510.12503", "title": "The Robustness of Differentiable Causal Discovery in Misspecified Scenarios", "abstract": "Causal discovery aims to learn causal relationships between variables from targeted data, making it a fundamental task in machine learning. However, causal discovery algorithms often rely on unverifiable causal assumptions, which are usually difficult to satisfy in real-world data, thereby limiting the broad application of causal discovery in practical scenarios. Inspired by these considerations, this work extensively benchmarks the empirical performance of various mainstream causal discovery algorithms, which assume i.i.d. data, under eight model assumption violations. Our experimental results show that differentiable causal discovery methods exhibit robustness under the metrics of Structural Hamming Distance and Structural Intervention Distance of the inferred graphs in commonly used challenging scenarios, except for scale variation. We also provide the theoretical explanations for the performance of differentiable causal discovery methods. Finally, our work aims to comprehensively benchmark the performance of recent differentiable causal discovery methods under model assumption violations, and provide the standard for reasonable evaluation of causal discovery, as well as to further promote its application in real-world scenarios.", "date": "2025-10-14", "categories": []}
{"id": "2402.03941", "title": "Discovering and Reasoning of Causality in the Hidden World with Large Language Models", "abstract": "Revealing hidden causal variables alongside the underlying causal mechanisms is essential to the development of science. Despite the progress in the past decades, existing practice in causal discovery (CD) heavily relies on high-quality measured variables, which are usually given by human experts. In fact, the lack of well-defined high-level variables behind unstructured data has been a longstanding roadblock to a broader real-world application of CD. This procedure can naturally benefit from an automated process that can suggest potential hidden variables in the system. Interestingly, Large language models (LLMs) are trained on massive observations of the world and have demonstrated great capability in processing unstructured data. To leverage the power of LLMs, we develop a new framework termed Causal representatiOn AssistanT (COAT) that incorporates the rich world knowledge of LLMs to propose useful measured variables for CD with respect to high-value target variables on their paired unstructured data. Instead of directly inferring causality with LLMs, COAT constructs feedback from intermediate CD results to LLMs to refine the proposed variables. Given the target variable and the paired unstructured data, we first develop COAT-MB that leverages the predictivity of the proposed variables to iteratively uncover the Markov Blanket of the target variable. Built upon COAT-MB, COAT-PAG further extends to uncover a more complete causal graph, i.e., Partial Ancestral Graph, by iterating over the target variables and actively seeking new high-level variables. Moreover, the reliable CD capabilities of COAT also extend the debiased causal inference to unstructured data by discovering an adjustment set. We establish theoretical guarantees for the CD results and verify their efficiency and reliability across realistic benchmarks and real-world case studies.", "date": "2024-02-06", "categories": []}
{"id": "2510.09846", "title": "CALM: A Causal Analysis Language Model for Tabular Data in Complex Systems with Local Scores, Conditional Independence Tests, and Relation Attributes", "abstract": "Causal discovery from observational data is fundamental to scientific fields like biology, where controlled experiments are often impractical. However, existing methods, including constraint-based (e.g., PC, causalMGM) and score-based approaches (e.g., NOTEARS), face significant limitations. These include an inability to resolve causal direction, restrictions to linear associations, sensitivity to violations of the faithfulness assumption, and inefficiency in searching vast hypothesis spaces. While large language models (LLMs) offer powerful reasoning capabilities, their application is hindered by a fundamental discrepancy: they are designed for text, while most causal data is tabular. To address these challenges, we introduce CALM, a novel causal analysis language model specifically designed for tabular data in complex systems. CALM leverages a Mamba-based architecture to classify causal patterns from pairwise variable relationships. It integrates a comprehensive suite of evidence, including local causal scores, conditional independence tests, and relational attributes, to capture a wide spectrum of linear, nonlinear, and conditional causal mechanisms. Trained on a diverse corpus of synthetic data (from linear, mixed, and nonlinear models) and 10 real-world biological datasets with rigorously validated causal relationships, our model ensures robustness and generalizability. Empirical evaluation demonstrates that CALM significantly outperforms existing methods in both simulation studies, achieving over 91% accuracy, and in a real-world application identifying causal factors in Hepatitis C virus progression. This work represents a significant step towards accurate and generalizable causal discovery by successfully adapting the pattern recognition capabilities of language models to the intricacies of tabular data.", "date": "2025-10-10", "categories": []}
{"id": "2407.19638", "title": "On the Reliability of Large Language Models for Causal Discovery", "abstract": "This study investigates the efficacy of Large Language Models (LLMs) in causal discovery. Using newly available open-source LLMs, OLMo and BLOOM, which provide access to their pre-training corpora, we investigate how LLMs address causal discovery through three research questions. We examine: (i) the impact of memorization for accurate causal relation prediction, (ii) the influence of incorrect causal relations in pre-training data, and (iii) the contextual nuances that influence LLMs' understanding of causal relations. Our findings indicate that while LLMs are effective in recognizing causal relations that occur frequently in pre-training data, their ability to generalize to new or rare causal relations is limited. Moreover, the presence of incorrect causal relations significantly undermines the confidence of LLMs in corresponding correct causal relations, and the contextual information critically affects the outcomes of LLMs to discern causal connections between random variables.", "date": "2024-07-29", "categories": []}
{"id": "2505.16620", "title": "CausalDynamics: A large-scale benchmark for structural discovery of dynamical causal models", "abstract": "Causal discovery for dynamical systems poses a major challenge in fields where active interventions are infeasible. Most methods used to investigate these systems and their associated benchmarks are tailored to deterministic, low-dimensional and weakly nonlinear time-series data. To address these limitations, we present CausalDynamics, a large-scale benchmark and extensible data generation framework to advance the structural discovery of dynamical causal models. Our benchmark consists of true causal graphs derived from thousands of both linearly and nonlinearly coupled ordinary and stochastic differential equations as well as two idealized climate models. We perform a comprehensive evaluation of state-of-the-art causal discovery algorithms for graph reconstruction on systems with noisy, confounded, and lagged dynamics. CausalDynamics consists of a plug-and-play, build-your-own coupling workflow that enables the construction of a hierarchy of physical systems. We anticipate that our framework will facilitate the development of robust causal discovery algorithms that are broadly applicable across domains while addressing their unique challenges. We provide a user-friendly implementation and documentation on https://kausable.github.io/CausalDynamics.", "date": "2025-05-22", "categories": []}
{"id": "2510.09217", "title": "IRIS: An Iterative and Integrated Framework for Verifiable Causal Discovery in the Absence of Tabular Data", "abstract": "Causal discovery is fundamental to scientific research, yet traditional statistical algorithms face significant challenges, including expensive data collection, redundant computation for known relations, and unrealistic assumptions. While recent LLM-based methods excel at identifying commonly known causal relations, they fail to uncover novel relations. We introduce IRIS (Iterative Retrieval and Integrated System for Real-Time Causal Discovery), a novel framework that addresses these limitations. Starting with a set of initial variables, IRIS automatically collects relevant documents, extracts variables, and uncovers causal relations. Our hybrid causal discovery method combines statistical algorithms and LLM-based methods to discover known and novel causal relations. In addition to causal discovery on initial variables, the missing variable proposal component of IRIS identifies and incorporates missing variables to expand the causal graphs. Our approach enables real-time causal discovery from only a set of initial variables without requiring pre-existing datasets.", "date": "2025-10-10", "categories": []}
{"id": "2510.08207", "title": "DODO: Causal Structure Learning with Budgeted Interventions", "abstract": "Artificial Intelligence has achieved remarkable advancements in recent years, yet much of its progress relies on identifying increasingly complex correlations. Enabling causality awareness in AI has the potential to enhance its performance by enabling a deeper understanding of the underlying mechanisms of the environment. In this paper, we introduce DODO, an algorithm defining how an Agent can autonomously learn the causal structure of its environment through repeated interventions. We assume a scenario where an Agent interacts with a world governed by a causal Directed Acyclic Graph (DAG), which dictates the system's dynamics but remains hidden from the Agent. The Agent's task is to accurately infer the causal DAG, even in the presence of noise. To achieve this, the Agent performs interventions, leveraging causal inference techniques to analyze the statistical significance of observed changes. Results show better performance for DODO, compared to observational approaches, in all but the most limited resource conditions. DODO is often able to reconstruct with as low as zero errors the structure of the causal graph. In the most challenging configuration, DODO outperforms the best baseline by +0.25 F1 points.", "date": "2025-10-09", "categories": []}
{"id": "2506.07844", "title": "Conditional Local Independence Testing for It\\^o processes with Applications to Dynamic Causal Discovery", "abstract": "Inferring causal relationships from dynamical systems is the central interest of many scientific inquiries. Conditional local independence, which describes whether the evolution of one process is influenced by another process given additional processes, is important for causal learning in such systems. In this paper, we propose a hypothesis test for conditional local independence in It\\^o processes. Our test is grounded in the semimartingale decomposition of the It\\^o process, with which we introduce a stochastic integral process that is a martingale under the null hypothesis. We then apply a test for the martingale property, quantifying potential deviation from local independence. The test statistics is estimated using the optimal filtering equation. We show the consistency of the estimation, thereby establishing the level and power of our test. Numerical verification and a real-world application to causal discovery in brain resting-state fMRIs are conducted.", "date": "2025-06-09", "categories": []}
{"id": "2401.16661", "title": "Generalization of LiNGAM that allows confounding", "abstract": "LiNGAM determines the variable order from cause to effect using additive noise models, but it faces challenges with confounding. Previous methods maintained LiNGAM's fundamental structure while trying to identify and address variables affected by confounding. As a result, these methods required significant computational resources regardless of the presence of confounding, and they did not ensure the detection of all confounding types. In contrast, this paper enhances LiNGAM by introducing LiNGAM-MMI, a method that quantifies the magnitude of confounding using KL divergence and arranges the variables to minimize its impact. This method efficiently achieves a globally optimal variable order through the shortest path problem formulation. LiNGAM-MMI processes data as efficiently as traditional LiNGAM in scenarios without confounding while effectively addressing confounding situations. Our experimental results suggest that LiNGAM-MMI more accurately determines the correct variable order, both in the presence and absence of confounding. The code is in the supplementary file in this link: https://github.com/SkyJoyTianle/ISIT2024.", "date": "2024-01-30", "categories": []}
{"id": "2403.14125", "title": "Learning causal graphs using variable grouping according to ancestral relationship", "abstract": "Several causal discovery algorithms have been proposed. However, when the sample size is small relative to the number of variables, the accuracy of estimating causal graphs using existing methods decreases. And some methods are not feasible when the sample size is smaller than the number of variables. To circumvent these problems, some researchers proposed causal structure learning algorithms using divide-and-conquer approaches. For learning the entire causal graph, the approaches first split variables into several subsets according to the conditional independence relationships among the variables, then apply a conventional causal discovery algorithm to each subset and merge the estimated results. Since the divide-and-conquer approach reduces the number of variables to which a causal structure learning algorithm is applied, it is expected to improve the estimation accuracy of causal graphs, especially when the sample size is small relative to the number of variables and the model is sparse. However, existing methods are either computationally expensive or do not provide sufficient accuracy when the sample size is small. This paper proposes a new algorithm for grouping variables based the ancestral relationships among the variables, under the LiNGAM assumption, where the causal relationships are linear, and the mutually independent noise are distributed as continuous non-Gaussian distributions. We call the proposed algorithm CAG. The time complexity of the ancestor finding in CAG is shown to be cubic to the number of variables. Extensive computer experiments confirm that the proposed method outperforms the original DirectLiNGAM without grouping variables and other divide-and-conquer approaches not only in estimation accuracy but also in computation time when the sample size is small relative to the number of variables and the model is sparse.", "date": "2024-03-21", "categories": []}
{"id": "2510.01562", "title": "Large-Scale Bayesian Causal Discovery with Interventional Data", "abstract": "Inferring the causal relationships among a set of variables in the form of a directed acyclic graph (DAG) is an important but notoriously challenging problem. Recently, advancements in high-throughput genomic perturbation screens have inspired development of methods that leverage interventional data to improve model identification. However, existing methods still suffer poor performance on large-scale tasks and fail to quantify uncertainty. Here, we propose Interventional Bayesian Causal Discovery (IBCD), an empirical Bayesian framework for causal discovery with interventional data. Our approach models the likelihood of the matrix of total causal effects, which can be approximated by a matrix normal distribution, rather than the full data matrix. We place a spike-and-slab horseshoe prior on the edges and separately learn data-driven weights for scale-free and Erd\\H{o}s-R\\'enyi structures from observational data, treating each edge as a latent variable to enable uncertainty-aware inference. Through extensive simulation, we show that IBCD achieves superior structure recovery compared to existing baselines. We apply IBCD to CRISPR perturbation (Perturb-seq) data on 521 genes, demonstrating that edge posterior inclusion probabilities enable identification of robust graph structures.", "date": "2025-10-02", "categories": []}
{"id": "2510.02117", "title": "DAG DECORation: Continuous Optimization for Structure Learning under Hidden Confounding", "abstract": "We study structure learning for linear Gaussian SEMs in the presence of latent confounding. Existing continuous methods excel when errors are independent, while deconfounding-first pipelines rely on pervasive factor structure or nonlinearity. We propose \\textsc{DECOR}, a single likelihood-based and fully differentiable estimator that jointly learns a DAG and a correlated noise model. Our theory gives simple sufficient conditions for global parameter identifiability: if the mixed graph is bow free and the noise covariance has a uniform eigenvalue margin, then the map from $(\\B,\\OmegaMat)$ to the observational covariance is injective, so both the directed structure and the noise are uniquely determined. The estimator alternates a smooth-acyclic graph update with a convex noise update and can include a light bow complementarity penalty or a post hoc reconciliation step. On synthetic benchmarks that vary confounding density, graph density, latent rank, and dimension with $n<p$, \\textsc{DECOR} matches or outperforms strong baselines and is especially robust when confounding is non-pervasive, while remaining competitive under pervasiveness.", "date": "2025-10-02", "categories": []}
{"id": "2408.16218", "title": "Large-Scale Targeted Cause Discovery via Learning from Simulated Data", "abstract": "We propose a novel machine learning approach for inferring causal variables of a target variable from observations. Our focus is on directly inferring a set of causal factors without requiring full causal graph reconstruction, which is computationally challenging in large-scale systems. The identified causal set consists of all potential regulators of the target variable under experimental settings, enabling efficient regulation through intervention. To achieve this, we train a neural network using supervised learning on simulated data to infer causality. By employing a subsampled-ensemble inference strategy, our approach scales with linear complexity in the number of variables, efficiently scaling up to thousands of variables. Empirical results demonstrate superior performance in identifying causal relationships within large-scale gene regulatory networks, outperforming existing methods that emphasize full-graph discovery. We validate our model's generalization capability across out-of-distribution graph structures and generating mechanisms, including gene regulatory networks of E. coli and the human K562 cell line. Implementation codes are available at https://github.com/snu-mllab/Targeted-Cause-Discovery.", "date": "2024-08-29", "categories": []}
{"id": "2311.06012", "title": "Double Machine Learning Based Structure Identification from Temporal Data", "abstract": "Learning the causes of time-series data is a fundamental task in many applications, spanning from finance to earth sciences or bio-medical applications. Common approaches for this task are based on vector auto-regression, and they do not take into account unknown confounding between potential causes. However, in settings with many potential causes and noisy data, these approaches may be substantially biased. Furthermore, potential causes may be correlated in practical applications or even contain cycles. To address these challenges, we propose a new double machine learning based method for structure identification from temporal data (DR-SIT). We provide theoretical guarantees, showing that our method asymptotically recovers the true underlying causal structure. Our analysis extends to cases where the potential causes have cycles, and they may even be confounded. We further perform extensive experiments to showcase the superior performance of our method. Code: https://github.com/sdi1100041/TMLR_submission_DR_SIT", "date": "2023-11-10", "categories": []}
{"id": "2505.16288", "title": "No Black Boxes: Interpretable and Interactable Predictive Healthcare with Knowledge-Enhanced Agentic Causal Discovery", "abstract": "Deep learning models trained on extensive Electronic Health Records (EHR) data have achieved high accuracy in diagnosis prediction, offering the potential to assist clinicians in decision-making and treatment planning. However, these models lack two crucial features that clinicians highly value: interpretability and interactivity. The ``black-box'' nature of these models makes it difficult for clinicians to understand the reasoning behind predictions, limiting their ability to make informed decisions. Additionally, the absence of interactive mechanisms prevents clinicians from incorporating their own knowledge and experience into the decision-making process. To address these limitations, we propose II-KEA, a knowledge-enhanced agent-driven causal discovery framework that integrates personalized knowledge databases and agentic LLMs. II-KEA enhances interpretability through explicit reasoning and causal analysis, while also improving interactivity by allowing clinicians to inject their knowledge and experience through customized knowledge bases and prompts. II-KEA is evaluated on both MIMIC-III and MIMIC-IV, demonstrating superior performance along with enhanced interpretability and interactivity, as evidenced by its strong results from extensive case studies.", "date": "2025-05-22", "categories": []}
{"id": "2509.23570", "title": "Improving constraint-based discovery with robust propagation and reliable LLM priors", "abstract": "Learning causal structure from observational data is central to scientific modeling and decision-making. Constraint-based methods aim to recover conditional independence (CI) relations in a causal directed acyclic graph (DAG). Classical approaches such as PC and subsequent methods orient v-structures first and then propagate edge directions from these seeds, assuming perfect CI tests and exhaustive search of separating subsets -- assumptions often violated in practice, leading to cascading errors in the final graph. Recent work has explored using large language models (LLMs) as experts, prompting sets of nodes for edge directions, and could augment edge orientation when assumptions are not met. However, such methods implicitly assume perfect experts, which is unrealistic for hallucination-prone LLMs. We propose MosaCD, a causal discovery method that propagates edges from a high-confidence set of seeds derived from both CI tests and LLM annotations. To filter hallucinations, we introduce shuffled queries that exploit LLMs' positional bias, retaining only high-confidence seeds. We then apply a novel confidence-down propagation strategy that orients the most reliable edges first, and can be integrated with any skeleton-based discovery method. Across multiple real-world graphs, MosaCD achieves higher accuracy in final graph construction than existing constraint-based methods, largely due to the improved reliability of initial seeds and robust propagation strategies.", "date": "2025-09-28", "categories": []}
{"id": "2509.23992", "title": "Guide: Generalized-Prior and Data Encoders for DAG Estimation", "abstract": "Modern causal discovery methods face critical limitations in scalability, computational efficiency, and adaptability to mixed data types, as evidenced by benchmarks on node scalability (30, $\\le 50$, $\\ge 70$ nodes), computational energy demands, and continuous/non-continuous data handling. While traditional algorithms like PC, GES, and ICA-LiNGAM struggle with these challenges, exhibiting prohibitive energy costs for higher-order nodes and poor scalability beyond 70 nodes, we propose \\textbf{GUIDE}, a framework that integrates Large Language Model (LLM)-generated adjacency matrices with observational data through a dual-encoder architecture. GUIDE uniquely optimizes computational efficiency, reducing runtime on average by $\\approx 42%$ compared to RL-BIC and KCRL methods, while achieving an average $\\approx 117%$ improvement in accuracy over both NOTEARS and GraN-DAG individually. During training, GUIDE's reinforcement learning agent dynamically balances reward maximization (accuracy) and penalty avoidance (DAG constraints), enabling robust performance across mixed data types and scalability to $\\ge 70$ nodes -- a setting where baseline methods fail.", "date": "2025-09-28", "categories": []}
{"id": "2502.20115", "title": "Multi-View Causal Discovery without Non-Gaussianity: Identifiability and Algorithms", "abstract": "Causal discovery is a difficult problem that typically relies on strong assumptions on the data-generating model, such as non-Gaussianity. In practice, many modern applications provide multiple related views of the same system, which has rarely been considered for causal discovery. Here, we leverage this multi-view structure to achieve causal discovery with weak assumptions. We propose a multi-view linear Structural Equation Model (SEM) that extends the well-known framework of non-Gaussian disturbances by alternatively leveraging correlation over views. We prove the identifiability of the model for acyclic SEMs. Subsequently, we propose several multi-view causal discovery algorithms, inspired by single-view algorithms (DirectLiNGAM, PairwiseLiNGAM, and ICA-LiNGAM). The new methods are validated through simulations and applications on neuroimaging data, where they enable the estimation of causal graphs between brain regions.", "date": "2025-02-27", "categories": []}
{"id": "2407.07338", "title": "Towards Complete Causal Explanation with Expert Knowledge", "abstract": "We study the problem of restricting a Markov equivalence class of maximal ancestral graphs (MAGs) to only those MAGs that contain certain edge marks, which we refer to as expert or orientation knowledge. Such a restriction of the Markov equivalence class can be uniquely represented by a restricted essential ancestral graph. Our contributions are several-fold. First, we prove certain properties for the entire Markov equivalence class including a conjecture from Ali et al. (2009). Second, we present several new sound graphical orientation rules for adding orientation knowledge to an essential ancestral graph. We also show that some orientation rules of Zhang (2008b) are not needed for restricting the Markov equivalence class with orientation knowledge. Third, we provide an algorithm for including this orientation knowledge and show that in certain settings the output of our algorithm is a restricted essential ancestral graph. Finally, outside of the specified settings, we provide an algorithm for checking whether a graph is a restricted essential graph and discuss its runtime. This work can be seen as a generalization of Meek (1995) to settings which allow for latent confounding.", "date": "2024-07-10", "categories": []}
{"id": "2409.02604", "title": "Context-Aware Reasoning On Parametric Knowledge for Inferring Causal Variables", "abstract": "Scientific discovery catalyzes human intellectual advances, driven by the cycle of hypothesis generation, experimental design, evaluation, and assumption refinement. Central to this process is causal inference, uncovering the mechanisms behind observed phenomena. While randomized experiments provide strong inferences, they are often infeasible due to ethical or practical constraints. However, observational studies are prone to confounding or mediating biases. While crucial, identifying such backdoor paths is expensive and heavily depends on scientists' domain knowledge to generate hypotheses. We introduce a novel benchmark where the objective is to complete a partial causal graph. We design a benchmark with varying difficulty levels with over 4000 queries. We show the strong ability of LLMs to hypothesize the backdoor variables between a cause and its effect. Unlike simple knowledge memorization of fixed associations, our task requires the LLM to reason according to the context of the entire graph.", "date": "2024-09-04", "categories": []}
{"id": "2507.00093", "title": "$\\sigma$-Maximal Ancestral Graphs", "abstract": "Maximal Ancestral Graphs (MAGs) provide an abstract representation of Directed Acyclic Graphs (DAGs) with latent (selection) variables. These graphical objects encode information about ancestral relations and d-separations of the DAGs they represent. This abstract representation has been used amongst others to prove the soundness and completeness of the FCI algorithm for causal discovery, and to derive a do-calculus for its output. One significant inherent limitation of MAGs is that they rule out the possibility of cyclic causal relationships. In this work, we address that limitation. We introduce and study a class of graphical objects that we coin ''$\\sigma$-Maximal Ancestral Graphs'' (''$\\sigma$-MAGs''). We show how these graphs provide an abstract representation of (possibly cyclic) Directed Graphs (DGs) with latent (selection) variables, analogously to how MAGs represent DAGs. We study the properties of these objects and provide a characterization of their Markov equivalence classes.", "date": "2025-06-30", "categories": []}
{"id": "2509.16397", "title": "GRID: Graph-based Reasoning for Intervention and Discovery in Built Environments", "abstract": "Manual HVAC fault diagnosis in commercial buildings takes 8-12 hours per incident and achieves only 60 percent diagnostic accuracy, reflecting analytics that stop at correlation instead of causation. To close this gap, we present GRID (Graph-based Reasoning for Intervention and Discovery), a three-stage causal discovery pipeline that combines constraint-based search, neural structural equation modeling, and language model priors to recover directed acyclic graphs from building sensor data. Across six benchmarks: synthetic rooms, EnergyPlus simulation, the ASHRAE Great Energy Predictor III dataset, and a live office testbed, GRID achieves F1 scores ranging from 0.65 to 1.00, with exact recovery (F1 = 1.00) in three controlled environments (Base, Hidden, Physical) and strong performance on real-world data (F1 = 0.89 on ASHRAE, 0.86 in noisy conditions). The method outperforms ten baseline approaches across all evaluation scenarios. Intervention scheduling achieves low operational impact in most scenarios (cost <= 0.026) while reducing risk metrics compared to baseline approaches. The framework integrates constraint-based methods, neural architectures, and domain-specific language model prompts to address the observational-causal gap in building analytics.", "date": "2025-09-19", "categories": []}
{"id": "2509.16463", "title": "Entropic Causal Inference: Graph Identifiability", "abstract": "Entropic causal inference is a recent framework for learning the causal graph between two variables from observational data by finding the information-theoretically simplest structural explanation of the data, i.e., the model with smallest entropy. In our work, we first extend the causal graph identifiability result in the two-variable setting under relaxed assumptions. We then show the first identifiability result using the entropic approach for learning causal graphs with more than two nodes. Our approach utilizes the property that ancestrality between a source node and its descendants can be determined using the bivariate entropic tests. We provide a sound sequential peeling algorithm for general graphs that relies on this property. We also propose a heuristic algorithm for small graphs that shows strong empirical performance. We rigorously evaluate the performance of our algorithms on synthetic data generated from a variety of models, observing improvement over prior work. Finally we test our algorithms on real-world datasets.", "date": "2025-09-19", "categories": []}
{"id": "2509.12497", "title": "Prediction and Causality of functional MRI and synthetic signal using a Zero-Shot Time-Series Foundation Model", "abstract": "Time-series forecasting and causal discovery are central in neuroscience, as predicting brain activity and identifying causal relationships between neural populations and circuits can shed light on the mechanisms underlying cognition and disease. With the rise of foundation models, an open question is how they compare to traditional methods for brain signal forecasting and causality analysis, and whether they can be applied in a zero-shot setting. In this work, we evaluate a foundation model against classical methods for inferring directional interactions from spontaneous brain activity measured with functional magnetic resonance imaging (fMRI) in humans. Traditional approaches often rely on Wiener-Granger causality. We tested the forecasting ability of the foundation model in both zero-shot and fine-tuned settings, and assessed causality by comparing Granger-like estimates from the model with standard Granger causality. We validated the approach using synthetic time series generated from ground-truth causal models, including logistic map coupling and Ornstein-Uhlenbeck processes. The foundation model achieved competitive zero-shot forecasting fMRI time series (mean absolute percentage error of 0.55 in controls and 0.27 in patients). Although standard Granger causality did not show clear quantitative differences between models, the foundation model provided a more precise detection of causal interactions.\n  Overall, these findings suggest that foundation models offer versatility, strong zero-shot performance, and potential utility for forecasting and causal discovery in time-series data.", "date": "2025-09-15", "categories": []}
{"id": "2509.12387", "title": "Causal-Symbolic Meta-Learning (CSML): Inducing Causal World Models for Few-Shot Generalization", "abstract": "Modern deep learning models excel at pattern recognition but remain fundamentally limited by their reliance on spurious correlations, leading to poor generalization and a demand for massive datasets. We argue that a key ingredient for human-like intelligence-robust, sample-efficient learning-stems from an understanding of causal mechanisms. In this work, we introduce Causal-Symbolic Meta-Learning (CSML), a novel framework that learns to infer the latent causal structure of a task distribution. CSML comprises three key modules: a perception module that maps raw inputs to disentangled symbolic representations; a differentiable causal induction module that discovers the underlying causal graph governing these symbols and a graph-based reasoning module that leverages this graph to make predictions. By meta-learning a shared causal world model across a distribution of tasks, CSML can rapidly adapt to novel tasks, including those requiring reasoning about interventions and counterfactuals, from only a handful of examples. We introduce CausalWorld, a new physics-based benchmark designed to test these capabilities. Our experiments show that CSML dramatically outperforms state-of-the-art meta-learning and neuro-symbolic baselines, particularly on tasks demanding true causal inference.", "date": "2025-09-15", "categories": []}
{"id": "2509.07701", "title": "Building causation links in stochastic nonlinear systems from data", "abstract": "Causal relationships play a fundamental role in understanding the world around us. The ability to identify and understand cause-effect relationships is critical to making informed decisions, predicting outcomes, and developing effective strategies. However, deciphering causal relationships from observational data is a difficult task, as correlations alone may not provide definitive evidence of causality. In recent years, the field of machine learning (ML) has emerged as a powerful tool, offering new opportunities for uncovering hidden causal mechanisms and better understanding complex systems. In this work, we address the issue of detecting the intrinsic causal links of a large class of complex systems in the framework of the response theory in physics. We develop some theoretical ideas put forward by [1], and technically we use state-of-the-art ML techniques to build up models from data. We consider both linear stochastic and non-linear systems. Finally, we compute the asymptotic efficiency of the linear response based causal predictor in a case of large scale Markov process network of linear interactions.", "date": "2025-09-09", "categories": []}
{"id": "2509.02130", "title": "Online Identification of IT Systems through Active Causal Learning", "abstract": "Identifying a causal model of an IT system is fundamental to many branches of systems engineering and operation. Such a model can be used to predict the effects of control actions, optimize operations, diagnose failures, detect intrusions, etc., which is central to achieving the longstanding goal of automating network and system management tasks. Traditionally, causal models have been designed and maintained by domain experts. This, however, proves increasingly challenging with the growing complexity and dynamism of modern IT systems. In this paper, we present the first principled method for online, data-driven identification of an IT system in the form of a causal model. The method, which we call active causal learning, estimates causal functions that capture the dependencies among system variables in an iterative fashion using Gaussian process regression based on system measurements, which are collected through a rollout-based intervention policy. We prove that this method is optimal in the Bayesian sense and that it produces effective interventions. Experimental validation on a testbed shows that our method enables accurate identification of a causal system model while inducing low interference with system operations.", "date": "2025-09-02", "categories": []}
{"id": "2509.00538", "title": "Identifying Causal Direction via Dense Functional Classes", "abstract": "We address the problem of determining the causal direction between two univariate, continuous-valued variables, X and Y, under the assumption of no hidden confounders. In general, it is not possible to make definitive statements about causality without some assumptions on the underlying model. To distinguish between cause and effect, we propose a bivariate causal score based on the Minimum Description Length (MDL) principle, using functions that possess the density property on a compact real interval. We prove the identifiability of these causal scores under specific conditions. These conditions can be easily tested. Gaussianity of the noise in the causal model equations is not assumed, only that the noise is low. The well-studied class of cubic splines possesses the density property on a compact real interval. We propose LCUBE as an instantiation of the MDL-based causal score utilizing cubic regression splines. LCUBE is an identifiable method that is also interpretable, simple, and very fast. It has only one hyperparameter. Empirical evaluations compared to state-of-the-art methods demonstrate that LCUBE achieves superior precision in terms of AUDRC on the real-world Tuebingen cause-effect pairs dataset. It also shows superior average precision across common 10 benchmark datasets and achieves above average precision on 13 datasets.", "date": "2025-08-30", "categories": []}
{"id": "2509.00987", "title": "Causal MAS: A Survey of Large Language Model Architectures for Discovery and Effect Estimation", "abstract": "Large Language Models (LLMs) have demonstrated remarkable capabilities in various reasoning and generation tasks. However, their proficiency in complex causal reasoning, discovery, and estimation remains an area of active development, often hindered by issues like hallucination, reliance on spurious correlations, and difficulties in handling nuanced, domain-specific, or personalized causal relationships. Multi-agent systems, leveraging the collaborative or specialized abilities of multiple LLM-based agents, are emerging as a powerful paradigm to address these limitations. This review paper explores the burgeoning field of causal multi-agent LLMs. We examine how these systems are designed to tackle different facets of causality, including causal reasoning and counterfactual analysis, causal discovery from data, and the estimation of causal effects. We delve into the diverse architectural patterns and interaction protocols employed, from pipeline-based processing and debate frameworks to simulation environments and iterative refinement loops. Furthermore, we discuss the evaluation methodologies, benchmarks, and diverse application domains where causal multi-agent LLMs are making an impact, including scientific discovery, healthcare, fact-checking, and personalized systems. Finally, we highlight the persistent challenges, open research questions, and promising future directions in this synergistic field, aiming to provide a comprehensive overview of its current state and potential trajectory.", "date": "2025-08-31", "categories": []}
{"id": "2509.01352", "title": "Causal Sensitivity Identification using Generative Learning", "abstract": "In this work, we propose a novel generative method to identify the causal impact and apply it to prediction tasks. We conduct causal impact analysis using interventional and counterfactual perspectives. First, applying interventions, we identify features that have a causal influence on the predicted outcome, which we refer to as causally sensitive features, and second, applying counterfactuals, we evaluate how changes in the cause affect the effect. Our method exploits the Conditional Variational Autoencoder (CVAE) to identify the causal impact and serve as a generative predictor. We are able to reduce confounding bias by identifying causally sensitive features. We demonstrate the effectiveness of our method by recommending the most likely locations a user will visit next in their spatiotemporal trajectory influenced by the causal relationships among various features. Experiments on the large-scale GeoLife [Zheng et al., 2010] dataset and the benchmark Asia Bayesian network validate the ability of our method to identify causal impact and improve predictive performance.", "date": "2025-09-01", "categories": []}
{"id": "2509.01621", "title": "Effects of Distributional Biases on Gradient-Based Causal Discovery in the Bivariate Categorical Case", "abstract": "Gradient-based causal discovery shows great potential for deducing causal structure from data in an efficient and scalable way. Those approaches however can be susceptible to distributional biases in the data they are trained on. We identify two such biases: Marginal Distribution Asymmetry, where differences in entropy skew causal learning toward certain factorizations, and Marginal Distribution Shift Asymmetry, where repeated interventions cause faster shifts in some variables than in others. For the bivariate categorical setup with Dirichlet priors, we illustrate how these biases can occur even in controlled synthetic data. To examine their impact on gradient-based methods, we employ two simple models that derive causal factorizations by learning marginal or conditional data distributions - a common strategy in gradient-based causal discovery. We demonstrate how these models can be susceptible to both biases. We additionally show how the biases can be controlled. An empirical evaluation of two related, existing approaches indicates that eliminating competition between possible causal factorizations can make models robust to the presented biases.", "date": "2025-09-01", "categories": []}
{"id": "2509.01887", "title": "Design of Experiment for Discovering Directed Mixed Graph", "abstract": "We study the problem of experimental design for accurately identifying the causal graph structure of a simple structural causal model (SCM), where the underlying graph may include both cycles and bidirected edges induced by latent confounders. The presence of cycles renders it impossible to recover the graph skeleton using observational data alone, while confounding can further invalidate traditional conditional independence (CI) tests in certain scenarios. To address these challenges, we establish lower bounds on both the maximum number of variables that can be intervened upon in a single experiment and the total number of experiments required to identify all directed edges and non-adjacent bidirected edges. Leveraging both CI tests and do see tests, and accounting for $d$ separation and $\\sigma$ separation, we develop two classes of algorithms, i.e., bounded and unbounded, that can recover all causal edges except for double adjacent bidirected edges. We further show that, up to logarithmic factors, the proposed algorithms are tight with respect to the derived lower bounds.", "date": "2025-09-02", "categories": []}
{"id": "2305.10032", "title": "A Survey on Causal Discovery: Theory and Practice", "abstract": "Understanding the laws that govern a phenomenon is the core of scientific progress. This is especially true when the goal is to model the interplay between different aspects in a causal fashion. Indeed, causal inference itself is specifically designed to quantify the underlying relationships that connect a cause to its effect. Causal discovery is a branch of the broader field of causality in which causal graphs are recovered from data (whenever possible), enabling the identification and estimation of causal effects. In this paper, we explore recent advancements in causal discovery in a unified manner, provide a consistent overview of existing algorithms developed under different settings, report useful tools and data, present real-world applications to understand why and how these methods can be fruitfully exploited.", "date": "2023-05-17", "categories": []}
{"id": "2306.16902", "title": "Integrating Large Language Model for Improved Causal Discovery", "abstract": "Recovering the structure of causal graphical models from observational data is an essential yet challenging task for causal discovery in scientific scenarios. Domain-specific causal discovery usually relies on expert validation or prior analysis to improve the reliability of recovered causality, which is yet limited by the scarcity of expert resources. Recently, Large Language Models (LLM) have been used for causal analysis across various domain-specific scenarios, suggesting its potential as autonomous expert roles in guiding data-based structure learning. However, integrating LLMs into causal discovery faces challenges due to inaccuracies in LLM-based reasoning on revealing the actual causal structure. To address this challenge, we propose an error-tolerant LLM-driven causal discovery framework. The error-tolerant mechanism is designed three-fold with sufficient consideration on potential inaccuracies. In the LLM-based reasoning process, an accuracy-oriented prompting strategy restricts causal analysis to a reliable range. Next, a knowledge-to-structure transition aligns LLM-derived causal statements with structural causal interactions. In the structure learning process, the goodness-of-fit to data and adherence to LLM-derived priors are balanced to further address prior inaccuracies. Evaluation of eight real-world causal structures demonstrates the efficacy of our LLM-driven approach in improving data-based causal discovery, along with its robustness to inaccurate LLM-derived priors. Codes are available at https://github.com/tyMadara/LLM-CD.", "date": "2023-06-29", "categories": []}
{"id": "2508.18873", "title": "MOCHA: Discovering Multi-Order Dynamic Causality in Temporal Point Processes", "abstract": "Discovering complex causal dependencies in temporal point processes (TPPs) is critical for modeling real-world event sequences. Existing methods typically rely on static or first-order causal structures, overlooking the multi-order and time-varying nature of causal relationships. In this paper, we propose MOCHA, a novel framework for discovering multi-order dynamic causality in TPPs. MOCHA characterizes multi-order influences as multi-hop causal paths over a latent time-evolving graph. To model such dynamics, we introduce a time-varying directed acyclic graph (DAG) with learnable structural weights, where acyclicity and sparsity constraints are enforced to ensure structural validity. We design an end-to-end differentiable framework that jointly models causal discovery and TPP dynamics, enabling accurate event prediction and revealing interpretable structures. Extensive experiments on real-world datasets demonstrate that MOCHA not only achieves state-of-the-art performance in event prediction, but also reveals meaningful and interpretable causal structures.", "date": "2025-08-26", "categories": []}
{"id": "2508.15928", "title": "Transforming Causality: Transformer-Based Temporal Causal Discovery with Prior Knowledge Integration", "abstract": "We introduce a novel framework for temporal causal discovery and inference that addresses two key challenges: complex nonlinear dependencies and spurious correlations. Our approach employs a multi-layer Transformer-based time-series forecaster to capture long-range, nonlinear temporal relationships among variables. After training, we extract the underlying causal structure and associated time lags from the forecaster using gradient-based analysis, enabling the construction of a causal graph. To mitigate the impact of spurious causal relationships, we introduce a prior knowledge integration mechanism based on attention masking, which consistently enforces user-excluded causal links across multiple Transformer layers. Extensive experiments show that our method significantly outperforms other state-of-the-art approaches, achieving a 12.8% improvement in F1-score for causal discovery and 98.9% accuracy in estimating causal lags.", "date": "2025-08-21", "categories": []}
{"id": "2409.05500", "title": "Scalable Time-Series Causal Discovery with Approximate Causal Ordering", "abstract": "Causal discovery in time-series data presents a significant computational challenge. Standard algorithms are often prohibitively expensive for datasets with many variables or samples. This study introduces and validates a heuristic approximation of the VarLiNGAM algorithm to address this scalability problem. The standard VarLiNGAM method relies on an iterative search, recalculating statistical dependencies after each step. Our heuristic modifies this procedure by omitting the iterative refinement. This change permits a one-time precomputation of all necessary statistical values. The algorithmic modification reduces the time complexity from $O(m^3n)$ to $O(m^2n + m^3)$ while keeping the space complexity at $O(m^2)$, where $m$ is the number of variables and $n$ is the number of samples. While an approximation, our approach retains VarLiNGAM's essential structure and empirical reliability. On large-scale financial data with up to 400 variables, our algorithm achieves a 7--13x speedup over the standard implementation and a 4.5x speedup over a GPU-accelerated version. Evaluations across medical imaging, web server monitoring, and finance demonstrate the heuristic's robustness and practical scalability. This work offers a validated balance between computational efficiency and discovery quality, making large-scale causal analysis feasible on personal computers.", "date": "2024-09-09", "categories": []}
{"id": "2507.17792", "title": "Causal Mechanism Estimation in Multi-Sensor Systems Across Multiple Domains", "abstract": "To gain deeper insights into a complex sensor system through the lens of causality, we present common and individual causal mechanism estimation (CICME), a novel three-step approach to inferring causal mechanisms from heterogeneous data collected across multiple domains. By leveraging the principle of Causal Transfer Learning (CTL), CICME is able to reliably detect domain-invariant causal mechanisms when provided with sufficient samples. The identified common causal mechanisms are further used to guide the estimation of the remaining causal mechanisms in each domain individually. The performance of CICME is evaluated on linear Gaussian models under scenarios inspired from a manufacturing process. Building upon existing continuous optimization-based causal discovery methods, we show that CICME leverages the benefits of applying causal discovery on the pooled data and repeatedly on data from individual domains, and it even outperforms both baseline methods under certain scenarios.", "date": "2025-07-23", "categories": []}
{"id": "2508.13607", "title": "Bounding Causal Effects and Counterfactuals", "abstract": "Causal inference often hinges on strong assumptions - such as no unmeasured confounding or perfect compliance - that are rarely satisfied in practice. Partial identification offers a principled alternative: instead of relying on unverifiable assumptions to estimate causal effects precisely, it derives bounds that reflect the uncertainty inherent in the data. Despite its theoretical appeal, partial identification remains underutilized in applied work, in part due to the fragmented nature of existing methods and the lack of practical guidance. This thesis addresses these challenges by systematically comparing a diverse set of bounding algorithms across multiple causal scenarios. We implement, extend, and unify state-of-the-art methods - including symbolic, optimization-based, and information-theoretic approaches - within a common evaluation framework. In particular, we propose an extension of a recently introduced entropy-bounded method, making it applicable to counterfactual queries such as the Probability of Necessity and Sufficiency (PNS). Our empirical study spans thousands of randomized simulations involving both discrete and continuous data-generating processes. We assess each method in terms of bound tightness, computational efficiency, and robustness to assumption violations. To support practitioners, we distill our findings into a practical decision tree for algorithm selection and train a machine learning model to predict the best-performing method based on observable data characteristics.\n  All implementations are released as part of an open-source Python package, CausalBoundingEngine, which enables users to apply and compare bounding methods through a unified interface.", "date": "2025-08-19", "categories": []}
{"id": "2508.13967", "title": "A PC Algorithm for Max-Linear Bayesian Networks", "abstract": "Max-linear Bayesian networks (MLBNs) are a relatively recent class of structural equation models which arise when the random variables involved have heavy-tailed distributions. Unlike most directed graphical models, MLBNs are typically not faithful to d-separation and thus classical causal discovery algorithms such as the PC algorithm or greedy equivalence search can not be used to accurately recover the true graph structure. In this paper, we begin the study of constraint-based discovery algorithms for MLBNs given an oracle for testing conditional independence in the true, unknown graph. We show that if the oracle is given by the $\\ast$-separation criteria in the true graph, then the PC algorithm remains consistent despite the presence of additional CI statements implied by $\\ast$-separation. We also introduce a new causal discovery algorithm named \"PCstar\" which assumes faithfulness to $C^\\ast$-separation and is able to orient additional edges which cannot be oriented with only d- or $\\ast$-separation.", "date": "2025-08-19", "categories": []}
{"id": "2505.07503", "title": "Identifying Causal Direction via Variational Bayesian Compression", "abstract": "Telling apart the cause and effect between two random variables with purely observational data is a challenging problem that finds applications in various scientific disciplines. A key principle utilized in this task is the algorithmic Markov condition, which postulates that the joint distribution, when factorized according to the causal direction, yields a more succinct codelength compared to the anti-causal direction. Previous approaches approximate these codelengths by relying on simple functions or Gaussian processes (GPs) with easily evaluable complexity, compromising between model fitness and computational complexity. To address these limitations, we propose leveraging the variational Bayesian learning of neural networks as an interpretation of the codelengths. This allows the improvement of model fitness, while maintaining the succinctness of the codelengths, and the avoidance of the significant computational complexity of the GP-based approaches. Extensive experiments on both synthetic and real-world benchmarks in cause-effect identification demonstrate the effectiveness of our proposed method, showing promising performance enhancements on several datasets in comparison to most related methods.", "date": "2025-05-12", "categories": []}
{"id": "2508.09447", "title": "NEXICA: Discovering Road Traffic Causality (Extended arXiv Version)", "abstract": "Road traffic congestion is a persistent problem. Focusing resources on the causes of congestion is a potentially efficient strategy for reducing slowdowns. We present NEXICA, an algorithm to discover which parts of the highway system tend to cause slowdowns on other parts of the highway. We use time series of road speeds as inputs to our causal discovery algorithm. Finding other algorithms inadequate, we develop a new approach that is novel in three ways. First, it concentrates on just the presence or absence of events in the time series, where an event indicates the temporal beginning of a traffic slowdown. Second, we develop a probabilistic model using maximum likelihood estimation to compute the probabilities of spontaneous and caused slowdowns between two locations on the highway. Third, we train a binary classifier to identify pairs of cause/effect locations trained on pairs of road locations where we are reasonably certain a priori of their causal connections, both positive and negative. We test our approach on six months of road speed data from 195 different highway speed sensors in the Los Angeles area, showing that our approach is superior to state-of-the-art baselines in both accuracy and computation speed.", "date": "2025-08-13", "categories": []}
{"id": "2407.13313", "title": "Sortability of Time Series Data", "abstract": "Evaluating the performance of causal discovery algorithms that aim to find causal relationships between time-dependent processes remains a challenging topic. In this paper, we show that certain characteristics of datasets, such as varsortability (Reisach et al. 2021) and $R^2$-sortability (Reisach et al. 2023), also occur in datasets for autocorrelated stationary time series. We illustrate this empirically using four types of data: simulated data based on SVAR models and Erd\\H{o}s-R\\'enyi graphs, the data used in the 2019 causality-for-climate challenge (Runge et al. 2019), real-world river stream datasets, and real-world data generated by the Causal Chamber of (Gamella et al. 2024). To do this, we adapt var- and $R^2$-sortability to time series data. We also investigate the extent to which the performance of score-based causal discovery methods goes hand in hand with high sortability. Arguably, our most surprising finding is that the investigated real-world datasets exhibit high varsortability and low $R^2$-sortability indicating that scales may carry a significant amount of causal information.", "date": "2024-07-18", "categories": []}
{"id": "2508.07221", "title": "LLM-based Agents for Automated Confounder Discovery and Subgroup Analysis in Causal Inference", "abstract": "Estimating individualized treatment effects from observational data presents a persistent challenge due to unmeasured confounding and structural bias. Causal Machine Learning (causal ML) methods, such as causal trees and doubly robust estimators, provide tools for estimating conditional average treatment effects. These methods have limited effectiveness in complex real-world environments due to the presence of latent confounders or those described in unstructured formats. Moreover, reliance on domain experts for confounder identification and rule interpretation introduces high annotation cost and scalability concerns. In this work, we proposed Large Language Model-based agents for automated confounder discovery and subgroup analysis that integrate agents into the causal ML pipeline to simulate domain expertise. Our framework systematically performs subgroup identification and confounding structure discovery by leveraging the reasoning capabilities of LLM-based agents, which reduces human dependency while preserving interpretability. Experiments on real-world medical datasets show that our proposed approach enhances treatment effect estimation robustness by narrowing confidence intervals and uncovering unrecognized confounding biases. Our findings suggest that LLM-based agents offer a promising path toward scalable, trustworthy, and semantically aware causal inference.", "date": "2025-08-10", "categories": []}
{"id": "2401.09641", "title": "Functional Linear Non-Gaussian Acyclic Model for Causal Discovery", "abstract": "In causal discovery, non-Gaussianity has been used to characterize the complete configuration of a Linear Non-Gaussian Acyclic Model (LiNGAM), encompassing both the causal ordering of variables and their respective connection strengths. However, LiNGAM can only deal with the finite-dimensional case. To expand this concept, we extend the notion of variables to encompass vectors and even functions, leading to the Functional Linear Non-Gaussian Acyclic Model (Func-LiNGAM). Our motivation stems from the desire to identify causal relationships in brain-effective connectivity tasks involving, for example, fMRI and EEG datasets. We demonstrate why the original LiNGAM fails to handle these inherently infinite-dimensional datasets and explain the availability of functional data analysis from both empirical and theoretical perspectives. {We establish theoretical guarantees of the identifiability of the causal relationship among non-Gaussian random vectors and even random functions in infinite-dimensional Hilbert spaces.} To address the issue of sparsity in discrete time points within intrinsic infinite-dimensional functional data, we propose optimizing the coordinates of the vectors using functional principal component analysis. Experimental results on synthetic data verify the ability of the proposed framework to identify causal relationships among multivariate functions using the observed samples. For real data, we focus on analyzing the brain connectivity patterns derived from fMRI data.", "date": "2024-01-17", "categories": []}
{"id": "2508.01848", "title": "Causal Discovery in Multivariate Time Series through Mutual Information Featurization", "abstract": "Discovering causal relationships in complex multivariate time series is a fundamental scientific challenge. Traditional methods often falter, either by relying on restrictive linear assumptions or on conditional independence tests that become uninformative in the presence of intricate, non-linear dynamics. This paper proposes a new paradigm, shifting from statistical testing to pattern recognition. We hypothesize that a causal link creates a persistent and learnable asymmetry in the flow of information through a system's temporal graph, even when clear conditional independencies are obscured. We introduce Temporal Dependency to Causality (TD2C), a supervised learning framework that operationalizes this hypothesis. TD2C learns to recognize these complex causal signatures from a rich set of information-theoretic and statistical descriptors. Trained exclusively on a diverse collection of synthetic time series, TD2C demonstrates remarkable zero-shot generalization to unseen dynamics and established, realistic benchmarks. Our results show that TD2C achieves state-of-the-art performance, consistently outperforming established methods, particularly in high-dimensional and non-linear settings. By reframing the discovery problem, our work provides a robust and scalable new tool for uncovering causal structures in complex systems.", "date": "2025-08-03", "categories": []}
{"id": "2211.10085", "title": "Identifying Unique Spatial-Temporal Bayesian Network without Markov Equivalence", "abstract": "Identifying vanilla Bayesian network to model spatial-temporal causality can be a critical yet challenging task. Different Markovian-equivalent directed acyclic graphs would be identified if the identifiability is not satisfied. To address this issue, Directed Cyclic Graph is proposed to drop the directed acyclic constraint. But it does not always hold, and cannot model dynamical time-series process. Then, Full Time Graph is proposed with introducing high-order time delay. Full Time Graph has no Markov equivalence class by assuming no instantaneous effects. But, it also assumes that the causality is invariant with varying time, that is not always satisfied in the spatio-temporal scenarios. Thus, in this work, a Spatial-Temporal Bayesian Network (STBN) is proposed to theoretically model the spatial-temporal causality from the perspective of information transfer. STBN explains the disappearance of network structure $X\\rightarrow Z \\rightarrow Y$ and $X\\leftarrow Z \\leftarrow Y$ by the principle of information path blocking. And finally, the uniqueness of STBN is proved. Based on this, a High-order Causal Entropy (HCE) algorithm is also proposed to uniquely identify STBN under time complexity $\\mathcal{O}(n^3\\tau_{max})$, where $n$ is the number of variables and $\\tau_{max}$ is the maximum time delay. Numerical experiments are conducted with comparison to other baseline algorithms. The results show that HCE algorithm obtains state-of-the-art identification accuracy. The code is available at https://github.com/KMY-SEU/HCE.", "date": "2022-11-18", "categories": []}
{"id": "2508.00658", "title": "Multi-Band Variable-Lag Granger Causality: A Unified Framework for Causal Time Series Inference across Frequencies", "abstract": "Understanding causal relationships in time series is fundamental to many domains, including neuroscience, economics, and behavioral science. Granger causality is one of the well-known techniques for inferring causality in time series. Typically, Granger causality frameworks have a strong fix-lag assumption between cause and effect, which is often unrealistic in complex systems. While recent work on variable-lag Granger causality (VLGC) addresses this limitation by allowing a cause to influence an effect with different time lags at each time point, it fails to account for the fact that causal interactions may vary not only in time delay but also across frequency bands. For example, in brain signals, alpha-band activity may influence another region with a shorter delay than slower delta-band oscillations. In this work, we formalize Multi-Band Variable-Lag Granger Causality (MB-VLGC) and propose a novel framework that generalizes traditional VLGC by explicitly modeling frequency-dependent causal delays. We provide a formal definition of MB-VLGC, demonstrate its theoretical soundness, and propose an efficient inference pipeline. Extensive experiments across multiple domains demonstrate that our framework significantly outperforms existing methods on both synthetic and real-world datasets, confirming its broad applicability to any type of time series data. Code and datasets are publicly available.", "date": "2025-08-01", "categories": []}
{"id": "2507.23488", "title": "Causal Reasoning in Pieces: Modular In-Context Learning for Causal Discovery", "abstract": "Causal inference remains a fundamental challenge for large language models. Recent advances in internal reasoning with large language models have sparked interest in whether state-of-the-art reasoning models can robustly perform causal discovery-a task where conventional models often suffer from severe overfitting and near-random performance under data perturbations. We study causal discovery on the Corr2Cause benchmark using the emergent OpenAI's o-series and DeepSeek-R model families and find that these reasoning-first architectures achieve significantly greater native gains than prior approaches. To capitalize on these strengths, we introduce a modular in-context pipeline inspired by the Tree-of-Thoughts and Chain-of-Thoughts methodologies, yielding nearly three-fold improvements over conventional baselines. We further probe the pipeline's impact by analyzing reasoning chain length, complexity, and conducting qualitative and quantitative comparisons between conventional and reasoning models. Our findings suggest that while advanced reasoning models represent a substantial leap forward, carefully structured in-context frameworks are essential to maximize their capabilities and offer a generalizable blueprint for causal discovery across diverse domains.", "date": "2025-07-31", "categories": []}
{"id": "2507.21792", "title": "Hybrid Causal Identification and Causal Mechanism Clustering", "abstract": "Bivariate causal direction identification is a fundamental and vital problem in the causal inference field. Among binary causal methods, most methods based on additive noise only use one single causal mechanism to construct a causal model. In the real world, observations are always collected in different environments with heterogeneous causal relationships. Therefore, on observation data, this paper proposes a Mixture Conditional Variational Causal Inference model (MCVCI) to infer heterogeneous causality. Specifically, according to the identifiability of the Hybrid Additive Noise Model (HANM), MCVCI combines the superior fitting capabilities of the Gaussian mixture model and the neural network and elegantly uses the likelihoods obtained from the probabilistic bounds of the mixture conditional variational auto-encoder as causal decision criteria. Moreover, we model the casual heterogeneity into cluster numbers and propose the Mixture Conditional Variational Causal Clustering (MCVCC) method, which can reveal causal mechanism expression. Compared with state-of-the-art methods, the comprehensive best performance demonstrates the effectiveness of the methods proposed in this paper on several simulated and real data.", "date": "2025-07-29", "categories": []}
{"id": "2507.20349", "title": "From Observations to Causations: A GNN-based Probabilistic Prediction Framework for Causal Discovery", "abstract": "Causal discovery from observational data is challenging, especially with large datasets and complex relationships. Traditional methods often struggle with scalability and capturing global structural information. To overcome these limitations, we introduce a novel graph neural network (GNN)-based probabilistic framework that learns a probability distribution over the entire space of causal graphs, unlike methods that output a single deterministic graph. Our framework leverages a GNN that encodes both node and edge attributes into a unified graph representation, enabling the model to learn complex causal structures directly from data. The GNN model is trained on a diverse set of synthetic datasets augmented with statistical and information-theoretic measures, such as mutual information and conditional entropy, capturing both local and global data properties. We frame causal discovery as a supervised learning problem, directly predicting the entire graph structure. Our approach demonstrates superior performance, outperforming both traditional and recent non-GNN-based methods, as well as a GNN-based approach, in terms of accuracy and scalability on synthetic and real-world datasets without further training. This probabilistic framework significantly improves causal structure learning, with broad implications for decision-making and scientific discovery across various fields.", "date": "2025-07-27", "categories": []}
{"id": "2506.20933", "title": "Lower Bounds on the Size of Markov Equivalence Classes", "abstract": "Causal discovery algorithms typically recover causal graphs only up to their Markov equivalence classes unless additional parametric assumptions are made. The sizes of these equivalence classes reflect the limits of what can be learned about the underlying causal graph from purely observational data. Under the assumptions of acyclicity, causal sufficiency, and a uniform model prior, Markov equivalence classes are known to be small on average. In this paper, we show that this is no longer the case when any of these assumptions is relaxed. Specifically, we prove exponentially large lower bounds for the expected size of Markov equivalence classes in three settings: sparse random directed acyclic graphs, uniformly random acyclic directed mixed graphs, and uniformly random directed cyclic graphs.", "date": "2025-06-26", "categories": []}
{"id": "2507.18903", "title": "Probably Approximately Correct Causal Discovery", "abstract": "The discovery of causal relationships is a foundational problem in artificial intelligence, statistics, epidemiology, economics, and beyond. While elegant theories exist for accurate causal discovery given infinite data, real-world applications are inherently resource-constrained. Effective methods for inferring causal relationships from observational data must perform well under finite data and time constraints, where \"performing well\" implies achieving high, though not perfect accuracy. In his seminal paper A Theory of the Learnable, Valiant highlighted the importance of resource constraints in supervised machine learning, introducing the concept of Probably Approximately Correct (PAC) learning as an alternative to exact learning. Inspired by Valiant's work, we propose the Probably Approximately Correct Causal (PACC) Discovery framework, which extends PAC learning principles to the causal field. This framework emphasizes both computational and sample efficiency for established causal methods such as propensity score techniques and instrumental variable approaches. Furthermore, we show that it can also provide theoretical guarantees for other widely used methods, such as the Self-Controlled Case Series (SCCS) method, which had previously lacked such guarantees.", "date": "2025-07-25", "categories": []}
{"id": "2507.09439", "title": "Dynamic Sparse Causal-Attention Temporal Networks for Interpretable Causality Discovery in Multivariate Time Series", "abstract": "Understanding causal relationships in multivariate time series (MTS) is essential for effective decision-making in fields such as finance and marketing, where complex dependencies and lagged effects challenge conventional analytical approaches. We introduce Dynamic Sparse Causal-Attention Temporal Networks for Interpretable Causality Discovery in MTS (DyCAST-Net), a novel architecture designed to enhance causal discovery by integrating dilated temporal convolutions and dynamic sparse attention mechanisms. DyCAST-Net effectively captures multiscale temporal dependencies through dilated convolutions while leveraging an adaptive thresholding strategy in its attention mechanism to eliminate spurious connections, ensuring both accuracy and interpretability. A statistical shuffle test validation further strengthens robustness by filtering false positives and improving causal inference reliability. Extensive evaluations on financial and marketing datasets demonstrate that DyCAST-Net consistently outperforms existing models such as TCDF, GCFormer, and CausalFormer. The model provides a more precise estimation of causal delays and significantly reduces false discoveries, particularly in noisy environments. Moreover, attention heatmaps offer interpretable insights, uncovering hidden causal patterns such as the mediated effects of advertising on consumer behavior and the influence of macroeconomic indicators on financial markets. Case studies illustrate DyCAST-Net's ability to detect latent mediators and lagged causal factors, making it particularly effective in high-dimensional, dynamic settings. The model's architecture enhanced by RMSNorm stabilization and causal masking ensures scalability and adaptability across diverse application domains", "date": "2025-07-13", "categories": []}
{"id": "2507.09742", "title": "Causality-informed Anomaly Detection in Partially Observable Sensor Networks: Moving beyond Correlations", "abstract": "Nowadays, as AI-driven manufacturing becomes increasingly popular, the volume of data streams requiring real-time monitoring continues to grow. However, due to limited resources, it is impractical to place sensors at every location to detect unexpected shifts. Therefore, it is necessary to develop an optimal sensor placement strategy that enables partial observability of the system while detecting anomalies as quickly as possible. Numerous approaches have been proposed to address this challenge; however, most existing methods consider only variable correlations and neglect a crucial factor: Causality. Moreover, although a few techniques incorporate causal analysis, they rely on interventions-artificially creating anomalies-to identify causal effects, which is impractical and might lead to catastrophic losses. In this paper, we introduce a causality-informed deep Q-network (Causal DQ) approach for partially observable sensor placement in anomaly detection. By integrating causal information at each stage of Q-network training, our method achieves faster convergence and tighter theoretical error bounds. Furthermore, the trained causal-informed Q-network significantly reduces the detection time for anomalies under various settings, demonstrating its effectiveness for sensor placement in large-scale, real-world data streams. Beyond the current implementation, our technique's fundamental insights can be applied to various reinforcement learning problems, opening up new possibilities for real-world causality-informed machine learning methods in engineering applications.", "date": "2025-07-13", "categories": []}
{"id": "2507.07898", "title": "Efficient Causal Discovery for Autoregressive Time Series", "abstract": "In this study, we present a novel constraint-based algorithm for causal structure learning specifically designed for nonlinear autoregressive time series. Our algorithm significantly reduces computational complexity compared to existing methods, making it more efficient and scalable to larger problems. We rigorously evaluate its performance on synthetic datasets, demonstrating that our algorithm not only outperforms current techniques, but also excels in scenarios with limited data availability. These results highlight its potential for practical applications in fields requiring efficient and accurate causal inference from nonlinear time series data.", "date": "2025-07-10", "categories": []}
{"id": "2507.06888", "title": "Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants", "abstract": "Federated causal discovery aims to uncover the causal relationships between entities while protecting data privacy, which has significant importance and numerous applications in real-world scenarios. Existing federated causal structure learning methods primarily focus on horizontal federated settings. However, in practical situations, different clients may not necessarily contain data on the same variables. In a single client, the incomplete set of variables can easily lead to spurious causal relationships, thereby affecting the information transmitted to other clients. To address this issue, we comprehensively consider causal structure learning methods under both horizontal and vertical federated settings. We provide the identification theories and methods for learning causal structure in the horizontal and vertical federal setting via higher-order cumulants. Specifically, we first aggregate higher-order cumulant information from all participating clients to construct global cumulant estimates. These global estimates are then used for recursive source identification, ultimately yielding a global causal strength matrix. Our approach not only enables the reconstruction of causal graphs but also facilitates the estimation of causal strength coefficients. Our algorithm demonstrates superior performance in experiments conducted on both synthetic data and real-world data.", "date": "2025-07-09", "categories": []}
{"id": "2505.20697", "title": "Generating Hypotheses of Dynamic Causal Graphs in Neuroscience: Leveraging Generative Factor Models of Observed Time Series", "abstract": "The field of hypothesis generation promises to reduce costs in neuroscience by narrowing the range of interventional studies needed to study various phenomena. Existing machine learning methods can generate scientific hypotheses from complex datasets, but many approaches assume causal relationships are static over time, limiting their applicability to systems with dynamic, state-dependent behavior, such as the brain. While some techniques attempt dynamic causal discovery through factor models, they often restrict relationships to linear patterns or impose other simplifying assumptions. We propose a novel method that models dynamic graphs as a conditionally weighted superposition of static graphs, where each static graph can capture nonlinear relationships. This approach enables the detection of complex, time-varying interactions between variables beyond linear limitations. Our method improves f1-scores of predicted dynamic causal patterns by roughly 22-28% on average over baselines in some of our experiments, with some improvements reaching well over 60%. A case study on real brain data demonstrates our method's ability to uncover relationships linked to specific behavioral states, offering valuable insights into neural dynamics.", "date": "2025-05-27", "categories": []}
{"id": "2406.10481", "title": "DCILP: A Distributed Approach for Large-Scale Causal Structure Learning", "abstract": "Causal learning tackles the computationally demanding task of estimating causal graphs. This paper introduces a new divide-and-conquer approach for causal graph learning, called DCILP. In the divide phase, the Markov blanket MB($X_i$) of each variable $X_i$ is identified, and causal learning subproblems associated with each MB($X_i$) are independently addressed in parallel. This approach benefits from a more favorable ratio between the number of data samples and the number of variables considered. In counterpart, it can be adversely affected by the presence of hidden confounders, as variables external to MB($X_i$) might influence those within it. The reconciliation of the local causal graphs generated during the divide phase is a challenging combinatorial optimization problem, especially in large-scale applications. The main novelty of DCILP is an original formulation of this reconciliation as an integer linear programming (ILP) problem, which can be delegated and efficiently handled by an ILP solver. Through experiments on medium to large scale graphs, and comparisons with state-of-the-art methods, DCILP demonstrates significant improvements in terms of computational complexity, while preserving the learning accuracy on real-world problem and suffering at most a slight loss of accuracy on synthetic problems.", "date": "2024-06-15", "categories": []}
{"id": "2506.23374", "title": "When Additive Noise Meets Unobserved Mediators: Bivariate Denoising Diffusion for Causal Discovery", "abstract": "Distinguishing cause and effect from bivariate observational data is a foundational problem in many disciplines, but challenging without additional assumptions. Additive noise models (ANMs) are widely used to enable sample-efficient bivariate causal discovery. However, conventional ANM-based methods fail when unobserved mediators corrupt the causal relationship between variables. This paper makes three key contributions: first, we rigorously characterize why standard ANM approaches break down in the presence of unmeasured mediators. Second, we demonstrate that prior solutions for hidden mediation are brittle in finite sample settings, limiting their practical utility. To address these gaps, we propose Bivariate Denoising Diffusion (BiDD) for causal discovery, a method designed to handle latent noise introduced by unmeasured mediators. Unlike prior methods that infer directionality through mean squared error loss comparisons, our approach introduces a novel independence test statistic: during the noising and denoising processes for each variable, we condition on the other variable as input and evaluate the independence of the predicted noise relative to this input. We prove asymptotic consistency of BiDD under the ANM, and conjecture that it performs well under hidden mediation. Experiments on synthetic and real-world data demonstrate consistent performance, outperforming existing methods in mediator-corrupted settings while maintaining strong performance in mediator-free settings.", "date": "2025-06-29", "categories": []}
{"id": "2409.14593", "title": "Testing Causal Models with Hidden Variables in Polynomial Delay via Conditional Independencies", "abstract": "Testing a hypothesized causal model against observational data is a key prerequisite for many causal inference tasks. A natural approach is to test whether the conditional independence relations (CIs) assumed in the model hold in the data. While a model can assume exponentially many CIs (with respect to the number of variables), testing all of them is both impractical and unnecessary. Causal graphs, which encode these CIs in polynomial space, give rise to local Markov properties that enable model testing with a significantly smaller subset of CIs. Model testing based on local properties requires an algorithm to list the relevant CIs. However, existing algorithms for realistic settings with hidden variables and non-parametric distributions can take exponential time to produce even a single CI constraint. In this paper, we introduce the c-component local Markov property (C-LMP) for causal graphs with hidden variables. Since C-LMP can still invoke an exponential number of CIs, we develop a polynomial delay algorithm to list these CIs in poly-time intervals. To our knowledge, this is the first algorithm that enables poly-delay testing of CIs in causal graphs with hidden variables against arbitrary data distributions. Experiments on real-world and synthetic data demonstrate the practicality of our algorithm.", "date": "2024-09-22", "categories": []}
{"id": "2506.20169", "title": "Causal discovery in deterministic discrete LTI-DAE systems", "abstract": "Discovering pure causes or driver variables in deterministic LTI systems is of vital importance in the data-driven reconstruction of causal networks. A recent work by Kathari and Tangirala, proposed in 2022, formulated the causal discovery method as a constraint identification problem. The constraints are identified using a dynamic iterative PCA (DIPCA)-based approach for dynamical systems corrupted with Gaussian measurement errors. The DIPCA-based method works efficiently for dynamical systems devoid of any algebraic relations. However, several dynamical systems operate under feedback control and/or are coupled with conservation laws, leading to differential-algebraic (DAE) or mixed causal systems. In this work, a method, namely the partition of variables (PoV), for causal discovery in LTI-DAE systems is proposed. This method is superior to the method that was presented by Kathari and Tangirala (2022), as PoV also works for pure dynamical systems, which are devoid of algebraic equations. The proposed method identifies the causal drivers up to a minimal subset. PoV deploys DIPCA to first determine the number of algebraic relations ($n_a$), the number of dynamical relations ($n_d$) and the constraint matrix. Subsequently, the subsets are identified through an admissible partitioning of the constraint matrix by finding the condition number of it. Case studies are presented to demonstrate the effectiveness of the proposed method.", "date": "2025-06-25", "categories": []}
{"id": "2410.23499", "title": "Tangent Space Causal Inference: Leveraging Vector Fields for Causal Discovery in Dynamical Systems", "abstract": "Causal discovery with time series data remains a challenging yet increasingly important task across many scientific domains. Convergent cross mapping (CCM) and related methods have been proposed to study time series that are generated by dynamical systems, where traditional approaches like Granger causality are unreliable. However, CCM often yields inaccurate results depending upon the quality of the data. We propose the Tangent Space Causal Inference (TSCI) method for detecting causalities in dynamical systems. TSCI works by considering vector fields as explicit representations of the systems' dynamics and checks for the degree of synchronization between the learned vector fields. The TSCI approach is model-agnostic and can be used as a drop-in replacement for CCM and its generalizations. We first present a basic version of the TSCI algorithm, which is shown to be more effective than the basic CCM algorithm with very little additional computation. We additionally present augmented versions of TSCI that leverage the expressive power of latent variable models and deep learning. We validate our theory on standard systems, and we demonstrate improved causal inference performance across a number of benchmark tasks.", "date": "2024-10-30", "categories": []}
{"id": "2411.10154", "title": "Continuous Bayesian Model Selection for Multivariate Causal Discovery", "abstract": "Current causal discovery approaches require restrictive model assumptions in the absence of interventional data to ensure structure identifiability. These assumptions often do not hold in real-world applications leading to a loss of guarantees and poor performance in practice. Recent work has shown that, in the bivariate case, Bayesian model selection can greatly improve performance by exchanging restrictive modelling for more flexible assumptions, at the cost of a small probability of making an error. Our work shows that this approach is useful in the important multivariate case as well. We propose a scalable algorithm leveraging a continuous relaxation of the discrete model selection problem. Specifically, we employ the Causal Gaussian Process Conditional Density Estimator (CGP-CDE) as a Bayesian non-parametric model, using its hyperparameters to construct an adjacency matrix. This matrix is then optimised using the marginal likelihood and an acyclicity regulariser, giving the maximum a posteriori causal graph. We demonstrate the competitiveness of our approach, showing it is advantageous to perform multivariate causal discovery without infeasible assumptions using Bayesian model selection.", "date": "2024-11-15", "categories": []}
{"id": "2506.19459", "title": "Tagged for Direction: Pinning Down Causal Edge Directions with Precision", "abstract": "Not every causal relation between variables is equal, and this can be leveraged for the task of causal discovery. Recent research shows that pairs of variables with particular type assignments induce a preference on the causal direction of other pairs of variables with the same type. Although useful, this assignment of a specific type to a variable can be tricky in practice. We propose a tag-based causal discovery approach where multiple tags are assigned to each variable in a causal graph. Existing causal discovery approaches are first applied to direct some edges, which are then used to determine edge relations between tags. Then, these edge relations are used to direct the undirected edges. Doing so improves upon purely type-based relations, where the assumption of type consistency lacks robustness and flexibility due to being restricted to single types for each variable. Our experimental evaluations show that this boosts causal discovery and that these high-level tag relations fit common knowledge.", "date": "2025-06-24", "categories": []}
{"id": "2506.18285", "title": "Learning Causal Graphs at Scale: A Foundation Model Approach", "abstract": "Due to its human-interpretability and invariance properties, Directed Acyclic Graph (DAG) has been a foundational tool across various areas of AI research, leading to significant advancements. However, DAG learning remains highly challenging, due to its super-exponential growth in computational cost and identifiability issues, particularly in small-sample regimes. To address these two challenges, in this work we leverage the recent success of linear transformers and develop a foundation model approach for discovering multiple order-consistent DAGs across tasks. In particular, we propose Attention-DAG (ADAG), a novel attention-mechanism-based architecture for learning multiple linear Structural Equation Models (SEMs). ADAG learns the mapping from observed data to both graph structure and parameters via a nonlinear attention-based kernel, enabling efficient multi-task estimation of the underlying linear SEMs. By formulating the learning process across multiple tasks as a continuous optimization problem, the pre-trained ADAG model captures the common structural properties as a shared low-dimensional prior, thereby reducing the ill-posedness of downstream DAG learning tasks in small-sample regimes. We evaluate our proposed approach on benchmark synthetic datasets and find that ADAG achieves substantial improvements in both DAG learning accuracy and zero-shot inference efficiency. To the best of our knowledge, this is the first practical approach for pre-training a foundation model specifically designed for DAG learning, representing a step toward more efficient and generalizable down-stream applications in causal discovery.", "date": "2025-06-23", "categories": []}
{"id": "2410.11759", "title": "LoSAM: Local Search in Additive Noise Models with Mixed Mechanisms and General Noise for Global Causal Discovery", "abstract": "Inferring causal relationships from observational data is crucial when experiments are costly or infeasible. Additive noise models (ANMs) enable unique directed acyclic graph (DAG) identification, but existing sample-efficient ANM methods often rely on restrictive assumptions on the data generating process, limiting their applicability to real-world settings. We propose local search in additive noise models, LoSAM, a topological ordering method for learning a unique DAG in ANMs with mixed causal mechanisms and general noise distributions. We introduce new causal substructures and criteria for identifying roots and leaves, enabling efficient top-down learning. We prove asymptotic consistency and polynomial runtime, ensuring scalability and sample efficiency. We test LoSAM on synthetic and real-world data, demonstrating state-of-the-art performance across all mixed mechanism settings.", "date": "2024-10-15", "categories": []}
{"id": "2411.05331", "title": "Discovering Latent Causal Graphs from Spatiotemporal Data", "abstract": "Many important phenomena in scientific fields like climate, neuroscience, and epidemiology are naturally represented as spatiotemporal gridded data with complex interactions. Inferring causal relationships from these data is a challenging problem compounded by the high dimensionality of such data and the correlations between spatially proximate points. We present SPACY (SPAtiotemporal Causal discoverY), a novel framework based on variational inference, designed to model latent time series and their causal relationships from spatiotemporal data. SPACY alleviates the high-dimensional challenge by discovering causal structures in the latent space. To aggregate spatially proximate, correlated grid points, we use spatial factors, parametrized by spatial kernel functions, to map observational time series to latent representations. Theoretically, we generalize the problem to a continuous spatial domain and establish identifiability when the observations arise from a nonlinear, invertible function of the product of latent series and spatial factors. Using this approach, we avoid assumptions that are often unverifiable, including those about instantaneous effects or sufficient variability. Empirically, SPACY outperforms state-of-the-art baselines on synthetic data, even in challenging settings where existing methods struggle, while remaining scalable for large grids. SPACY also identifies key known phenomena from real-world climate data. An implementation of SPACY is available at https://github.com/Rose-STL-Lab/SPACY/", "date": "2024-11-08", "categories": []}
{"id": "2412.01953", "title": "The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications", "abstract": "Causal discovery aims to automatically uncover causal relationships from data, a capability with significant potential across many scientific disciplines. However, its real-world applications remain limited. Current methods often rely on unrealistic assumptions and are evaluated only on simple synthetic toy datasets, often with inadequate evaluation metrics. In this paper, we substantiate these claims by performing a systematic review of the recent causal discovery literature. We present applications in biology, neuroscience, and Earth sciences - fields where causal discovery holds promise for addressing key challenges. We highlight available simulated and real-world datasets from these domains and discuss common assumption violations that have spurred the development of new methods. Our goal is to encourage the community to adopt better evaluation practices by utilizing realistic datasets and more adequate metrics.", "date": "2024-12-02", "categories": []}
{"id": "2506.11756", "title": "Causal Effect Identification in Heterogeneous Environments from Higher-Order Moments", "abstract": "We investigate the estimation of the causal effect of a treatment variable on an outcome in the presence of a latent confounder. We first show that the causal effect is identifiable under certain conditions when data is available from multiple environments, provided that the target causal effect remains invariant across these environments. Secondly, we propose a moment-based algorithm for estimating the causal effect as long as only a single parameter of the data-generating mechanism varies across environments -- whether it be the exogenous noise distribution or the causal relationship between two variables. Conversely, we prove that identifiability is lost if both exogenous noise distributions of both the latent and treatment variables vary across environments. Finally, we propose a procedure to identify which parameter of the data-generating mechanism has varied across the environments and evaluate the performance of our proposed methods through experiments on synthetic data.", "date": "2025-06-13", "categories": []}
{"id": "2501.18990", "title": "Permutation-Based Rank Test in the Presence of Discretization and Application in Causal Discovery with Mixed Data", "abstract": "Recent advances have shown that statistical tests for the rank of cross-covariance matrices play an important role in causal discovery. These rank tests include partial correlation tests as special cases and provide further graphical information about latent variables. Existing rank tests typically assume that all the continuous variables can be perfectly measured, and yet, in practice many variables can only be measured after discretization. For example, in psychometric studies, the continuous level of certain personality dimensions of a person can only be measured after being discretized into order-preserving options such as disagree, neutral, and agree. Motivated by this, we propose Mixed data Permutation-based Rank Test (MPRT), which properly controls the statistical errors even when some or all variables are discretized. Theoretically, we establish the exchangeability and estimate the asymptotic null distribution by permutations; as a consequence, MPRT can effectively control the Type I error in the presence of discretization while previous methods cannot. Empirically, our method is validated by extensive experiments on synthetic data and real-world data to demonstrate its effectiveness as well as applicability in causal discovery.", "date": "2025-01-31", "categories": []}
{"id": "2506.10378", "title": "Discovering Hierarchical Latent Capabilities of Language Models via Causal Representation Learning", "abstract": "Faithful evaluation of language model capabilities is crucial for deriving actionable insights that can inform model development. However, rigorous causal evaluations in this domain face significant methodological challenges, including complex confounding effects and prohibitive computational costs associated with extensive retraining. To tackle these challenges, we propose a causal representation learning framework wherein observed benchmark performance is modeled as a linear transformation of a few latent capability factors. Crucially, these latent factors are identified as causally interrelated after appropriately controlling for the base model as a common confounder. Applying this approach to a comprehensive dataset encompassing over 1500 models evaluated across six benchmarks from the Open LLM Leaderboard, we identify a concise three-node linear causal structure that reliably explains the observed performance variations. Further interpretation of this causal structure provides substantial scientific insights beyond simple numerical rankings: specifically, we reveal a clear causal direction starting from general problem-solving capabilities, advancing through instruction-following proficiency, and culminating in mathematical reasoning ability. Our results underscore the essential role of carefully controlling base model variations during evaluation, a step critical to accurately uncovering the underlying causal relationships among latent model capabilities.", "date": "2025-06-12", "categories": []}
{"id": "2408.05860", "title": "Root Cause Attribution of Delivery Risks via Causal Discovery with Reinforcement Learning", "abstract": "This paper presents a novel approach to root cause attribution of delivery risks within supply chains by integrating causal discovery with reinforcement learning. As supply chains become increasingly complex, traditional methods of root cause analysis struggle to capture the intricate interrelationships between various factors, often leading to spurious correlations and suboptimal decision-making. Our approach addresses these challenges by leveraging causal discovery to identify the true causal relationships between operational variables, and reinforcement learning to iteratively refine the causal graph. This method enables the accurate identification of key drivers of late deliveries, such as shipping mode and delivery status, and provides actionable insights for optimizing supply chain performance. We apply our approach to a real-world supply chain dataset, demonstrating its effectiveness in uncovering the underlying causes of delivery delays and offering strategies for mitigating these risks. The findings have significant implications for improving operational efficiency, customer satisfaction, and overall profitability within supply chains.", "date": "2024-08-11", "categories": []}
{"id": "2506.09286", "title": "Causal Graph Recovery in Neuroimaging through Answer Set Programming", "abstract": "Learning graphical causal structures from time series data presents significant challenges, especially when the measurement frequency does not match the causal timescale of the system. This often leads to a set of equally possible underlying causal graphs due to information loss from sub-sampling (i.e., not observing all possible states of the system throughout time). Our research addresses this challenge by incorporating the effects of sub-sampling in the derivation of causal graphs, resulting in more accurate and intuitive outcomes. We use a constraint optimization approach, specifically answer set programming (ASP), to find the optimal set of answers. ASP not only identifies the most probable underlying graph, but also provides an equivalence class of possible graphs for expert selection. In addition, using ASP allows us to leverage graph theory to further prune the set of possible solutions, yielding a smaller, more accurate answer set significantly faster than traditional approaches. We validate our approach on both simulated data and empirical structural brain connectivity, and demonstrate its superiority over established methods in these experiments. We further show how our method can be used as a meta-approach on top of established methods to obtain, on average, 12% improvement in F1 score. In addition, we achieved state of the art results in terms of precision and recall of reconstructing causal graph from sub-sampled time series data. Finally, our method shows robustness to varying degrees of sub-sampling on realistic simulations, whereas other methods perform worse for higher rates of sub-sampling.", "date": "2025-06-10", "categories": []}
{"id": "2502.05122", "title": "Distinguishing Cause from Effect with Causal Velocity Models", "abstract": "Bivariate structural causal models (SCM) are often used to infer causal direction by examining their goodness-of-fit under restricted model classes. In this paper, we describe a parametrization of bivariate SCMs in terms of a causal velocity by viewing the cause variable as time in a dynamical system. The velocity implicitly defines counterfactual curves via the solution of initial value problems where the observation specifies the initial condition. Using tools from measure transport, we obtain a unique correspondence between SCMs and the score function of the generated distribution via its causal velocity. Based on this, we derive an objective function that directly regresses the velocity against the score function, the latter of which can be estimated non-parametrically from observational data. We use this to develop a method for bivariate causal discovery that extends beyond known model classes such as additive or location scale noise, and that requires no assumptions on the noise distributions. When the score is estimated well, the objective is also useful for detecting model non-identifiability and misspecification. We present positive results in simulation and benchmark experiments where many existing methods fail, and perform ablation studies to examine the method's sensitivity to accurate score estimation.", "date": "2025-02-07", "categories": []}
{"id": "2506.08771", "title": "Paths to Causality: Finding Informative Subgraphs Within Knowledge Graphs for Knowledge-Based Causal Discovery", "abstract": "Inferring causal relationships between variable pairs is crucial for understanding multivariate interactions in complex systems. Knowledge-based causal discovery -- which involves inferring causal relationships by reasoning over the metadata of variables (e.g., names or textual context) -- offers a compelling alternative to traditional methods that rely on observational data. However, existing methods using Large Language Models (LLMs) often produce unstable and inconsistent results, compromising their reliability for causal inference. To address this, we introduce a novel approach that integrates Knowledge Graphs (KGs) with LLMs to enhance knowledge-based causal discovery. Our approach identifies informative metapath-based subgraphs within KGs and further refines the selection of these subgraphs using Learning-to-Rank-based models. The top-ranked subgraphs are then incorporated into zero-shot prompts, improving the effectiveness of LLMs in inferring the causal relationship. Extensive experiments on biomedical and open-domain datasets demonstrate that our method outperforms most baselines by up to 44.4 points in F1 scores, evaluated across diverse LLMs and KGs. Our code and datasets are available on GitHub: https://github.com/susantiyuni/path-to-causality", "date": "2025-06-10", "categories": []}
{"id": "2412.17717", "title": "Fast Causal Discovery by Approximate Kernel-based Generalized Score Functions with Linear Computational Complexity", "abstract": "Score-based causal discovery methods can effectively identify causal relationships by evaluating candidate graphs and selecting the one with the highest score. One popular class of scores is kernel-based generalized score functions, which can adapt to a wide range of scenarios and work well in practice because they circumvent assumptions about causal mechanisms and data distributions. Despite these advantages, kernel-based generalized score functions pose serious computational challenges in time and space, with a time complexity of $\\mathcal{O}(n^3)$ and a memory complexity of $\\mathcal{O}(n^2)$, where $n$ is the sample size. In this paper, we propose an approximate kernel-based generalized score function with $\\mathcal{O}(n)$ time and space complexities by using low-rank technique and designing a set of rules to handle the complex composite matrix operations required to calculate the score, as well as developing sampling algorithms for different data types to benefit the handling of diverse data types efficiently. Our extensive causal discovery experiments on both synthetic and real-world data demonstrate that compared to the state-of-the-art method, our method can not only significantly reduce computational costs, but also achieve comparable accuracy, especially for large datasets.", "date": "2024-12-23", "categories": []}
{"id": "2506.05120", "title": "Nonlinear Causal Discovery for Grouped Data", "abstract": "Inferring cause-effect relationships from observational data has gained significant attention in recent years, but most methods are limited to scalar random variables. In many important domains, including neuroscience, psychology, social science, and industrial manufacturing, the causal units of interest are groups of variables rather than individual scalar measurements. Motivated by these applications, we extend nonlinear additive noise models to handle random vectors, establishing a two-step approach for causal graph learning: First, infer the causal order among random vectors. Second, perform model selection to identify the best graph consistent with this order. We introduce effective and novel solutions for both steps in the vector case, demonstrating strong performance in simulations. Finally, we apply our method to real-world assembly line data with partial knowledge of causal ordering among variable groups.", "date": "2025-06-05", "categories": []}
{"id": "2506.03068", "title": "Causal Explainability of Machine Learning in Heart Failure Prediction from Electronic Health Records", "abstract": "The importance of clinical variables in the prognosis of the disease is explained using statistical correlation or machine learning (ML). However, the predictive importance of these variables may not represent their causal relationships with diseases. This paper uses clinical variables from a heart failure (HF) patient cohort to investigate the causal explainability of important variables obtained in statistical and ML contexts. Due to inherent regression modeling, popular causal discovery methods strictly assume that the cause and effect variables are numerical and continuous. This paper proposes a new computational framework to enable causal structure discovery (CSD) and score the causal strength of mixed-type (categorical, numerical, binary) clinical variables for binary disease outcomes. In HF classification, we investigate the association between the importance rank order of three feature types: correlated features, features important for ML predictions, and causal features. Our results demonstrate that CSD modeling for nonlinear causal relationships is more meaningful than its linear counterparts. Feature importance obtained from nonlinear classifiers (e.g., gradient-boosting trees) strongly correlates with the causal strength of variables without differentiating cause and effect variables. Correlated variables can be causal for HF, but they are rarely identified as effect variables. These results can be used to add the causal explanation of variables important for ML-based prediction modeling.", "date": "2025-06-03", "categories": []}
{"id": "2412.13667", "title": "Exploring Multi-Modal Data with Tool-Augmented LLM Agents for Precise Causal Discovery", "abstract": "Causal discovery is an imperative foundation for decision-making across domains, such as smart health, AI for drug discovery and AIOps. Traditional statistical causal discovery methods, while well-established, predominantly rely on observational data and often overlook the semantic cues inherent in cause-and-effect relationships. The advent of Large Language Models (LLMs) has ushered in an affordable way of leveraging the semantic cues for knowledge-driven causal discovery, but the development of LLMs for causal discovery lags behind other areas, particularly in the exploration of multi-modal data. To bridge the gap, we introduce MATMCD, a multi-agent system powered by tool-augmented LLMs. MATMCD has two key agents: a Data Augmentation agent that retrieves and processes modality-augmented data, and a Causal Constraint agent that integrates multi-modal data for knowledge-driven reasoning. The proposed design of the inner-workings ensures successful cooperation of the agents. Our empirical study across seven datasets suggests the significant potential of multi-modality enhanced causal discovery.", "date": "2024-12-18", "categories": []}
{"id": "2506.00402", "title": "Causal Structure Discovery for Error Diagnostics of Children's ASR", "abstract": "Children's automatic speech recognition (ASR) often underperforms compared to that of adults due to a confluence of interdependent factors: physiological (e.g., smaller vocal tracts), cognitive (e.g., underdeveloped pronunciation), and extrinsic (e.g., vocabulary limitations, background noise). Existing analysis methods examine the impact of these factors in isolation, neglecting interdependencies-such as age affecting ASR accuracy both directly and indirectly via pronunciation skills. In this paper, we introduce a causal structure discovery to unravel these interdependent relationships among physiology, cognition, extrinsic factors, and ASR errors. Then, we employ causal quantification to measure each factor's impact on children's ASR. We extend the analysis to fine-tuned models to identify which factors are mitigated by fine-tuning and which remain largely unaffected. Experiments on Whisper and Wav2Vec2.0 demonstrate the generalizability of our findings across different ASR systems.", "date": "2025-05-31", "categories": []}
{"id": "2506.00844", "title": "LLM Cannot Discover Causality, and Should Be Restricted to Non-Decisional Support in Causal Discovery", "abstract": "This paper critically re-evaluates LLMs' role in causal discovery and argues against their direct involvement in determining causal relationships. We demonstrate that LLMs' autoregressive, correlation-driven modeling inherently lacks the theoretical grounding for causal reasoning and introduces unreliability when used as priors in causal discovery algorithms. Through empirical studies, we expose the limitations of existing LLM-based methods and reveal that deliberate prompt engineering (e.g., injecting ground-truth knowledge) could overstate their performance, helping to explain the consistently favorable results reported in much of the current literature. Based on these findings, we strictly confined LLMs' role to a non-decisional auxiliary capacity: LLMs should not participate in determining the existence or directionality of causal relationships, but can assist the search process for causal graphs (e.g., LLM-based heuristic search). Experiments across various settings confirm that, by strictly isolating LLMs from causal decision-making, LLM-guided heuristic search can accelerate the convergence and outperform both traditional and LLM-based methods in causal structure learning. We conclude with a call for the community to shift focus from naively applying LLMs to developing specialized models and training method that respect the core principles of causal discovery.", "date": "2025-06-01", "categories": []}
{"id": "2506.01361", "title": "TimeGraph: Synthetic Benchmark Datasets for Robust Time-Series Causal Discovery", "abstract": "Robust causal discovery in time series datasets depends on reliable benchmark datasets with known ground-truth causal relationships. However, such datasets remain scarce, and existing synthetic alternatives often overlook critical temporal properties inherent in real-world data, including nonstationarity driven by trends and seasonality, irregular sampling intervals, and the presence of unobserved confounders. To address these challenges, we introduce TimeGraph, a comprehensive suite of synthetic time-series benchmark datasets that systematically incorporates both linear and nonlinear dependencies while modeling key temporal characteristics such as trends, seasonal effects, and heterogeneous noise patterns. Each dataset is accompanied by a fully specified causal graph featuring varying densities and diverse noise distributions and is provided in two versions: one including unobserved confounders and one without, thereby offering extensive coverage of real-world complexity while preserving methodological neutrality. We further demonstrate the utility of TimeGraph through systematic evaluations of state-of-the-art causal discovery algorithms including PCMCI+, LPCMCI, and FGES across a diverse array of configurations and metrics. Our experiments reveal significant variations in algorithmic performance under realistic temporal conditions, underscoring the need for robust synthetic benchmarks in the fair and transparent assessment of causal discovery methods. The complete TimeGraph suite, including dataset generation scripts, evaluation metrics, and recommended experimental protocols, is freely available to facilitate reproducible research and foster community-driven advancements in time-series causal discovery.", "date": "2025-06-02", "categories": []}
{"id": "2408.13448", "title": "Reinforcement Learning for Causal Discovery without Acyclicity Constraints", "abstract": "Recently, reinforcement learning (RL) has proved a promising alternative for conventional local heuristics in score-based approaches to learning directed acyclic causal graphs (DAGs) from observational data. However, the intricate acyclicity constraint still challenges the efficient exploration of the vast space of DAGs in existing methods. In this study, we introduce ALIAS (reinforced dAg Learning wIthout Acyclicity conStraints), a novel approach to causal discovery powered by the RL machinery. Our method features an efficient policy for generating DAGs in just a single step with an optimal quadratic complexity, fueled by a novel parametrization of DAGs that directly translates a continuous space to the space of all DAGs, bypassing the need for explicitly enforcing acyclicity constraints. This approach enables us to navigate the search space more effectively by utilizing policy gradient methods and established scoring functions. In addition, we provide compelling empirical evidence for the strong performance of ALIAS in comparison with state-of-the-arts in causal discovery over increasingly difficult experiment conditions on both synthetic and real datasets.", "date": "2024-08-24", "categories": []}
{"id": "2410.03380", "title": "Identifying biological perturbation targets through causal differential networks", "abstract": "Identifying variables responsible for changes to a biological system enables applications in drug target discovery and cell engineering. Given a pair of observational and interventional datasets, the goal is to isolate the subset of observed variables that were the targets of the intervention. Directly applying causal discovery algorithms is challenging: the data may contain thousands of variables with as few as tens of samples per intervention, and biological systems do not adhere to classical causality assumptions. We propose a causality-inspired approach to address this practical setting. First, we infer noisy causal graphs from the observational and interventional data. Then, we learn to map the differences between these graphs, along with additional statistical features, to sets of variables that were intervened upon. Both modules are jointly trained in a supervised framework, on simulated and real data that reflect the nature of biological interventions. This approach consistently outperforms baselines for perturbation modeling on seven single-cell transcriptomics datasets. We also demonstrate significant improvements over current causal discovery methods for predicting soft and hard intervention targets across a variety of synthetic data.", "date": "2024-10-04", "categories": []}
{"id": "2501.02333", "title": "On The Causal Network Of Face-selective Regions In Human Brain During Movie Watching", "abstract": "Understanding the causal interactions in some brain tasks, such as face processing, remains a challenging and ambiguous process for researchers. In this study, we address this issue by employing a novel causal discovery method -Directed Acyclic Graphs via M-matrices for Acyclicity (DAGMA)- to investigate the causal structure of the brain's face-selective network and gain deeper insights into its mechanism. Using fMRI data of natural movie stimuli, we extract causal network of face-selective regions and analyze how frames containing faces influence this network. Specifically, our findings reveal that the presence of faces in the stimuli, causally affects the number of identified connections within the network. Additionally, our results highlight the crucial role of subcortical regions in satisfying causal sufficiency, emphasizing it's importance in causal studies of brain. This study provides a new perspective on understanding the causal architecture of the face-selective network of the brain, motivating further research on neural causality.", "date": "2025-01-04", "categories": []}
{"id": "2505.23944", "title": "Retrieval Augmented Generation based Large Language Models for Causality Mining", "abstract": "Causality detection and mining are important tasks in information retrieval due to their enormous use in information extraction, and knowledge graph construction. To solve these tasks, in existing literature there exist several solutions -- both unsupervised and supervised. However, the unsupervised methods suffer from poor performance and they often require significant human intervention for causal rule selection, leading to poor generalization across different domains. On the other hand, supervised methods suffer from the lack of large training datasets. Recently, large language models (LLMs) with effective prompt engineering are found to be effective to overcome the issue of unavailability of large training dataset. Yet, in existing literature, there does not exist comprehensive works on causality detection and mining using LLM prompting. In this paper, we present several retrieval-augmented generation (RAG) based dynamic prompting schemes to enhance LLM performance in causality detection and extraction tasks. Extensive experiments over three datasets and five LLMs validate the superiority of our proposed RAG-based dynamic prompting over other static prompting schemes.", "date": "2025-05-29", "categories": []}
{"id": "2409.15219", "title": "MotifDisco: Motif Causal Discovery For Time Series Motifs", "abstract": "Many time series, particularly health data streams, can be best understood as a sequence of phenomenon or events, which we call \\textit{motifs}. A time series motif is a short trace segment which may implicitly capture an underlying phenomenon within the time series. Specifically, we focus on glucose traces collected from continuous glucose monitors (CGMs), which inherently contain motifs representing underlying human behaviors such as eating and exercise. The ability to identify and quantify \\textit{causal} relationships amongst motifs can provide a mechanism to better understand and represent these patterns, useful for improving deep learning and generative models and for advanced technology development (e.g., personalized coaching and artificial insulin delivery systems). However, no previous work has developed causal discovery methods for time series motifs. Therefore, in this paper we develop MotifDisco (\\textbf{motif} \\textbf{disco}very of causality), a novel causal discovery framework to learn causal relations amongst motifs from time series traces. We formalize a notion of \\textit{Motif Causality (MC)}, inspired from Granger Causality and Transfer Entropy, and develop a Graph Neural Network-based framework that learns causality between motifs by solving an unsupervised link prediction problem. We integrate MC with three model use cases of forecasting, anomaly detection and clustering, to showcase the use of MC as a building block for downstream tasks. Finally, we evaluate our framework on different health data streams and find that Motif Causality provides a significant performance improvement in all use cases.", "date": "2024-09-23", "categories": []}
{"id": "2503.08245", "title": "ExMAG: Learning of Maximally Ancestral Graphs", "abstract": "In mixed graphs, there are both directed and undirected edges. An extension of acyclicity to this mixed-graph setting is known as maximally ancestral graphs. This extension is of considerable interest in causal learning in the presence of confounders. There, directed edges represent a clear direction of causality, while undirected edges represent confounding. We propose a score-based branch-and-cut algorithm for learning maximally ancestral graphs. The algorithm produces more accurate results than state-of-the-art methods, while being faster to run on small and medium-sized synthetic instances.", "date": "2025-03-11", "categories": []}
{"id": "2505.15866", "title": "Multi-omic Causal Discovery using Genotypes and Gene Expression", "abstract": "Causal discovery in multi-omic datasets is crucial for understanding the bigger picture of gene regulatory mechanisms, but remains challenging due to high dimensionality, differentiation of direct from indirect relationships, and hidden confounders. We introduce GENESIS (GEne Network inference from Expression SIgnals and SNPs), a constraint-based algorithm that leverages the natural causal precedence of genotypes to infer ancestral relationships in transcriptomic data. Unlike traditional causal discovery methods that start with a fully connected graph, GENESIS initialises an empty ancestrality matrix and iteratively populates it with direct, indirect or non-causal relationships using a series of provably sound marginal and conditional independence tests. By integrating genotypes as fixed causal anchors, GENESIS provides a principled ``head start'' to classical causal discovery algorithms, restricting the search space to biologically plausible edges. We test GENESIS on synthetic and real-world genomic datasets. This framework offers a powerful avenue for uncovering causal pathways in complex traits, with promising applications to functional genomics, drug discovery, and precision medicine.", "date": "2025-05-21", "categories": []}
{"id": "2505.14828", "title": "Deep Koopman operator framework for causal discovery in nonlinear dynamical systems", "abstract": "We use a deep Koopman operator-theoretic formalism to develop a novel causal discovery algorithm, Kausal. Causal discovery aims to identify cause-effect mechanisms for better scientific understanding, explainable decision-making, and more accurate modeling. Standard statistical frameworks, such as Granger causality, lack the ability to quantify causal relationships in nonlinear dynamics due to the presence of complex feedback mechanisms, timescale mixing, and nonstationarity. This presents a challenge in studying many real-world systems, such as the Earth's climate. Meanwhile, Koopman operator methods have emerged as a promising tool for approximating nonlinear dynamics in a linear space of observables. In Kausal, we propose to leverage this powerful idea for causal analysis where optimal observables are inferred using deep learning. Causal estimates are then evaluated in a reproducing kernel Hilbert space, and defined as the distance between the marginal dynamics of the effect and the joint dynamics of the cause-effect observables. Our numerical experiments demonstrate Kausal's superior ability in discovering and characterizing causal signals compared to existing approaches of prescribed observables. Lastly, we extend our analysis to observations of El Ni\\~no-Southern Oscillation highlighting our algorithm's applicability to real-world phenomena. Our code is available at https://github.com/juannat7/kausal.", "date": "2025-05-20", "categories": []}
{"id": "2505.14396", "title": "Causal Cartographer: From Mapping to Reasoning Over Counterfactual Worlds", "abstract": "Causal world models are systems that can answer counterfactual questions about an environment of interest, i.e. predict how it would have evolved if an arbitrary subset of events had been realized differently. It requires understanding the underlying causes behind chains of events and conducting causal inference for arbitrary unseen distributions. So far, this task eludes foundation models, notably large language models (LLMs), which do not have demonstrated causal reasoning capabilities beyond the memorization of existing causal relationships. Furthermore, evaluating counterfactuals in real-world applications is challenging since only the factual world is observed, limiting evaluation to synthetic datasets. We address these problems by explicitly extracting and modeling causal relationships and propose the Causal Cartographer framework. First, we introduce a graph retrieval-augmented generation agent tasked to retrieve causal relationships from data. This approach allows us to construct a large network of real-world causal relationships that can serve as a repository of causal knowledge and build real-world counterfactuals. In addition, we create a counterfactual reasoning agent constrained by causal relationships to perform reliable step-by-step causal inference. We show that our approach can extract causal knowledge and improve the robustness of LLMs for causal reasoning tasks while reducing inference costs and spurious correlations.", "date": "2025-05-20", "categories": []}
{"id": "2308.15395", "title": "The CausalBench challenge: A machine learning contest for gene network inference from single-cell perturbation data", "abstract": "In drug discovery, mapping interactions between genes within cellular systems is a crucial early step. Such maps are not only foundational for understanding the molecular mechanisms underlying disease biology but also pivotal for formulating hypotheses about potential targets for new medicines. Recognizing the need to elevate the construction of these gene-gene interaction networks, especially from large-scale, real-world datasets of perturbed single cells, the CausalBench Challenge was initiated. This challenge aimed to inspire the machine learning community to enhance state-of-the-art methods, emphasizing better utilization of expansive genetic perturbation data. Using the framework provided by the CausalBench benchmark, participants were tasked with refining the current methodologies or proposing new ones. This report provides an analysis and summary of the methods submitted during the challenge to give a partial image of the state of the art at the time of the challenge. Notably, the winning solutions significantly improved performance compared to previous baselines, establishing a new state of the art for this critical task in biology and medicine.", "date": "2023-08-29", "categories": []}
{"id": "2405.18314", "title": "Deriving Causal Order from Single-Variable Interventions: Guarantees & Algorithm", "abstract": "Targeted and uniform interventions to a system are crucial for unveiling causal relationships. While several methods have been developed to leverage interventional data for causal structure learning, their practical application in real-world scenarios often remains challenging. Recent benchmark studies have highlighted these difficulties, even when large numbers of single-variable intervention samples are available. In this work, we demonstrate, both theoretically and empirically, that such datasets contain a wealth of causal information that can be effectively extracted under realistic assumptions about the data distribution. More specifically, we introduce a novel variant of interventional faithfulness, which relies on comparisons between the marginal distributions of each variable across observational and interventional settings, and we introduce a score on causal orders. Under this assumption, we are able to prove strong theoretical guarantees on the optimum of our score that also hold for large-scale settings. To empirically verify our theory, we introduce Intersort, an algorithm designed to infer the causal order from datasets containing large numbers of single-variable interventions by approximately optimizing our score. Intersort outperforms baselines (GIES, DCDI, PC and EASE) on almost all simulated data settings replicating common benchmarks in the field. Our proposed novel approach to modeling interventional datasets thus offers a promising avenue for advancing causal inference, highlighting significant potential for further enhancements under realistic assumptions.", "date": "2024-05-28", "categories": []}
{"id": "2412.02878", "title": "Modeling and Discovering Direct Causes for Predictive Models", "abstract": "We introduce a causal modeling framework that captures the input-output behavior of predictive models (e.g., machine learning models). The framework enables us to identify features that directly cause the predictions, which has broad implications for data collection and model evaluation. We then present sound and complete algorithms for discovering direct causes (from data) under some assumptions. Furthermore, we propose a novel independence rule that can be integrated with the algorithms to accelerate the discovery process, as we demonstrate both theoretically and empirically.", "date": "2024-12-03", "categories": []}
{"id": "2402.01454", "title": "Integrating Large Language Models in Causal Discovery: A Statistical Causal Approach", "abstract": "In practical statistical causal discovery (SCD), embedding domain expert knowledge as constraints into the algorithm is important for reasonable causal models reflecting the broad knowledge of domain experts, despite the challenges in the systematic acquisition of background knowledge. To overcome these challenges, this paper proposes a novel method for causal inference, in which SCD and knowledge-based causal inference (KBCI) with a large language model (LLM) are synthesized through ``statistical causal prompting (SCP)'' for LLMs and prior knowledge augmentation for SCD. The experiments in this work have revealed that the results of LLM-KBCI and SCD augmented with LLM-KBCI approach the ground truths, more than the SCD result without prior knowledge. These experiments have also revealed that the SCD result can be further improved if the LLM undergoes SCP. Furthermore, with an unpublished real-world dataset, we have demonstrated that the background knowledge provided by the LLM can improve the SCD on this dataset, even if this dataset has never been included in the training data of the LLM. For future practical application of this proposed method across important domains such as healthcare, we also thoroughly discuss the limitations, risks of critical errors, expected improvement of techniques around LLMs, and realistic integration of expert checks of the results into this automatic process, with SCP simulations under various conditions both in successful and failure scenarios. The careful and appropriate application of the proposed approach in this work, with improvement and customization for each domain, can thus address challenges such as dataset biases and limitations, illustrating the potential of LLMs to improve data-driven causal inference across diverse scientific domains.\n  The code used in this work is publicly available at: www.github.com/mas-takayama/LLM-and-SCD", "date": "2024-02-02", "categories": []}
{"id": "2412.19507", "title": "Hybrid Local Causal Discovery", "abstract": "Local causal discovery aims to learn and distinguish the direct causes and effects of a target variable from observed data. Existing constraint-based local causal discovery methods use AND or OR rules in constructing the local causal skeleton, but using either rule alone is prone to produce cascading errors in the learned local causal skeleton, and thus impacting the inference of local causal relationships. On the other hand, directly applying score-based global causal discovery methods to local causal discovery may randomly return incorrect results due to the existence of local equivalence classes. To address the above issues, we propose a Hybrid Local Causal Discovery algorithm, called HLCD. Specifically, HLCD initially utilizes a constraint-based approach combined with the OR rule to obtain a candidate skeleton and then employs a score-based method to eliminate redundant portions in the candidate skeleton. Furthermore, during the local causal orientation phase, HLCD distinguishes between V-structures and equivalence classes by comparing the local structure scores between the two, thereby avoiding orientation interference caused by local equivalence classes. We conducted extensive experiments with seven state-of-the-art competitors on 14 benchmark Bayesian network datasets, and the experimental results demonstrate that HLCD significantly outperforms existing local causal discovery algorithms.", "date": "2024-12-27", "categories": []}
{"id": "2505.06542", "title": "dcFCI: Robust Causal Discovery Under Latent Confounding, Unfaithfulness, and Mixed Data", "abstract": "Causal discovery is central to inferring causal relationships from observational data. In the presence of latent confounding, algorithms such as Fast Causal Inference (FCI) learn a Partial Ancestral Graph (PAG) representing the true model's Markov Equivalence Class. However, their correctness critically depends on empirical faithfulness, the assumption that observed (in)dependencies perfectly reflect those of the underlying causal model, which often fails in practice due to limited sample sizes. To address this, we introduce the first nonparametric score to assess a PAG's compatibility with observed data, even with mixed variable types. This score is both necessary and sufficient to characterize structural uncertainty and distinguish between distinct PAGs. We then propose data-compatible FCI (dcFCI), the first hybrid causal discovery algorithm to jointly address latent confounding, empirical unfaithfulness, and mixed data types. dcFCI integrates our score into an (Anytime)FCI-guided search that systematically explores, ranks, and validates candidate PAGs. Experiments on synthetic and real-world scenarios demonstrate that dcFCI significantly outperforms state-of-the-art methods, often recovering the true PAG even in small and heterogeneous datasets. Examining top-ranked PAGs further provides valuable insights into structural uncertainty, supporting more robust and informed causal reasoning and decision-making.", "date": "2025-05-10", "categories": []}
{"id": "2504.03122", "title": "From Observation to Orientation: an Adaptive Integer Programming Approach to Intervention Design", "abstract": "Using both observational and experimental data, a causal discovery process can identify the causal relationships between variables. A unique adaptive intervention design paradigm is presented in this work, where causal directed acyclic graphs (DAGs) are for effectively recovered with practical budgetary considerations. In order to choose treatments that optimize information gain under these considerations, an iterative integer programming (IP) approach is proposed, which drastically reduces the number of experiments required. Simulations over a broad range of graph sizes and edge densities are used to assess the effectiveness of the suggested approach. Results show that the proposed adaptive IP approach achieves full causal graph recovery with fewer intervention iterations and variable manipulations than random intervention baselines, and it is also flexible enough to accommodate a variety of practical constraints.", "date": "2025-04-04", "categories": []}
{"id": "2504.21261", "title": "Multi-Domain Causal Discovery in Bijective Causal Models", "abstract": "  We consider the problem of causal discovery (a.k.a., causal structure\nlearning) in a multi-domain setting. We assume that the causal functions are\ninvariant across the domains, while the distribution of the exogenous noise may\nvary. Under causal sufficiency (i.e., no confounders exist), we show that the\ncausal diagram can be discovered under less restrictive functional assumptions\ncompared to previous work. What enables causal discovery in this setting is\nbijective generation mechanisms (BGM), which ensures that the functional\nrelation between the exogenous noise $E$ and the endogenous variable $Y$ is\nbijective and differentiable in both directions at every level of the cause\nvariable $X = x$. BGM generalizes a variety of models including additive noise\nmodel, LiNGAM, post-nonlinear model, and location-scale noise model. Further,\nwe derive a statistical test to find the parents set of the target variable.\nExperiments on various synthetic and real-world datasets validate our\ntheoretical findings.\n", "date": "2025-04-30", "categories": []}
{"id": "2409.08295", "title": "Higher order definition of causality by optimally conditioned transfer\n  entropy", "abstract": "  The description of the dynamics of complex systems, in particular the capture\nof the interaction structure and causal relationships between elements of the\nsystem, is one of the central questions of interdisciplinary research. While\nthe characterization of pairwise causal interactions is a relatively ripe field\nwith established theoretical concepts and the current focus is on technical\nissues of their efficient estimation, it turns out that the standard concepts\nsuch as Granger causality or transfer entropy may not faithfully reflect\npossible synergies or interactions of higher orders, phenomena highly relevant\nfor many real-world complex systems. In this paper, we propose a generalization\nand refinement of the information-theoretic approach to causal inference,\nenabling the description of truly multivariate, rather than multiple pairwise,\ncausal interactions, and moving thus from causal networks to causal\nhypernetworks. In particular, while keeping the ability to control for\nmediating variables or common causes, in case of purely synergetic interactions\nsuch as the exclusive disjunction, it ascribes the causal role to the\nmultivariate causal set but \\emph{not} to individual inputs, distinguishing it\nthus from the case of e.g. two additive univariate causes. We demonstrate this\nconcept by application to illustrative theoretical examples as well as a\nbiophysically realistic simulation of biological neuronal dynamics recently\nreported to employ synergetic computations.\n", "date": "2024-08-30", "categories": []}
{"id": "2504.20172", "title": "Causal Identification in Time Series Models", "abstract": "  In this paper, we analyze the applicability of the Causal Identification\nalgorithm to causal time series graphs with latent confounders. Since these\ngraphs extend over infinitely many time steps, deciding whether causal effects\nacross arbitrary time intervals are identifiable appears to require computation\non graph segments of unbounded size. Even for deciding the identifiability of\nintervention effects on variables that are close in time, no bound is known on\nhow many time steps in the past need to be considered. We give a first bound of\nthis kind that only depends on the number of variables per time step and the\nmaximum time lag of any direct or latent causal effect. More generally, we show\nthat applying the Causal Identification algorithm to a constant-size segment of\nthe time series graph is sufficient to decide identifiability of causal\neffects, even across unbounded time intervals.\n", "date": "2025-04-28", "categories": []}
{"id": "2411.06990", "title": "Causal-discovery-based root-cause analysis and its application in\n  time-series prediction error diagnosis", "abstract": "  Recent rapid advancements of machine learning have greatly enhanced the\naccuracy of prediction models, but most models remain \"black boxes\", making\nprediction error diagnosis challenging, especially with outliers. This lack of\ntransparency hinders trust and reliability in industrial applications.\nHeuristic attribution methods, while helpful, often fail to capture true causal\nrelationships, leading to inaccurate error attributions. Various root-cause\nanalysis methods have been developed using Shapley values, yet they typically\nrequire predefined causal graphs, limiting their applicability for prediction\nerrors in machine learning models. To address these limitations, we introduce\nthe Causal-Discovery-based Root-Cause Analysis (CD-RCA) method that estimates\ncausal relationships between the prediction error and the explanatory\nvariables, without needing a pre-defined causal graph. By simulating synthetic\nerror data, CD-RCA can identify variable contributions to outliers in\nprediction errors by Shapley values. Extensive experiments show CD-RCA\noutperforms current heuristic attribution methods.\n", "date": "2024-11-11", "categories": []}
{"id": "2402.14781", "title": "Effective Bayesian Causal Inference via Structural Marginalisation and\n  Autoregressive Orders", "abstract": "  The traditional two-stage approach to causal inference first identifies a\nsingle causal model (or equivalence class of models), which is then used to\nanswer causal queries. However, this neglects any epistemic model uncertainty.\nIn contrast, Bayesian causal inference does incorporate epistemic uncertainty\ninto query estimates via Bayesian marginalisation (posterior averaging) over\nall causal models. While principled, this marginalisation over entire causal\nmodels, i.e., both causal structures (graphs) and mechanisms, poses a\ntremendous computational challenge. In this work, we address this challenge by\ndecomposing structure marginalisation into the marginalisation over (i) causal\norders and (ii) directed acyclic graphs (DAGs) given an order. We can\nmarginalise the latter in closed form by limiting the number of parents per\nvariable and utilising Gaussian processes to model mechanisms. To marginalise\nover orders, we use a sampling-based approximation, for which we devise a novel\nauto-regressive distribution over causal orders (ARCO). Our method outperforms\nstate-of-the-art in structure learning on simulated non-linear additive noise\nbenchmarks, and yields competitive results on real-world data. Furthermore, we\ncan accurately infer interventional distributions and average causal effects.\n", "date": "2024-02-22", "categories": []}
{"id": "2410.06407", "title": "A Skewness-Based Criterion for Addressing Heteroscedastic Noise in\n  Causal Discovery", "abstract": "  Real-world data often violates the equal-variance assumption\n(homoscedasticity), making it essential to account for heteroscedastic noise in\ncausal discovery. In this work, we explore heteroscedastic symmetric noise\nmodels (HSNMs), where the effect $Y$ is modeled as $Y = f(X) + \\sigma(X)N$,\nwith $X$ as the cause and $N$ as independent noise following a symmetric\ndistribution. We introduce a novel criterion for identifying HSNMs based on the\nskewness of the score (i.e., the gradient of the log density) of the data\ndistribution. This criterion establishes a computationally tractable\nmeasurement that is zero in the causal direction but nonzero in the anticausal\ndirection, enabling the causal direction discovery. We extend this\nskewness-based criterion to the multivariate setting and propose SkewScore, an\nalgorithm that handles heteroscedastic noise without requiring the extraction\nof exogenous noise. We also conduct a case study on the robustness of SkewScore\nin a bivariate model with a latent confounder, providing theoretical insights\ninto its performance. Empirical studies further validate the effectiveness of\nthe proposed method.\n", "date": "2024-10-08", "categories": []}
{"id": "2504.13263", "title": "Causal-Copilot: An Autonomous Causal Analysis Agent", "abstract": "  Causal analysis plays a foundational role in scientific discovery and\nreliable decision-making, yet it remains largely inaccessible to domain experts\ndue to its conceptual and algorithmic complexity. This disconnect between\ncausal methodology and practical usability presents a dual challenge: domain\nexperts are unable to leverage recent advances in causal learning, while causal\nresearchers lack broad, real-world deployment to test and refine their methods.\nTo address this, we introduce Causal-Copilot, an autonomous agent that\noperationalizes expert-level causal analysis within a large language model\nframework. Causal-Copilot automates the full pipeline of causal analysis for\nboth tabular and time-series data -- including causal discovery, causal\ninference, algorithm selection, hyperparameter optimization, result\ninterpretation, and generation of actionable insights. It supports interactive\nrefinement through natural language, lowering the barrier for non-specialists\nwhile preserving methodological rigor. By integrating over 20 state-of-the-art\ncausal analysis techniques, our system fosters a virtuous cycle -- expanding\naccess to advanced causal methods for domain experts while generating rich,\nreal-world applications that inform and advance causal theory. Empirical\nevaluations demonstrate that Causal-Copilot achieves superior performance\ncompared to existing baselines, offering a reliable, scalable, and extensible\nsolution that bridges the gap between theoretical sophistication and real-world\napplicability in causal analysis. A live interactive demo of Causal-Copilot is\navailable at https://causalcopilot.com/.\n", "date": "2025-04-17", "categories": []}
{"id": "2504.14937", "title": "Causal DAG Summarization (Full Version)", "abstract": "  Causal inference aids researchers in discovering cause-and-effect\nrelationships, leading to scientific insights. Accurate causal estimation\nrequires identifying confounding variables to avoid false discoveries. Pearl's\ncausal model uses causal DAGs to identify confounding variables, but incorrect\nDAGs can lead to unreliable causal conclusions. However, for high dimensional\ndata, the causal DAGs are often complex beyond human verifiability. Graph\nsummarization is a logical next step, but current methods for general-purpose\ngraph summarization are inadequate for causal DAG summarization. This paper\naddresses these challenges by proposing a causal graph summarization objective\nthat balances graph simplification for better understanding while retaining\nessential causal information for reliable inference. We develop an efficient\ngreedy algorithm and show that summary causal DAGs can be directly used for\ninference and are more robust to misspecification of assumptions, enhancing\nrobustness for causal inference. Experimenting with six real-life datasets, we\ncompared our algorithm to three existing solutions, showing its effectiveness\nin handling high-dimensional data and its ability to generate summary DAGs that\nensure both reliable causal inference and robustness against misspecifications.\n", "date": "2025-04-21", "categories": []}
{"id": "2405.01744", "title": "ALCM: Autonomous LLM-Augmented Causal Discovery Framework", "abstract": "  To perform effective causal inference in high-dimensional datasets,\ninitiating the process with causal discovery is imperative, wherein a causal\ngraph is generated based on observational data. However, obtaining a complete\nand accurate causal graph poses a formidable challenge, recognized as an NP-\nhard problem. Recently, the advent of Large Language Models (LLMs) has ushered\nin a new era, indicating their emergent capabilities and widespread\napplicability in facilitating causal reasoning across diverse domains, such as\nmedicine, finance, and science. The expansive knowledge base of LLMs holds the\npotential to elevate the field of causal reasoning by offering\ninterpretability, making inferences, generalizability, and uncovering novel\ncausal structures. In this paper, we introduce a new framework, named\nAutonomous LLM-Augmented Causal Discovery Framework (ALCM), to synergize\ndata-driven causal discovery algorithms and LLMs, automating the generation of\na more resilient, accurate, and explicable causal graph. The ALCM consists of\nthree integral components: causal structure learning, causal wrapper, and\nLLM-driven causal refiner. These components autonomously collaborate within a\ndynamic environment to address causal discovery questions and deliver plausible\ncausal graphs. We evaluate the ALCM framework by implementing two\ndemonstrations on seven well-known datasets. Experimental results demonstrate\nthat ALCM outperforms existing LLM methods and conventional data-driven causal\nreasoning mechanisms. This study not only shows the effectiveness of the ALCM\nbut also underscores new research directions in leveraging the causal reasoning\ncapabilities of LLMs.\n", "date": "2024-05-02", "categories": []}
{"id": "2410.13054", "title": "Systems with Switching Causal Relations: A Meta-Causal Perspective", "abstract": "  Most work on causality in machine learning assumes that causal relationships\nare driven by a constant underlying process. However, the flexibility of\nagents' actions or tipping points in the environmental process can change the\nqualitative dynamics of the system. As a result, new causal relationships may\nemerge, while existing ones change or disappear, resulting in an altered causal\ngraph. To analyze these qualitative changes on the causal graph, we propose the\nconcept of meta-causal states, which groups classical causal models into\nclusters based on equivalent qualitative behavior and consolidates specific\nmechanism parameterizations. We demonstrate how meta-causal states can be\ninferred from observed agent behavior, and discuss potential methods for\ndisentangling these states from unlabeled data. Finally, we direct our analysis\ntowards the application of a dynamical system, showing that meta-causal states\ncan also emerge from inherent system dynamics, and thus constitute more than a\ncontext-dependent framework in which mechanisms emerge only as a result of\nexternal factors.\n", "date": "2024-10-16", "categories": []}
{"id": "2504.12594", "title": "Meta-Dependence in Conditional Independence Testing", "abstract": "  Constraint-based causal discovery algorithms utilize many statistical tests\nfor conditional independence to uncover networks of causal dependencies. These\napproaches to causal discovery rely on an assumed correspondence between the\ngraphical properties of a causal structure and the conditional independence\nproperties of observed variables, known as the causal Markov condition and\nfaithfulness. Finite data yields an empirical distribution that is \"close\" to\nthe actual distribution. Across these many possible empirical distributions,\nthe correspondence to the graphical properties can break down for different\nconditional independencies, and multiple violations can occur at the same time.\nWe study this \"meta-dependence\" between conditional independence properties\nusing the following geometric intuition: each conditional independence property\nconstrains the space of possible joint distributions to a manifold. The\n\"meta-dependence\" between conditional independences is informed by the position\nof these manifolds relative to the true probability distribution. We provide a\nsimple-to-compute measure of this meta-dependence using information projections\nand consolidate our findings empirically using both synthetic and real-world\ndata.\n", "date": "2025-04-17", "categories": []}
{"id": "2406.16899", "title": "Prompting or Fine-tuning? Exploring Large Language Models for Causal\n  Graph Validation", "abstract": "  This study explores the capability of Large Language Models (LLMs) to\nevaluate causality in causal graphs generated by conventional statistical\ncausal discovery methods-a task traditionally reliant on manual assessment by\nhuman subject matter experts. To bridge this gap in causality assessment, LLMs\nare employed to evaluate the causal relationships by determining whether a\ncausal connection between variable pairs can be inferred from textual context.\nOur study compares two approaches: (1) prompting-based method for zero-shot and\nfew-shot causal inference and, (2) fine-tuning language models for the causal\nrelation prediction task. While prompt-based LLMs have demonstrated versatility\nacross various NLP tasks, our experiments on biomedical and general-domain\ndatasets show that fine-tuned models consistently outperform them, achieving up\nto a 20.5-point improvement in F1 score-even when using smaller-parameter\nlanguage models. These findings provide valuable insights into the strengths\nand limitations of both approaches for causal graph evaluation.\n", "date": "2024-05-29", "categories": []}
{"id": "2504.10936", "title": "Can LLMs Leverage Observational Data? Towards Data-Driven Causal\n  Discovery with LLMs", "abstract": "  Causal discovery traditionally relies on statistical methods applied to\nobservational data, often requiring large datasets and assumptions about\nunderlying causal structures. Recent advancements in Large Language Models\n(LLMs) have introduced new possibilities for causal discovery by providing\ndomain expert knowledge. However, it remains unclear whether LLMs can\neffectively process observational data for causal discovery. In this work, we\nexplore the potential of LLMs for data-driven causal discovery by integrating\nobservational data for LLM-based reasoning. Specifically, we examine whether\nLLMs can effectively utilize observational data through two prompting\nstrategies: pairwise prompting and breadth first search (BFS)-based prompting.\nIn both approaches, we incorporate the observational data directly into the\nprompt to assess LLMs' ability to infer causal relationships from such data.\nExperiments on benchmark datasets show that incorporating observational data\nenhances causal discovery, boosting F1 scores by up to 0.11 point using both\npairwise and BFS LLM-based prompting, while outperforming traditional\nstatistical causal discovery baseline by up to 0.52 points. Our findings\nhighlight the potential and limitations of LLMs for data-driven causal\ndiscovery, demonstrating their ability to move beyond textual metadata and\neffectively interpret and utilize observational data for more informed causal\nreasoning. Our studies lays the groundwork for future advancements toward fully\nLLM-driven causal discovery.\n", "date": "2025-04-15", "categories": []}
{"id": "2504.10397", "title": "Can LLMs Assist Expert Elicitation for Probabilistic Causal Modeling?", "abstract": "  Objective: This study investigates the potential of Large Language Models\n(LLMs) as an alternative to human expert elicitation for extracting structured\ncausal knowledge and facilitating causal modeling in biometric and healthcare\napplications.\n  Material and Methods: LLM-generated causal structures, specifically Bayesian\nnetworks (BNs), were benchmarked against traditional statistical methods (e.g.,\nBayesian Information Criterion) using healthcare datasets. Validation\ntechniques included structural equation modeling (SEM) to verifying\nrelationships, and measures such as entropy, predictive accuracy, and\nrobustness to compare network structures.\n  Results and Discussion: LLM-generated BNs demonstrated lower entropy than\nexpert-elicited and statistically generated BNs, suggesting higher confidence\nand precision in predictions. However, limitations such as contextual\nconstraints, hallucinated dependencies, and potential biases inherited from\ntraining data require further investigation.\n  Conclusion: LLMs represent a novel frontier in expert elicitation for\nprobabilistic causal modeling, promising to improve transparency and reduce\nuncertainty in the decision-making using such models.\n", "date": "2025-04-14", "categories": []}
{"id": "2504.07459", "title": "Beyond LLMs: A Linguistic Approach to Causal Graph Generation from\n  Narrative Texts", "abstract": "  We propose a novel framework for generating causal graphs from narrative\ntexts, bridging high-level causality and detailed event-specific relationships.\nOur method first extracts concise, agent-centered vertices using large language\nmodel (LLM)-based summarization. We introduce an \"Expert Index,\" comprising\nseven linguistically informed features, integrated into a\nSituation-Task-Action-Consequence (STAC) classification model. This hybrid\nsystem, combining RoBERTa embeddings with the Expert Index, achieves superior\nprecision in causal link identification compared to pure LLM-based approaches.\nFinally, a structured five-iteration prompting process refines and constructs\nconnected causal graphs. Experiments on 100 narrative chapters and short\nstories demonstrate that our approach consistently outperforms GPT-4o and\nClaude 3.5 in causal graph quality, while maintaining readability. The\nopen-source tool provides an interpretable, efficient solution for capturing\nnuanced causal chains in narratives.\n", "date": "2025-04-10", "categories": []}
{"id": "2209.14664", "title": "Causal inference in drug discovery and development", "abstract": "  To discover new drugs is to seek and to prove causality. As an emerging\napproach leveraging human knowledge and creativity, data, and machine\nintelligence, causal inference holds the promise of reducing cognitive bias and\nimproving decision making in drug discovery. While it has been applied across\nthe value chain, the concepts and practice of causal inference remain obscure\nto many practitioners. This article offers a non-technical introduction to\ncausal inference, reviews its recent applications, and discusses opportunities\nand challenges of adopting the causal language in drug discovery and\ndevelopment.\n", "date": "2022-09-29", "categories": []}
{"id": "2310.15117", "title": "Causal Order: The Key to Leveraging Imperfect Experts in Causal\n  Inference", "abstract": "  Large Language Models (LLMs) have been used as experts to infer causal\ngraphs, often by repeatedly applying a pairwise prompt that asks about the\ncausal relationship of each variable pair. However, such experts, including\nhuman domain experts, cannot distinguish between direct and indirect effects\ngiven a pairwise prompt. Therefore, instead of the graph, we propose that\ncausal order be used as a more stable output interface for utilizing expert\nknowledge. Even when querying a perfect expert with a pairwise prompt, we show\nthat the inferred graph can have significant errors whereas the causal order is\nalways correct. In practice, however, LLMs are imperfect experts and we find\nthat pairwise prompts lead to multiple cycles. Hence, we propose the triplet\nmethod, a novel querying strategy that introduces an auxiliary variable for\nevery variable pair and instructs the LLM to avoid cycles within this triplet.\nIt then uses a voting-based ensemble method that results in higher accuracy and\nfewer cycles while ensuring cost efficiency. Across multiple real-world graphs,\nsuch a triplet-based method yields a more accurate order than the pairwise\nprompt, using both LLMs and human annotators. The triplet method enhances\nrobustness by repeatedly querying an expert with different auxiliary variables,\nenabling smaller models like Phi-3 and Llama-3 8B Instruct to surpass GPT-4\nwith pairwise prompting. For practical usage, we show how the expert-provided\ncausal order from the triplet method can be used to reduce error in downstream\ngraph discovery and effect inference tasks.\n", "date": "2023-10-23", "categories": []}
{"id": "2504.01424", "title": "On the Role of Priors in Bayesian Causal Learning", "abstract": "  In this work, we investigate causal learning of independent causal mechanisms\nfrom a Bayesian perspective. Confirming previous claims from the literature, we\nshow in a didactically accessible manner that unlabeled data (i.e., cause\nrealizations) do not improve the estimation of the parameters defining the\nmechanism. Furthermore, we observe the importance of choosing an appropriate\nprior for the cause and mechanism parameters, respectively. Specifically, we\nshow that a factorized prior results in a factorized posterior, which resonates\nwith Janzing and Sch\\\"olkopf's definition of independent causal mechanisms via\nthe Kolmogorov complexity of the involved distributions and with the concept of\nparameter independence of Heckerman et al.\n", "date": "2025-04-02", "categories": []}
{"id": "2504.01740", "title": "Stable Structure Learning with HC-Stable and Tabu-Stable Algorithms", "abstract": "  Many Bayesian Network structure learning algorithms are unstable, with the\nlearned graph sensitive to arbitrary dataset artifacts, such as the ordering of\ncolumns (i.e., variable order). PC-Stable attempts to address this issue for\nthe widely-used PC algorithm, prompting researchers to use the \"stable\" version\ninstead. However, this problem seems to have been overlooked for score-based\nalgorithms. In this study, we show that some widely-used score-based\nalgorithms, as well as hybrid and constraint-based algorithms, including\nPC-Stable, suffer from the same issue. We propose a novel solution for\nscore-based greedy hill-climbing that eliminates instability by determining a\nstable node order, leading to consistent results regardless of variable\nordering. Two implementations, HC-Stable and Tabu-Stable, are introduced.\nTabu-Stable achieves the highest BIC scores across all networks, and the\nhighest accuracy for categorical networks. These results highlight the\nimportance of addressing instability in structure learning and provide a robust\nand practical approach for future applications. This extends the scope and\nimpact of our previous work presented at Probabilistic Graphical Models 2024 by\nincorporating continuous variables. The implementation, along with usage\ninstructions, is freely available on GitHub at\nhttps://github.com/causal-iq/discovery.\n", "date": "2025-04-02", "categories": []}
{"id": "2503.09194", "title": "Addressing pitfalls in implicit unobserved confounding synthesis using\n  explicit block hierarchical ancestral sampling", "abstract": "  Unbiased data synthesis is crucial for evaluating causal discovery algorithms\nin the presence of unobserved confounding, given the scarcity of real-world\ndatasets. A common approach, implicit parameterization, encodes unobserved\nconfounding by modifying the off-diagonal entries of the idiosyncratic\ncovariance matrix while preserving positive definiteness. Within this approach,\nwe identify that state-of-the-art protocols have two distinct issues that\nhinder unbiased sampling from the complete space of causal models: first, we\ngive a detailed analysis of use of diagonally dominant constructions restricts\nthe spectrum of partial correlation matrices; and second, the restriction of\npossible graphical structures when sampling bidirected edges, unnecessarily\nruling out valid causal models. To address these limitations, we propose an\nimproved explicit modeling approach for unobserved confounding, leveraging\nblock-hierarchical ancestral generation of ground truth causal graphs.\nAlgorithms for converting the ground truth DAG into ancestral graph is provided\nso that the output of causal discovery algorithms could be compared with. We\ndraw connections between implicit and explicit parameterization, prove that our\napproach fully covers the space of causal models, including those generated by\nthe implicit parameterization, thus enabling more robust evaluation of methods\nfor causal discovery and inference.\n", "date": "2025-03-12", "categories": []}
{"id": "2402.01929", "title": "Sample, estimate, aggregate: A recipe for causal discovery foundation\n  models", "abstract": "  Causal discovery, the task of inferring causal structure from data, has the\npotential to uncover mechanistic insights from biological experiments,\nespecially those involving perturbations. However, causal discovery algorithms\nover larger sets of variables tend to be brittle against misspecification or\nwhen data are limited. For example, single-cell transcriptomics measures\nthousands of genes, but the nature of their relationships is not known, and\nthere may be as few as tens of cells per intervention setting. To mitigate\nthese challenges, we propose a foundation model-inspired approach: a supervised\nmodel trained on large-scale, synthetic data to predict causal graphs from\nsummary statistics -- like the outputs of classical causal discovery algorithms\nrun over subsets of variables and other statistical hints like inverse\ncovariance. Our approach is enabled by the observation that typical errors in\nthe outputs of a discovery algorithm remain comparable across datasets.\nTheoretically, we show that the model architecture is well-specified, in the\nsense that it can recover a causal graph consistent with graphs over subsets.\nEmpirically, we train the model to be robust to misspecification and\ndistribution shift using diverse datasets. Experiments on biological and\nsynthetic data confirm that this model generalizes well beyond its training\nset, runs on graphs with hundreds of variables in seconds, and can be easily\nadapted to different underlying data assumptions.\n", "date": "2024-02-02", "categories": []}
{"id": "2412.04981", "title": "Causal discovery with endogenous context variables", "abstract": "  Causal systems often exhibit variations of the underlying causal mechanisms\nbetween the variables of the system. Often, these changes are driven by\ndifferent environments or internal states in which the system operates, and we\nrefer to context variables as those variables that indicate this change in\ncausal mechanisms. An example are the causal relations in soil\nmoisture-temperature interactions and their dependence on soil moisture\nregimes: Dry soil triggers a dependence of soil moisture on latent heat, while\nenvironments with wet soil do not feature such a feedback, making it a\ncontext-specific property. Crucially, a regime or context variable such as soil\nmoisture need not be exogenous and can be influenced by the dynamical system\nvariables - precipitation can make a dry soil wet - leading to joint systems\nwith endogenous context variables. In this work we investigate the assumptions\nfor constraint-based causal discovery of context-specific information in\nsystems with endogenous context variables. We show that naive approaches such\nas learning different regime graphs on masked data, or pooling all data, can\nlead to uninformative results. We propose an adaptive constraint-based\ndiscovery algorithm and give a detailed discussion on the connection to\nstructural causal models, including sufficiency assumptions, which allow to\nprove the soundness of our algorithm and to interpret the results causally.\nNumerical experiments demonstrate the performance of the proposed method over\nalternative baselines, but they also unveil current limitations of our method.\n", "date": "2024-12-06", "categories": []}
{"id": "2503.19218", "title": "Analytic DAG Constraints for Differentiable DAG Learning", "abstract": "  Recovering the underlying Directed Acyclic Graph (DAG) structures from\nobservational data presents a formidable challenge, partly due to the\ncombinatorial nature of the DAG-constrained optimization problem. Recently,\nresearchers have identified gradient vanishing as one of the primary obstacles\nin differentiable DAG learning and have proposed several DAG constraints to\nmitigate this issue. By developing the necessary theory to establish a\nconnection between analytic functions and DAG constraints, we demonstrate that\nanalytic functions from the set $\\{f(x) = c_0 + \\sum_{i=1}^{\\infty}c_ix^i |\n\\forall i > 0, c_i > 0; r = \\lim_{i\\rightarrow \\infty}c_{i}/c_{i+1} > 0\\}$ can\nbe employed to formulate effective DAG constraints. Furthermore, we establish\nthat this set of functions is closed under several functional operators,\nincluding differentiation, summation, and multiplication. Consequently, these\noperators can be leveraged to create novel DAG constraints based on existing\nones. Using these properties, we design a series of DAG constraints and develop\nan efficient algorithm to evaluate them. Experiments in various settings\ndemonstrate that our DAG constraints outperform previous state-of-the-art\ncomparators. Our implementation is available at\nhttps://github.com/zzhang1987/AnalyticDAGLearning.\n", "date": "2025-03-24", "categories": []}
{"id": "2306.04777", "title": "Invariant Causal Set Covering Machines", "abstract": "  Rule-based models, such as decision trees, appeal to practitioners due to\ntheir interpretable nature. However, the learning algorithms that produce such\nmodels are often vulnerable to spurious associations and thus, they are not\nguaranteed to extract causally-relevant insights. In this work, we build on\nideas from the invariant causal prediction literature to propose Invariant\nCausal Set Covering Machines, an extension of the classical Set Covering\nMachine algorithm for conjunctions/disjunctions of binary-valued rules that\nprovably avoids spurious associations. We demonstrate both theoretically and\nempirically that our method can identify the causal parents of a variable of\ninterest in polynomial time.\n", "date": "2023-06-07", "categories": []}
{"id": "2407.18755", "title": "Score matching through the roof: linear, nonlinear, and latent variables\n  causal discovery", "abstract": "  Causal discovery from observational data holds great promise, but existing\nmethods rely on strong assumptions about the underlying causal structure, often\nrequiring full observability of all relevant variables. We tackle these\nchallenges by leveraging the score function $\\nabla \\log p(X)$ of observed\nvariables for causal discovery and propose the following contributions. First,\nwe fine-tune the existing identifiability results with the score on additive\nnoise models, showing that their assumption of nonlinearity of the causal\nmechanisms is not necessary. Second, we establish conditions for inferring\ncausal relations from the score even in the presence of hidden variables; this\nresult is two-faced: we demonstrate the score's potential to infer the\nequivalence class of causal graphs with hidden variables (while previous\nresults are restricted to the fully observable setting), and we provide\nsufficient conditions for identifying direct causes in latent variable models.\nBuilding on these insights, we propose a flexible algorithm suited for causal\ndiscovery on linear, nonlinear, and latent variable models, which we\nempirically validate.\n", "date": "2024-07-26", "categories": []}
{"id": "2503.17452", "title": "CausalRivers -- Scaling up benchmarking of causal discovery for\n  real-world time-series", "abstract": "  Causal discovery, or identifying causal relationships from observational\ndata, is a notoriously challenging task, with numerous methods proposed to\ntackle it. Despite this, in-the-wild evaluation of these methods is still\nlacking, as works frequently rely on synthetic data evaluation and sparse\nreal-world examples under critical theoretical assumptions. Real-world causal\nstructures, however, are often complex, making it hard to decide on a proper\ncausal discovery strategy. To bridge this gap, we introduce CausalRivers, the\nlargest in-the-wild causal discovery benchmarking kit for time-series data to\ndate. CausalRivers features an extensive dataset on river discharge that covers\nthe eastern German territory (666 measurement stations) and the state of\nBavaria (494 measurement stations). It spans the years 2019 to 2023 with a\n15-minute temporal resolution. Further, we provide additional data from a flood\naround the Elbe River, as an event with a pronounced distributional shift.\nLeveraging multiple sources of information and time-series meta-data, we\nconstructed two distinct causal ground truth graphs (Bavaria and eastern\nGermany). These graphs can be sampled to generate thousands of subgraphs to\nbenchmark causal discovery across diverse and challenging settings. To\ndemonstrate the utility of CausalRivers, we evaluate several causal discovery\napproaches through a set of experiments to identify areas for improvement.\nCausalRivers has the potential to facilitate robust evaluations and comparisons\nof causal discovery methods. Besides this primary purpose, we also expect that\nthis dataset will be relevant for connected areas of research, such as\ntime-series forecasting and anomaly detection. Based on this, we hope to push\nbenchmark-driven method development that fosters advanced techniques for causal\ndiscovery, as is the case for many other areas of machine learning.\n", "date": "2025-03-21", "categories": []}
{"id": "2503.17569", "title": "Fairness-Driven LLM-based Causal Discovery with Active Learning and\n  Dynamic Scoring", "abstract": "  Causal discovery (CD) plays a pivotal role in numerous scientific fields by\nclarifying the causal relationships that underlie phenomena observed in diverse\ndisciplines. Despite significant advancements in CD algorithms that enhance\nbias and fairness analyses in machine learning, their application faces\nchallenges due to the high computational demands and complexities of\nlarge-scale data. This paper introduces a framework that leverages Large\nLanguage Models (LLMs) for CD, utilizing a metadata-based approach akin to the\nreasoning processes of human experts. By shifting from pairwise queries to a\nmore scalable breadth-first search (BFS) strategy, the number of required\nqueries is reduced from quadratic to linear in terms of variable count, thereby\naddressing scalability concerns inherent in previous approaches. This method\nutilizes an Active Learning (AL) and a Dynamic Scoring Mechanism that\nprioritizes queries based on their potential information gain, combining mutual\ninformation, partial correlation, and LLM confidence scores to refine the\ncausal graph more efficiently and accurately. This BFS query strategy reduces\nthe required number of queries significantly, thereby addressing scalability\nconcerns inherent in previous approaches. This study provides a more scalable\nand efficient solution for leveraging LLMs in fairness-driven CD, highlighting\nthe effects of the different parameters on performance. We perform fairness\nanalyses on the inferred causal graphs, identifying direct and indirect effects\nof sensitive attributes on outcomes. A comparison of these analyses against\nthose from graphs produced by baseline methods highlights the importance of\naccurate causal graph construction in understanding bias and ensuring fairness\nin machine learning systems.\n", "date": "2025-03-21", "categories": []}
{"id": "2502.04210", "title": "Algorithmic causal structure emerging through compression", "abstract": "  We explore the relationship between causality, symmetry, and compression. We\nbuild on and generalize the known connection between learning and compression\nto a setting where causal models are not identifiable. We propose a framework\nwhere causality emerges as a consequence of compressing data across multiple\nenvironments. We define algorithmic causality as an alternative definition of\ncausality when traditional assumptions for causal identifiability do not hold.\nWe demonstrate how algorithmic causal and symmetric structures can emerge from\nminimizing upper bounds on Kolmogorov complexity, without knowledge of\nintervention targets. We hypothesize that these insights may also provide a\nnovel perspective on the emergence of causality in machine learning models,\nsuch as large language models, where causal relationships may not be explicitly\nidentifiable.\n", "date": "2025-02-06", "categories": []}
{"id": "2503.17055", "title": "Data-Driven Optimization of EV Charging Station Placement Using Causal\n  Discovery", "abstract": "  This paper addresses the critical challenge of optimizing electric vehicle\ncharging station placement through a novel data-driven methodology employing\ncausal discovery techniques. While traditional approaches prioritize economic\nfactors or power grid constraints, they often neglect empirical charging\npatterns that ultimately determine station utilization. We analyze extensive\ncharging data from Palo Alto and Boulder (337,344 events across 100 stations)\nto uncover latent relationships between station characteristics and\nutilization. Applying structural learning algorithms (NOTEARS and DAGMA) to\nthis data reveals that charging demand is primarily determined by three\nfactors: proximity to amenities, EV registration density, and adjacency to\nhigh-traffic routes. These findings, consistent across multiple algorithms and\nurban contexts, challenge conventional infrastructure distribution strategies.\nWe develop an optimization framework that translates these insights into\nactionable placement recommendations, identifying locations likely to\nexperience high utilization based on the discovered dependency structures. The\nresulting site selection model prioritizes strategic clustering in high-amenity\nareas with substantial EV populations rather than uniform spatial distribution.\nOur approach contributes a framework that integrates empirical charging\nbehavior into infrastructure planning, potentially enhancing both station\nutilization and user convenience. By focusing on data-driven insights instead\nof theoretical distribution models, we provide a more effective strategy for\nexpanding charging networks that can adjust to various stages of EV market\ndevelopment.\n", "date": "2025-03-21", "categories": []}
{"id": "2410.19464", "title": "LOCAL: Learning with Orientation Matrix to Infer Causal Structure from\n  Time Series Data", "abstract": "  Discovering the underlying Directed Acyclic Graph (DAG) from time series\nobservational data is highly challenging due to the dynamic nature and complex\nnonlinear interactions between variables. Existing methods typically search for\nthe optimal DAG by optimizing an objective function but face scalability\nchallenges, as their computational demands grow exponentially with the\ndimensional expansion of variables. To this end, we propose LOCAL, a highly\nefficient, easy-to-implement, and constraint-free method for recovering dynamic\ncausal structures. LOCAL is the first attempt to formulate a quasi-maximum\nlikelihood-based score function for learning the dynamic DAG equivalent to the\nground truth. Building on this, we introduce two adaptive modules that enhance\nthe algebraic characterization of acyclicity: Asymptotic Causal Mask Learning\n(ACML) and Dynamic Graph Parameter Learning (DGPL). ACML constructs causal\nmasks using learnable priority vectors and the Gumbel-Sigmoid function,\nensuring DAG formation while optimizing computational efficiency. DGPL\ntransforms causal learning into decomposed matrix products, capturing dynamic\ncausal structure in high-dimensional data and improving interpretability.\nExtensive experiments on synthetic and real-world datasets demonstrate that\nLOCAL significantly outperforms existing methods and highlight LOCAL's\npotential as a robust and efficient method for dynamic causal discovery.\n", "date": "2024-10-25", "categories": []}
{"id": "2503.15580", "title": "How Well Can AI Build SD Models?", "abstract": "  Introduction: As system dynamics (SD) embraces automation, AI offers\nefficiency but risks bias from missing data and flawed models. Models that omit\nmultiple perspectives and data threaten model quality, whether created by\nhumans or with the assistance of AI. To reduce uncertainty about how well AI\ncan build SD models, we introduce two metrics for evaluation of AI-generated\ncausal maps: technical correctness (causal translation) and adherence to\ninstructions (conformance).\n  Approach: We developed an open source project called sd-ai to provide a basis\nfor collaboration in the SD community, aiming to fully harness the potential of\nAI based tools like ChatGPT for dynamic modeling. Additionally, we created an\nevaluation theory along with a comprehensive suite of tests designed to\nevaluate any such tools developed within the sd-ai ecosystem.\n  Results: We tested 11 different LLMs on their ability to do causal\ntranslation as well as conform to user instruction. gpt-4.5-preview was the top\nperformer, scoring 92.9% overall, excelling in both tasks. o1 scored 100% in\ncausal translation. gpt-4o identified all causal links but struggled with\npositive polarity in decreasing terms. While gpt-4.5-preview and o1 are most\naccurate, gpt-4o is the cheapest.\n  Discussion: Causal translation and conformance tests applied to the sd-ai\nengine reveal significant variations across lLLMs, underscoring the need for\ncontinued evaluation to ensure responsible development of AI tools for dynamic\nmodeling. To address this, an open collaboration among tool developers,\nmodelers, and stakeholders is launched to standardize measures for evaluating\nthe capacity of AI tools to improve the modeling process.\n", "date": "2025-03-19", "categories": []}
{"id": "2503.15436", "title": "An extensive simulation study evaluating the interaction of resampling\n  techniques across multiple causal discovery contexts", "abstract": "  Despite the accelerating presence of exploratory causal analysis in modern\nscience and medicine, the available non-experimental methods for validating\ncausal models are not well characterized. One of the most popular methods is to\nevaluate the stability of model features after resampling the data, similar to\nresampling methods for estimating confidence intervals in statistics. Many\naspects of this approach have received little to no attention, however, such as\nwhether the choice of resampling method should depend on the sample size,\nalgorithms being used, or algorithm tuning parameters. We present theoretical\nresults proving that certain resampling methods closely emulate the assignment\nof specific values to algorithm tuning parameters. We also report the results\nof extensive simulation experiments, which verify the theoretical result and\nprovide substantial data to aid researchers in further characterizing\nresampling in the context of causal discovery analysis. Together, the\ntheoretical work and simulation results provide specific guidance on how\nresampling methods and tuning parameters should be selected in practice.\n", "date": "2025-03-19", "categories": []}
{"id": "2404.17644", "title": "A Conditional Independence Test in the Presence of Discretization", "abstract": "  Testing conditional independence has many applications, such as in Bayesian\nnetwork learning and causal discovery. Different test methods have been\nproposed. However, existing methods generally can not work when only\ndiscretized observations are available. Specifically, consider $X_1$,\n$\\tilde{X}_2$ and $X_3$ are observed variables, where $\\tilde{X}_2$ is a\ndiscretization of latent variables $X_2$. Applying existing test methods to the\nobservations of $X_1$, $\\tilde{X}_2$ and $X_3$ can lead to a false conclusion\nabout the underlying conditional independence of variables $X_1$, $X_2$ and\n$X_3$. Motivated by this, we propose a conditional independence test\nspecifically designed to accommodate the presence of such discretization. To\nachieve this, we design the bridge equations to recover the parameter\nreflecting the statistical information of the underlying latent continuous\nvariables. An appropriate test statistic and its asymptotic distribution under\nthe null hypothesis of conditional independence have also been derived. Both\ntheoretical results and empirical validation have been provided, demonstrating\nthe effectiveness of our test methods.\n", "date": "2024-04-26", "categories": []}
{"id": "2503.13833", "title": "Causal Discovery from Data Assisted by Large Language Models", "abstract": "  Knowledge driven discovery of novel materials necessitates the development of\nthe causal models for the property emergence. While in classical physical\nparadigm the causal relationships are deduced based on the physical principles\nor via experiment, rapid accumulation of observational data necessitates\nlearning causal relationships between dissimilar aspects of materials structure\nand functionalities based on observations. For this, it is essential to\nintegrate experimental data with prior domain knowledge. Here we demonstrate\nthis approach by combining high-resolution scanning transmission electron\nmicroscopy (STEM) data with insights derived from large language models (LLMs).\nBy fine-tuning ChatGPT on domain-specific literature, such as arXiv papers on\nferroelectrics, and combining obtained information with data-driven causal\ndiscovery, we construct adjacency matrices for Directed Acyclic Graphs (DAGs)\nthat map the causal relationships between structural, chemical, and\npolarization degrees of freedom in Sm-doped BiFeO3 (SmBFO). This approach\nenables us to hypothesize how synthesis conditions influence material\nproperties, particularly the coercive field (E0), and guides experimental\nvalidation. The ultimate objective of this work is to develop a unified\nframework that integrates LLM-driven literature analysis with data-driven\ndiscovery, facilitating the precise engineering of ferroelectric materials by\nestablishing clear connections between synthesis conditions and their resulting\nmaterial properties.\n", "date": "2025-03-18", "categories": []}
{"id": "2406.11601", "title": "Standardizing Structural Causal Models", "abstract": "  Synthetic datasets generated by structural causal models (SCMs) are commonly\nused for benchmarking causal structure learning algorithms. However, the\nvariances and pairwise correlations in SCM data tend to increase along the\ncausal ordering. Several popular algorithms exploit these artifacts, possibly\nleading to conclusions that do not generalize to real-world settings. Existing\nmetrics like $\\operatorname{Var}$-sortability and\n$\\operatorname{R^2}$-sortability quantify these patterns, but they do not\nprovide tools to remedy them. To address this, we propose\ninternally-standardized structural causal models (iSCMs), a modification of\nSCMs that introduces a standardization operation at each variable during the\ngenerative process. By construction, iSCMs are not\n$\\operatorname{Var}$-sortable. We also find empirical evidence that they are\nmostly not $\\operatorname{R^2}$-sortable for commonly-used graph families.\nMoreover, contrary to the post-hoc standardization of data generated by\nstandard SCMs, we prove that linear iSCMs are less identifiable from prior\nknowledge on the weights and do not collapse to deterministic relationships in\nlarge systems, which may make iSCMs a useful model in causal inference beyond\nthe benchmarking problem studied here. Our code is publicly available at:\nhttps://github.com/werkaaa/iscm.\n", "date": "2024-06-17", "categories": []}
{"id": "2503.09859", "title": "An Asymmetric Independence Model for Causal Discovery on Path Spaces", "abstract": "  We develop the theory linking 'E-separation' in directed mixed graphs (DMGs)\nwith conditional independence relations among coordinate processes in\nstochastic differential equations (SDEs), where causal relationships are\ndetermined by \"which variables enter the governing equation of which other\nvariables\". We prove a global Markov property for cyclic SDEs, which naturally\nextends to partially observed cyclic SDEs, because our asymmetric independence\nmodel is closed under marginalization. We then characterize the class of graphs\nthat encode the same set of independence relations, yielding a result analogous\nto the seminal 'same skeleton and v-structures' result for directed acyclic\ngraphs (DAGs). In the fully observed case, we show that each such equivalence\nclass of graphs has a greatest element as a parsimonious representation and\ndevelop algorithms to identify this greatest element from data. We conjecture\nthat a greatest element also exists under partial observations, which we verify\ncomputationally for graphs with up to four nodes.\n", "date": "2025-03-12", "categories": []}
{"id": "2502.17030", "title": "Your Assumed DAG is Wrong and Here's How To Deal With It", "abstract": "  Assuming a directed acyclic graph (DAG) that represents prior knowledge of\ncausal relationships between variables is a common starting point for\ncause-effect estimation. Existing literature typically invokes hypothetical\ndomain expert knowledge or causal discovery algorithms to justify this\nassumption. In practice, neither may propose a single DAG with high confidence.\nDomain experts are hesitant to rule out dependencies with certainty or have\nongoing disputes about relationships; causal discovery often relies on\nuntestable assumptions itself or only provides an equivalence class of DAGs and\nis commonly sensitive to hyperparameter and threshold choices. We propose an\nefficient, gradient-based optimization method that provides bounds for causal\nqueries over a collection of causal graphs -- compatible with imperfect prior\nknowledge -- that may still be too large for exhaustive enumeration. Our bounds\nachieve good coverage and sharpness for causal queries such as average\ntreatment effects in linear and non-linear synthetic settings as well as on\nreal-world data. Our approach aims at providing an easy-to-use and widely\napplicable rebuttal to the valid critique of `What if your assumed DAG is\nwrong?'.\n", "date": "2025-02-24", "categories": []}
{"id": "2503.06395", "title": "Causal Discovery and Inference towards Urban Elements and Associated\n  Factors", "abstract": "  To uncover the city's fundamental functioning mechanisms, it is important to\nacquire a deep understanding of complicated relationships among citizens,\nlocation, and mobility behaviors. Previous research studies have applied direct\ncorrelation analysis to investigate such relationships. Nevertheless, due to\nthe ubiquitous confounding effects, empirical correlation analysis may not\naccurately reflect underlying causal relationships among basic urban elements.\nIn this paper, we propose a novel urban causal computing framework to\ncomprehensively explore causalities and confounding effects among a variety of\nfactors across different types of urban elements. In particular, we design a\nreinforcement learning algorithm to discover the potential causal graph, which\ndepicts the causal relations between urban factors. The causal graph further\nserves as the guidance for estimating causal effects between pair-wise urban\nfactors by propensity score matching. After removing the confounding effects\nfrom correlations, we leverage significance levels of causal effects in\ndownstream urban mobility prediction tasks. Experimental studies on open-source\nurban datasets show that the discovered causal graph demonstrates a\nhierarchical structure, where citizens affect locations, and they both cause\nchanges in urban mobility behaviors. Experimental results in urban mobility\nprediction tasks further show that the proposed method can effectively reduce\nconfounding effects and enhance performance of urban computing tasks.\n", "date": "2025-03-09", "categories": []}
{"id": "2503.07302", "title": "When Selection Meets Intervention: Additional Complexities in Causal\n  Discovery", "abstract": "  We address the common yet often-overlooked selection bias in interventional\nstudies, where subjects are selectively enrolled into experiments. For\ninstance, participants in a drug trial are usually patients of the relevant\ndisease; A/B tests on mobile applications target existing users only, and gene\nperturbation studies typically focus on specific cell types, such as cancer\ncells. Ignoring this bias leads to incorrect causal discovery results. Even\nwhen recognized, the existing paradigm for interventional causal discovery\nstill fails to address it. This is because subtle differences in when and where\ninterventions happen can lead to significantly different statistical patterns.\nWe capture this dynamic by introducing a graphical model that explicitly\naccounts for both the observed world (where interventions are applied) and the\ncounterfactual world (where selection occurs while interventions have not been\napplied). We characterize the Markov property of the model, and propose a\nprovably sound algorithm to identify causal relations as well as selection\nmechanisms up to the equivalence class, from data with soft interventions and\nunknown targets. Through synthetic and real-world experiments, we demonstrate\nthat our algorithm effectively identifies true causal relations despite the\npresence of selection bias.\n", "date": "2025-03-10", "categories": []}
{"id": "2503.07475", "title": "Sample Complexity of Nonparametric Closeness Testing for Continuous\n  Distributions and Its Application to Causal Discovery with Hidden Confounding", "abstract": "  We study the problem of closeness testing for continuous distributions and\nits implications for causal discovery. Specifically, we analyze the sample\ncomplexity of distinguishing whether two multidimensional continuous\ndistributions are identical or differ by at least $\\epsilon$ in terms of\nKullback-Leibler (KL) divergence under non-parametric assumptions. To this end,\nwe propose an estimator of KL divergence which is based on the von Mises\nexpansion. Our closeness test attains optimal parametric rates under smoothness\nassumptions. Equipped with this test, which serves as a building block of our\ncausal discovery algorithm to identify the causal structure between two\nmultidimensional random variables, we establish sample complexity guarantees\nfor our causal discovery method. To the best of our knowledge, this work is the\nfirst work that provides sample complexity guarantees for distinguishing cause\nand effect in multidimensional non-linear models with non-Gaussian continuous\nvariables in the presence of unobserved confounding.\n", "date": "2025-03-10", "categories": []}
{"id": "2503.04347", "title": "Large Language Models for Zero-shot Inference of Causal Structures in\n  Biology", "abstract": "  Genes, proteins and other biological entities influence one another via\ncausal molecular networks. Causal relationships in such networks are mediated\nby complex and diverse mechanisms, through latent variables, and are often\nspecific to cellular context. It remains challenging to characterise such\nnetworks in practice. Here, we present a novel framework to evaluate large\nlanguage models (LLMs) for zero-shot inference of causal relationships in\nbiology. In particular, we systematically evaluate causal claims obtained from\nan LLM using real-world interventional data. This is done over one hundred\nvariables and thousands of causal hypotheses. Furthermore, we consider several\nprompting and retrieval-augmentation strategies, including large, and\npotentially conflicting, collections of scientific articles. Our results show\nthat with tailored augmentation and prompting, even relatively small LLMs can\ncapture meaningful aspects of causal structure in biological systems. This\nsupports the notion that LLMs could act as orchestration tools in biological\ndiscovery, by helping to distil current knowledge in ways amenable to\ndownstream analysis. Our approach to assessing LLMs with respect to\nexperimental data is relevant for a broad range of problems at the intersection\nof causal learning, LLMs and scientific discovery.\n", "date": "2025-03-06", "categories": []}
{"id": "2412.16577", "title": "A Meta-Learning Approach to Bayesian Causal Discovery", "abstract": "  Discovering a unique causal structure is difficult due to both inherent\nidentifiability issues, and the consequences of finite data. As such,\nuncertainty over causal structures, such as those obtained from a Bayesian\nposterior, are often necessary for downstream tasks. Finding an accurate\napproximation to this posterior is challenging, due to the large number of\npossible causal graphs, as well as the difficulty in the subproblem of finding\nposteriors over the functional relationships of the causal edges. Recent works\nhave used meta-learning to view the problem of estimating the maximum\na-posteriori causal graph as supervised learning. Yet, these methods are\nlimited when estimating the full posterior as they fail to encode key\nproperties of the posterior, such as correlation between edges and permutation\nequivariance with respect to nodes. Further, these methods also cannot reliably\nsample from the posterior over causal structures. To address these limitations,\nwe propose a Bayesian meta learning model that allows for sampling causal\nstructures from the posterior and encodes these key properties. We compare our\nmeta-Bayesian causal discovery against existing Bayesian causal discovery\nmethods, demonstrating the advantages of directly learning a posterior over\ncausal structure.\n", "date": "2024-12-21", "categories": []}
{"id": "2406.06348", "title": "Causal Discovery over High-Dimensional Structured Hypothesis Spaces with\n  Causal Graph Partitioning", "abstract": "  The aim in many sciences is to understand the mechanisms that underlie the\nobserved distribution of variables, starting from a set of initial hypotheses.\nCausal discovery allows us to infer mechanisms as sets of cause and effect\nrelationships in a generalized way -- without necessarily tailoring to a\nspecific domain. Causal discovery algorithms search over a structured\nhypothesis space, defined by the set of directed acyclic graphs, to find the\ngraph that best explains the data. For high-dimensional problems, however, this\nsearch becomes intractable and scalable algorithms for causal discovery are\nneeded to bridge the gap. In this paper, we define a novel causal graph\npartition that allows for divide-and-conquer causal discovery with theoretical\nguarantees. We leverage the idea of a superstructure -- a set of learned or\nexisting candidate hypotheses -- to partition the search space. We prove under\ncertain assumptions that learning with a causal graph partition always yields\nthe Markov Equivalence Class of the true causal graph. We show our algorithm\nachieves comparable accuracy and a faster time to solution for\nbiologically-tuned synthetic networks and networks up to ${10^4}$ variables.\nThis makes our method applicable to gene regulatory network inference and other\ndomains with high-dimensional structured hypothesis spaces.\n", "date": "2024-06-10", "categories": []}
{"id": "2503.01139", "title": "Can Large Language Models Help Experimental Design for Causal Discovery?", "abstract": "  Designing proper experiments and selecting optimal intervention targets is a\nlongstanding problem in scientific or causal discovery. Identifying the\nunderlying causal structure from observational data alone is inherently\ndifficult. Obtaining interventional data, on the other hand, is crucial to\ncausal discovery, yet it is usually expensive and time-consuming to gather\nsufficient interventional data to facilitate causal discovery. Previous\napproaches commonly utilize uncertainty or gradient signals to determine the\nintervention targets. However, numerical-based approaches may yield suboptimal\nresults due to the inaccurate estimation of the guiding signals at the\nbeginning when with limited interventional data. In this work, we investigate a\ndifferent approach, whether we can leverage Large Language Models (LLMs) to\nassist with the intervention targeting in causal discovery by making use of the\nrich world knowledge about the experimental design in LLMs. Specifically, we\npresent Large Language Model Guided Intervention Targeting (LeGIT) -- a robust\nframework that effectively incorporates LLMs to augment existing numerical\napproaches for the intervention targeting in causal discovery. Across 4\nrealistic benchmark scales, LeGIT demonstrates significant improvements and\nrobustness over existing methods and even surpasses humans, which demonstrates\nthe usefulness of LLMs in assisting with experimental design for scientific\ndiscovery.\n", "date": "2025-03-03", "categories": []}
{"id": "2402.18477", "title": "Signature Kernel Conditional Independence Tests in Causal Discovery for\n  Stochastic Processes", "abstract": "  Inferring the causal structure underlying stochastic dynamical systems from\nobservational data holds great promise in domains ranging from science and\nhealth to finance. Such processes can often be accurately modeled via\nstochastic differential equations (SDEs), which naturally imply causal\nrelationships via \"which variables enter the differential of which other\nvariables\". In this paper, we develop conditional independence (CI) constraints\non coordinate processes over selected intervals that are Markov with respect to\nthe acyclic dependence graph (allowing self-loops) induced by a general SDE\nmodel. We then provide a sound and complete causal discovery algorithm, capable\nof handling both fully and partially observed data, and uniquely recovering the\nunderlying or induced ancestral graph by exploiting time directionality\nassuming a CI oracle. Finally, to make our algorithm practically usable, we\nalso propose a flexible, consistent signature kernel-based CI test to infer\nthese constraints from data. We extensively benchmark the CI test in isolation\nand as part of our causal discovery algorithms, outperforming existing\napproaches in SDE models and beyond.\n", "date": "2024-02-28", "categories": []}
{"id": "2502.20925", "title": "Amortized Conditional Independence Testing", "abstract": "  Testing for the conditional independence structure in data is a fundamental\nand critical task in statistics and machine learning, which finds natural\napplications in causal discovery - a highly relevant problem to many scientific\ndisciplines. Existing methods seek to design explicit test statistics that\nquantify the degree of conditional dependence, which is highly challenging yet\ncannot capture nor utilize prior knowledge in a data-driven manner. In this\nstudy, an entirely new approach is introduced, where we instead propose to\namortize conditional independence testing and devise ACID - a novel\ntransformer-based neural network architecture that learns to test for\nconditional independence. ACID can be trained on synthetic data in a supervised\nlearning fashion, and the learned model can then be applied to any dataset of\nsimilar natures or adapted to new domains by fine-tuning with a negligible\ncomputational cost. Our extensive empirical evaluations on both synthetic and\nreal data reveal that ACID consistently achieves state-of-the-art performance\nagainst existing baselines under multiple metrics, and is able to generalize\nrobustly to unseen sample sizes, dimensionalities, as well as non-linearities\nwith a remarkably low inference time.\n", "date": "2025-02-28", "categories": []}
{"id": "2404.11922", "title": "Redefining the Shortest Path Problem Formulation of the Linear\n  Non-Gaussian Acyclic Model: Pairwise Likelihood Ratios, Prior Knowledge, and\n  Path Enumeration", "abstract": "  Effective causal discovery is essential for learning the causal graph from\nobservational data. The linear non-Gaussian acyclic model (LiNGAM) operates\nunder the assumption of a linear data generating process with non-Gaussian\nnoise in determining the causal graph. Its assumption of unmeasured confounders\nbeing absent, however, poses practical limitations. In response, empirical\nresearch has shown that the reformulation of LiNGAM as a shortest path problem\n(LiNGAM-SPP) addresses this limitation. Within LiNGAM-SPP, mutual information\nis chosen to serve as the measure of independence. A challenge is introduced -\nparameter tuning is now needed due to its reliance on kNN mutual information\nestimators. The paper proposes a threefold enhancement to the LiNGAM-SPP\nframework.\n  First, the need for parameter tuning is eliminated by using the pairwise\nlikelihood ratio in lieu of kNN-based mutual information. This substitution is\nvalidated on a general data generating process and benchmark real-world data\nsets, outperforming existing methods especially when given a larger set of\nfeatures. The incorporation of prior knowledge is then enabled by a\nnode-skipping strategy implemented on the graph representation of all causal\norderings to eliminate violations based on the provided input of relative\norderings. Flexibility relative to existing approaches is achieved. Last among\nthe three enhancements is the utilization of the distribution of paths in the\ngraph representation of all causal orderings. From this, crucial properties of\nthe true causal graph such as the presence of unmeasured confounders and\nsparsity may be inferred. To some extent, the expected performance of the\ncausal discovery algorithm may be predicted. The refinements above advance the\npracticality and performance of LiNGAM-SPP, showcasing the potential of\ngraph-search-based methodologies in advancing causal discovery.\n", "date": "2024-04-18", "categories": []}
{"id": "2502.19551", "title": "Extremely Greedy Equivalence Search", "abstract": "  The goal of causal discovery is to learn a directed acyclic graph from data.\nOne of the most well-known methods for this problem is Greedy Equivalence\nSearch (GES). GES searches for the graph by incrementally and greedily adding\nor removing edges to maximize a model selection criterion. It has strong\ntheoretical guarantees on infinite data but can fail in practice on finite\ndata. In this paper, we first identify some of the causes of GES's failure,\nfinding that it can get blocked in local optima, especially in denser graphs.\nWe then propose eXtremely Greedy Equivalent Search (XGES), which involves a new\nheuristic to improve the search strategy of GES while retaining its theoretical\nguarantees. In particular, XGES favors deleting edges early in the search over\ninserting edges, which reduces the possibility of the search ending in local\noptima. A further contribution of this work is an efficient algorithmic\nformulation of XGES (and GES). We benchmark XGES on simulated datasets with\nknown ground truth. We find that XGES consistently outperforms GES in\nrecovering the correct graphs, and it is 10 times faster. XGES implementations\nin Python and C++ are available at https://github.com/ANazaret/XGES.\n", "date": "2025-02-26", "categories": []}
{"id": "2502.16056", "title": "Since Faithfulness Fails: The Performance Limits of Neural Causal\n  Discovery", "abstract": "  Neural causal discovery methods have recently improved in terms of\nscalability and computational efficiency. However, our systematic evaluation\nhighlights significant room for improvement in their accuracy when uncovering\ncausal structures. We identify a fundamental limitation: neural networks cannot\nreliably distinguish between existing and non-existing causal relationships in\nthe finite sample regime. Our experiments reveal that neural networks, as used\nin contemporary causal discovery approaches, lack the precision needed to\nrecover ground-truth graphs, even for small graphs and relatively large sample\nsizes. Furthermore, we identify the faithfulness property as a critical\nbottleneck: (i) it is likely to be violated across any reasonable dataset size\nrange, and (ii) its violation directly undermines the performance of neural\ndiscovery methods. These findings lead us to conclude that progress within the\ncurrent paradigm is fundamentally constrained, necessitating a paradigm shift\nin this domain.\n", "date": "2025-02-22", "categories": []}
{"id": "2502.07891", "title": "The Observational Partial Order of Causal Structures with Latent\n  Variables", "abstract": "  For two causal structures with the same set of visible variables, one is said\nto observationally dominate the other if the set of distributions over the\nvisible variables realizable by the first contains the set of distributions\nover the visible variables realizable by the second. Knowing such dominance\nrelations is useful for adjudicating between these structures given\nobservational data. We here consider the problem of determining the partial\norder of equivalence classes of causal structures with latent variables\nrelative to observational dominance. We provide a complete characterization of\nthe dominance order in the case of three visible variables, and a partial\ncharacterization in the case of four visible variables. Our techniques also\nhelp to identify which observational equivalence classes have a set of\nrealizable distributions that is characterized by nontrivial inequality\nconstraints, analogous to Bell inequalities and instrumental inequalities. We\nfind evidence that as one increases the number of visible variables, the\nequivalence classes satisfying nontrivial inequality constraints become\nubiquitous. (Because such classes are the ones for which there can be a\ndifference in the distributions that are quantumly and classically realizable,\nthis implies that the potential for quantum-classical gaps is also ubiquitous.)\nFurthermore, we find evidence that constraint-based causal discovery algorithms\nthat rely solely on conditional independence constraints have a significantly\nweaker distinguishing power among observational equivalence classes than\nalgorithms that go beyond these (i.e., algorithms that also leverage nested\nMarkov constraints and inequality constraints).\n", "date": "2025-02-11", "categories": []}
{"id": "2311.01412", "title": "Causal Temporal Regime Structure Learning", "abstract": "  Understanding causal relationships in multivariate time series is essential\nfor predicting and controlling dynamic systems in fields like economics,\nneuroscience, and climate science. However, existing causal discovery methods\noften assume stationarity, limiting their effectiveness when time series\nconsist of sequential regimes, consecutive temporal segments with unknown\nboundaries and changing causal structures. In this work, we firstly introduce a\nframework to describe and model such time series. Then, we present CASTOR, a\nnovel method that concurrently learns the Directed Acyclic Graph (DAG) for each\nregime while determining the number of regimes and their sequential\narrangement. CASTOR optimizes the data log-likelihood using an\nexpectation-maximization algorithm, alternating between assigning regime\nindices (expectation step) and inferring causal relationships in each regime\n(maximization step). We establish the identifiability of the regimes and DAGs\nwithin our framework. Extensive experiments show that CASTOR consistently\noutperforms existing causal discovery models in detecting different regimes and\nlearning their DAGs across various settings, including linear and nonlinear\ncausal relationships, on both synthetic and real world datasets.\n", "date": "2023-11-02", "categories": []}
{"id": "2406.09207", "title": "Investigating potential causes of Sepsis with Bayesian network structure\n  learning", "abstract": "  Sepsis is a life-threatening and serious global health issue. This study\ncombines knowledge with available hospital data to investigate the potential\ncauses of Sepsis that can be affected by policy decisions. We investigate the\nunderlying causal structure of this problem by combining clinical expertise\nwith score-based, constraint-based, and hybrid structure learning algorithms. A\nnovel approach to model averaging and knowledge-based constraints was\nimplemented to arrive at a consensus structure for causal inference. The\nstructure learning process highlighted the importance of exploring data-driven\napproaches alongside clinical expertise. This includes discovering unexpected,\nalthough reasonable, relationships from a clinical perspective. Hypothetical\ninterventions on Chronic Obstructive Pulmonary Disease, Alcohol dependence, and\nDiabetes suggest that the presence of any of these risk factors in patients\nincreases the likelihood of Sepsis. This finding, alongside measuring the\neffect of these risk factors on Sepsis, has potential policy implications.\nRecognising the importance of prediction in improving health outcomes related\nto Sepsis, the model is also assessed in its ability to predict Sepsis by\nevaluating accuracy, sensitivity, and specificity. These three indicators all\nhad results around 70%, and the AUC was 80%, which means the causal structure\nof the model is reasonably accurate given that the models were trained on data\navailable for commissioning purposes only.\n", "date": "2024-06-13", "categories": []}
{"id": "2410.15939", "title": "CausalGraph2LLM: Evaluating LLMs for Causal Queries", "abstract": "  Causality is essential in scientific research, enabling researchers to\ninterpret true relationships between variables. These causal relationships are\noften represented by causal graphs, which are directed acyclic graphs. With the\nrecent advancements in Large Language Models (LLMs), there is an increasing\ninterest in exploring their capabilities in causal reasoning and their\npotential use to hypothesize causal graphs. These tasks necessitate the LLMs to\nencode the causal graph effectively for subsequent downstream tasks. In this\npaper, we introduce CausalGraph2LLM, a comprehensive benchmark comprising over\n700k queries across diverse causal graph settings to evaluate the causal\nreasoning capabilities of LLMs. We categorize the causal queries into two\ntypes: graph-level and node-level queries. We benchmark both open-sourced and\npropriety models for our study. Our findings reveal that while LLMs show\npromise in this domain, they are highly sensitive to the encoding used. Even\ncapable models like GPT-4 and Gemini-1.5 exhibit sensitivity to encoding, with\ndeviations of about $60\\%$. We further demonstrate this sensitivity for\ndownstream causal intervention tasks. Moreover, we observe that LLMs can often\ndisplay biases when presented with contextual information about a causal graph,\npotentially stemming from their parametric memory.\n", "date": "2024-10-21", "categories": []}
{"id": "2502.12707", "title": "CausalMan: A physics-based simulator for large-scale causality", "abstract": "  A comprehensive understanding of causality is critical for navigating and\noperating within today's complex real-world systems. The absence of realistic\ncausal models with known data generating processes complicates fair\nbenchmarking. In this paper, we present the CausalMan simulator, modeled after\na real-world production line. The simulator features a diverse range of linear\nand non-linear mechanisms and challenging-to-predict behaviors, such as\ndiscrete mode changes. We demonstrate the inadequacy of many state-of-the-art\napproaches and analyze the significant differences in their performance and\ntractability, both in terms of runtime and memory complexity. As a\ncontribution, we will release the CausalMan large-scale simulator. We present\ntwo derived datasets, and perform an extensive evaluation of both.\n", "date": "2025-02-18", "categories": []}
{"id": "2502.13132", "title": "Learning to Defer for Causal Discovery with Imperfect Experts", "abstract": "  Integrating expert knowledge, e.g. from large language models, into causal\ndiscovery algorithms can be challenging when the knowledge is not guaranteed to\nbe correct. Expert recommendations may contradict data-driven results, and\ntheir reliability can vary significantly depending on the domain or specific\nquery. Existing methods based on soft constraints or inconsistencies in\npredicted causal relationships fail to account for these variations in\nexpertise. To remedy this, we propose L2D-CD, a method for gauging the\ncorrectness of expert recommendations and optimally combining them with\ndata-driven causal discovery results. By adapting learning-to-defer (L2D)\nalgorithms for pairwise causal discovery (CD), we learn a deferral function\nthat selects whether to rely on classical causal discovery methods using\nnumerical data or expert recommendations based on textual meta-data. We\nevaluate L2D-CD on the canonical T\\\"ubingen pairs dataset and demonstrate its\nsuperior performance compared to both the causal discovery method and the\nexpert used in isolation. Moreover, our approach identifies domains where the\nexpert's performance is strong or weak. Finally, we outline a strategy for\ngeneralizing this approach to causal discovery on graphs with more than two\nvariables, paving the way for further research in this area.\n", "date": "2025-02-18", "categories": []}
{"id": "2310.14691", "title": "Identifiability of total effects from abstractions of time series causal\n  graphs", "abstract": "  We study the problem of identifiability of the total effect of an\nintervention from observational time series in the situation, common in\npractice, where one only has access to abstractions of the true causal graph.\nWe consider here two abstractions: the extended summary causal graph, which\nconflates all lagged causal relations but distinguishes between lagged and\ninstantaneous relations, and the summary causal graph which does not give any\nindication about the lag between causal relations. We show that the total\neffect is always identifiable in extended summary causal graphs and provide\nsufficient conditions for identifiability in summary causal graphs. We\nfurthermore provide adjustment sets allowing to estimate the total effect\nwhenever it is identifiable.\n", "date": "2023-10-23", "categories": []}
{"id": "2402.11068", "title": "Large Language Models for Causal Discovery: Current Landscape and Future\n  Directions", "abstract": "  Causal discovery (CD) and Large Language Models (LLMs) have emerged as\ntransformative fields in artificial intelligence that have evolved largely\nindependently. While CD specializes in uncovering cause-effect relationships\nfrom data, and LLMs excel at natural language processing and generation, their\nintegration presents unique opportunities for advancing causal understanding.\nThis survey examines how LLMs are transforming CD across three key dimensions:\ndirect causal extraction from text, integration of domain knowledge into\nstatistical methods, and refinement of causal structures. We systematically\nanalyze approaches that leverage LLMs for CD tasks, highlighting their\ninnovative use of metadata and natural language for causal inference. Our\nanalysis reveals both LLMs' potential to enhance traditional CD methods and\ntheir current limitations as imperfect expert systems. We identify key research\ngaps, outline evaluation frameworks and benchmarks for LLM-based causal\ndiscovery, and advocate future research efforts for leveraging LLMs in\ncausality research. As the first comprehensive examination of the synergy\nbetween LLMs and CD, this work lays the groundwork for future advances in the\nfield.\n", "date": "2024-02-16", "categories": []}
{"id": "2411.01292", "title": "Causal reasoning in difference graphs", "abstract": "  Understanding causal mechanisms across different populations is essential for\ndesigning effective public health interventions. Recently, difference graphs\nhave been introduced as a tool to visually represent causal variations between\ntwo distinct populations. While there has been progress in inferring these\ngraphs from data through causal discovery methods, there remains a gap in\nsystematically leveraging their potential to enhance causal reasoning. This\npaper addresses that gap by establishing conditions for identifying causal\nchanges and effects using difference graphs. It specifically focuses on\nidentifying total causal changes and total effects in a nonparametric setting,\nas well as direct causal changes and direct effects in a linear setting. In\ndoing so, it provides a novel approach to causal reasoning that holds potential\nfor various public health applications.\n", "date": "2024-11-02", "categories": []}
{"id": "2502.10883", "title": "Learning Identifiable Structures Helps Avoid Bias in DNN-based\n  Supervised Causal Learning", "abstract": "  Causal discovery is a structured prediction task that aims to predict causal\nrelations among variables based on their data samples. Supervised Causal\nLearning (SCL) is an emerging paradigm in this field. Existing Deep Neural\nNetwork (DNN)-based methods commonly adopt the \"Node-Edge approach\", in which\nthe model first computes an embedding vector for each variable-node, then uses\nthese variable-wise representations to concurrently and independently predict\nfor each directed causal-edge. In this paper, we first show that this\narchitecture has some systematic bias that cannot be mitigated regardless of\nmodel size and data size. We then propose SiCL, a DNN-based SCL method that\npredicts a skeleton matrix together with a v-tensor (a third-order tensor\nrepresenting the v-structures). According to the Markov Equivalence Class (MEC)\ntheory, both the skeleton and the v-structures are identifiable causal\nstructures under the canonical MEC setting, so predictions about skeleton and\nv-structures do not suffer from the identifiability limit in causal discovery,\nthus SiCL can avoid the systematic bias in Node-Edge architecture, and enable\nconsistent estimators for causal discovery. Moreover, SiCL is also equipped\nwith a specially designed pairwise encoder module with a unidirectional\nattention layer to model both internal and external relationships of pairs of\nnodes. Experimental results on both synthetic and real-world benchmarks show\nthat SiCL significantly outperforms other DNN-based SCL approaches.\n", "date": "2025-02-15", "categories": []}
{"id": "2502.11680", "title": "Spectral structure learning for clinical time series", "abstract": "  We develop and evaluate a structure learning algorithm for clinical time\nseries. Clinical time series are multivariate time series observed in multiple\npatients and irregularly sampled, challenging existing structure learning\nalgorithms. We assume that our times series are realizations of StructGP, a\nk-dimensional multi-output or multi-task stationary Gaussian process (GP), with\nindependent patients sharing the same covariance function. StructGP encodes\nordered conditional relations between time series, represented in a directed\nacyclic graph. We implement an adapted NOTEARS algorithm, which based on a\ndifferentiable definition of acyclicity, recovers the graph by solving a series\nof continuous optimization problems. Simulation results show that up to mean\ndegree 3 and 20 tasks, we reach a median recall of 0.93% [IQR, 0.86, 0.97]\nwhile keeping a median precision of 0.71% [0.57-0.84], for recovering directed\nedges. We further show that the regularization path is key to identifying the\ngraph. With StructGP, we proposed a model of time series dependencies, that\nflexibly adapt to different time series regularity, while enabling us to learn\nthese dependencies from observations.\n", "date": "2025-02-17", "categories": []}
{"id": "2502.07857", "title": "SNAP: Sequential Non-Ancestor Pruning for Targeted Causal Effect\n  Estimation With an Unknown Graph", "abstract": "  Causal discovery can be computationally demanding for large numbers of\nvariables. If we only wish to estimate the causal effects on a small subset of\ntarget variables, we might not need to learn the causal graph for all\nvariables, but only a small subgraph that includes the targets and their\nadjustment sets. In this paper, we focus on identifying causal effects between\ntarget variables in a computationally and statistically efficient way. This\ntask combines causal discovery and effect estimation, aligning the discovery\nobjective with the effects to be estimated. We show that definite non-ancestors\nof the targets are unnecessary to learn causal relations between the targets\nand to identify efficient adjustments sets. We sequentially identify and prune\nthese definite non-ancestors with our Sequential Non-Ancestor Pruning (SNAP)\nframework, which can be used either as a preprocessing step to standard causal\ndiscovery methods, or as a standalone sound and complete causal discovery\nalgorithm. Our results on synthetic and real data show that both approaches\nsubstantially reduce the number of independence tests and the computation time\nwithout compromising the quality of causal effect estimations.\n", "date": "2025-02-11", "categories": []}
{"id": "2312.11582", "title": "Shapley-PC: Constraint-based Causal Structure Learning with a Shapley\n  Inspired Framework", "abstract": "  Causal Structure Learning (CSL), also referred to as causal discovery,\namounts to extracting causal relations among variables in data. CSL enables the\nestimation of causal effects from observational data alone, avoiding the need\nto perform real life experiments. Constraint-based CSL leverages conditional\nindependence tests to perform causal discovery. We propose Shapley-PC, a novel\nmethod to improve constraint-based CSL algorithms by using Shapley values over\nthe possible conditioning sets, to decide which variables are responsible for\nthe observed conditional (in)dependences. We prove soundness, completeness and\nasymptotic consistency of Shapley-PC and run a simulation study showing that\nour proposed algorithm is superior to existing versions of PC.\n", "date": "2023-12-18", "categories": []}
{"id": "2407.16975", "title": "On the Parameter Identifiability of Partially Observed Linear Causal\n  Models", "abstract": "  Linear causal models are important tools for modeling causal dependencies and\nyet in practice, only a subset of the variables can be observed. In this paper,\nwe examine the parameter identifiability of these models by investigating\nwhether the edge coefficients can be recovered given the causal structure and\npartially observed data. Our setting is more general than that of prior\nresearch - we allow all variables, including both observed and latent ones, to\nbe flexibly related, and we consider the coefficients of all edges, whereas\nmost existing works focus only on the edges between observed variables.\nTheoretically, we identify three types of indeterminacy for the parameters in\npartially observed linear causal models. We then provide graphical conditions\nthat are sufficient for all parameters to be identifiable and show that some of\nthem are provably necessary. Methodologically, we propose a novel\nlikelihood-based parameter estimation method that addresses the variance\nindeterminacy of latent variables in a specific way and can asymptotically\nrecover the underlying parameters up to trivial indeterminacy. Empirical\nstudies on both synthetic and real-world datasets validate our identifiability\ntheory and the effectiveness of the proposed method in the finite-sample\nregime. Code: https://github.com/dongxinshuai/scm-identify.\n", "date": "2024-07-24", "categories": []}
{"id": "2409.09822", "title": "Causal Inference with Large Language Model: A Survey", "abstract": "  Causal inference has been a pivotal challenge across diverse domains such as\nmedicine and economics, demanding a complicated integration of human knowledge,\nmathematical reasoning, and data mining capabilities. Recent advancements in\nnatural language processing (NLP), particularly with the advent of large\nlanguage models (LLMs), have introduced promising opportunities for traditional\ncausal inference tasks. This paper reviews recent progress in applying LLMs to\ncausal inference, encompassing various tasks spanning different levels of\ncausation. We summarize the main causal problems and approaches, and present a\ncomparison of their evaluation results in different causal scenarios.\nFurthermore, we discuss key findings and outline directions for future\nresearch, underscoring the potential implications of integrating LLMs in\nadvancing causal inference methodologies.\n", "date": "2024-09-15", "categories": []}
{"id": "2501.11622", "title": "Causal Learning for Heterogeneous Subgroups Based on Nonlinear Causal\n  Kernel Clustering", "abstract": "  Due to the challenge posed by multi-source and heterogeneous data collected\nfrom diverse environments, causal relationships among features can exhibit\nvariations influenced by different time spans, regions, or strategies. This\ndiversity makes a single causal model inadequate for accurately representing\ncomplex causal relationships in all observational data, a crucial consideration\nin causal learning. To address this challenge, the nonlinear Causal Kernel\nClustering method is introduced for heterogeneous subgroup causal learning,\nhighlighting variations in causal relationships across diverse subgroups. The\nmain component for clustering heterogeneous subgroups lies in the construction\nof the $u$-centered sample mapping function with the property of unbiased\nestimation, which assesses the differences in potential nonlinear causal\nrelationships in various samples and supported by causal identifiability\ntheory. Experimental results indicate that the method performs well in\nidentifying heterogeneous subgroups and enhancing causal learning, leading to a\nreduction in prediction error.\n", "date": "2025-01-20", "categories": []}
{"id": "2502.03802", "title": "MXMap: A Multivariate Cross Mapping Framework for Causal Discovery in\n  Dynamical Systems", "abstract": "  Convergent Cross Mapping (CCM) is a powerful method for detecting causality\nin coupled nonlinear dynamical systems, providing a model-free approach to\ncapture dynamic causal interactions. Partial Cross Mapping (PCM) was introduced\nas an extension of CCM to address indirect causality in three-variable systems\nby comparing cross-mapping quality between direct cause-effect mapping and\nindirect mapping through an intermediate conditioning variable. However, PCM\nremains limited to univariate delay embeddings in its cross-mapping processes.\nIn this work, we extend PCM to the multivariate setting, introducing multiPCM,\nwhich leverages multivariate embeddings to more effectively distinguish\nindirect causal relationships. We further propose a multivariate cross-mapping\nframework (MXMap) for causal discovery in dynamical systems. This two-phase\nframework combines (1) pairwise CCM tests to establish an initial causal graph\nand (2) multiPCM to refine the graph by pruning indirect causal connections.\nThrough experiments on simulated data and the ERA5 Reanalysis weather dataset,\nwe demonstrate the effectiveness of MXMap. Additionally, MXMap is compared\nagainst several baseline methods, showing advantages in accuracy and causal\ngraph refinement.\n", "date": "2025-02-06", "categories": []}
{"id": "2501.08958", "title": "Kolmogorov-Arnold Networks for Time Series Granger Causality Inference", "abstract": "  We propose the Granger causality inference Kolmogorov-Arnold Networks\n(KANGCI), a novel architecture that extends the recently proposed\nKolmogorov-Arnold Networks (KAN) to the domain of causal inference. By\nextracting base weights from KAN layers and incorporating the sparsity-inducing\npenalty and ridge regularization, KANGCI effectively infers the Granger\ncausality from time series. Additionally, we propose an algorithm based on\ntime-reversed Granger causality that automatically selects causal relationships\nwith better inference performance from the original or time-reversed time\nseries or integrates the results to mitigate spurious connectivities.\nComprehensive experiments conducted on Lorenz-96, Gene regulatory networks,\nfMRI BOLD signals, VAR, and real-world EEG datasets demonstrate that the\nproposed model achieves competitive performance to state-of-the-art methods in\ninferring Granger causality from nonlinear, high-dimensional, and\nlimited-sample time series.\n", "date": "2025-01-15", "categories": []}
{"id": "2501.18859", "title": "A Deep Spatio-Temporal Architecture for Dynamic Effective Connectivity\n  Network Analysis Based on Dynamic Causal Discovery", "abstract": "  Dynamic effective connectivity networks (dECNs) reveal the changing directed\nbrain activity and the dynamic causal influences among brain regions, which\nfacilitate the identification of individual differences and enhance the\nunderstanding of human brain. Although the existing causal discovery methods\nhave shown promising results in effective connectivity network analysis, they\noften overlook the dynamics of causality, in addition to the incorporation of\nspatio-temporal information in brain activity data. To address these issues, we\npropose a deep spatio-temporal fusion architecture, which employs a dynamic\ncausal deep encoder to incorporate spatio-temporal information into dynamic\ncausality modeling, and a dynamic causal deep decoder to verify the discovered\ncausality. The effectiveness of the proposed method is first illustrated with\nsimulated data. Then, experimental results from Philadelphia Neurodevelopmental\nCohort (PNC) demonstrate the superiority of the proposed method in inferring\ndECNs, which reveal the dynamic evolution of directed flow between brain\nregions. The analysis shows the difference of dECNs between young adults and\nchildren. Specifically, the directed brain functional networks transit from\nfluctuating undifferentiated systems to more stable specialized networks as one\ngrows. This observation provides further evidence on the modularization and\nadaptation of brain networks during development, leading to higher cognitive\nabilities observed in young adults.\n", "date": "2025-01-31", "categories": []}
{"id": "2501.18337", "title": "Unfaithful Probability Distributions in Binary Triple of Causality\n  Directed Acyclic Graph", "abstract": "  Faithfulness is the foundation of probability distribution and graph in\ncausal discovery and causal inference. In this paper, several unfaithful\nprobability distribution examples are constructed in three--vertices binary\ncausality directed acyclic graph (DAG) structure, which are not faithful to\ncausal DAGs described in J.M.,Robins,et al. Uniform consistency in causal\ninference. Biometrika (2003),90(3): 491--515. And the general unfaithful\nprobability distribution with multiple independence and conditional\nindependence in binary triple causal DAG is given.\n", "date": "2025-01-30", "categories": []}
{"id": "2501.17354", "title": "Fundamental Computational Limits in Pursuing Invariant Causal Prediction\n  and Invariance-Guided Regularization", "abstract": "  Pursuing invariant prediction from heterogeneous environments opens the door\nto learning causality in a purely data-driven way and has several applications\nin causal discovery and robust transfer learning. However, existing methods\nsuch as ICP [Peters et al., 2016] and EILLS [Fan et al., 2024] that can attain\nsample-efficient estimation are based on exponential time algorithms. In this\npaper, we show that such a problem is intrinsically hard in computation: the\ndecision problem, testing whether a non-trivial prediction-invariant solution\nexists across two environments, is NP-hard even for the linear causal\nrelationship. In the world where P$\\neq$NP, our results imply that the\nestimation error rate can be arbitrarily slow using any computationally\nefficient algorithm. This suggests that pursuing causality is fundamentally\nharder than detecting associations when no prior assumption is pre-offered.\n  Given there is almost no hope of computational improvement under the worst\ncase, this paper proposes a method capable of attaining both computationally\nand statistically efficient estimation under additional conditions.\nFurthermore, our estimator is a distributionally robust estimator with an\nellipse-shaped uncertain set where more uncertainty is placed on spurious\ndirections than invariant directions, resulting in a smooth interpolation\nbetween the most predictive solution and the causal solution by varying the\ninvariance hyper-parameter. Non-asymptotic results and empirical applications\nsupport the claim.\n", "date": "2025-01-29", "categories": []}
{"id": "2208.10671", "title": "Cardinality-Regularized Hawkes-Granger Model", "abstract": "  We propose a new sparse Granger-causal learning framework for temporal event\ndata. We focus on a specific class of point processes called the Hawkes\nprocess. We begin by pointing out that most of the existing sparse causal\nlearning algorithms for the Hawkes process suffer from a singularity in maximum\nlikelihood estimation. As a result, their sparse solutions can appear only as\nnumerical artifacts. In this paper, we propose a mathematically well-defined\nsparse causal learning framework based on a cardinality-regularized Hawkes\nprocess, which remedies the pathological issues of existing approaches. We\nleverage the proposed algorithm for the task of instance-wise causal event\nanalysis, where sparsity plays a critical role. We validate the proposed\nframework with two real use-cases, one from the power grid and the other from\nthe cloud data center management domain.\n", "date": "2022-08-23", "categories": []}
{"id": "2501.14997", "title": "Causal Discovery via Bayesian Optimization", "abstract": "  Existing score-based methods for directed acyclic graph (DAG) learning from\nobservational data struggle to recover the causal graph accurately and\nsample-efficiently. To overcome this, in this study, we propose DrBO (DAG\nrecovery via Bayesian Optimization)-a novel DAG learning framework leveraging\nBayesian optimization (BO) to find high-scoring DAGs. We show that, by\nsophisticatedly choosing the promising DAGs to explore, we can find\nhigher-scoring ones much more efficiently. To address the scalability issues of\nconventional BO in DAG learning, we replace Gaussian Processes commonly\nemployed in BO with dropout neural networks, trained in a continual manner,\nwhich allows for (i) flexibly modeling the DAG scores without overfitting, (ii)\nincorporation of uncertainty into the estimated scores, and (iii) scaling with\nthe number of evaluations. As a result, DrBO is computationally efficient and\ncan find the accurate DAG in fewer trials and less time than existing\nstate-of-the-art methods. This is demonstrated through an extensive set of\nempirical evaluations on many challenging settings with both synthetic and real\ndata. Our implementation is available at https://github.com/baosws/DrBO.\n", "date": "2025-01-25", "categories": []}
{"id": "2501.10235", "title": "SpaceTime: Causal Discovery from Non-Stationary Time Series", "abstract": "  Understanding causality is challenging and often complicated by changing\ncausal relationships over time and across environments. Climate patterns, for\nexample, shift over time with recurring seasonal trends, while also depending\non geographical characteristics such as ecosystem variability. Existing methods\nfor discovering causal graphs from time series either assume stationarity, do\nnot permit both temporal and spatial distribution changes, or are unaware of\nlocations with the same causal relationships. In this work, we therefore unify\nthe three tasks of causal graph discovery in the non-stationary multi-context\nsetting, of reconstructing temporal regimes, and of partitioning datasets and\ntime intervals into those where invariant causal relationships hold. To\nconstruct a consistent score that forms the basis of our method, we employ the\nMinimum Description Length principle. Our resulting algorithm SPACETIME\nsimultaneously accounts for heterogeneity across space and non-stationarity\nover time. Given multiple time series, it discovers regime changepoints and a\ntemporal causal graph using non-parametric functional modeling and kernelized\ndiscrepancy testing. We also show that our method provides insights into\nreal-world phenomena such as river-runoff measured at different catchments and\nbiosphere-atmosphere interactions across ecosystems.\n", "date": "2025-01-17", "categories": []}
{"id": "2310.14975", "title": "The WHY in Business Processes: Discovery of Causal Execution\n  Dependencies", "abstract": "  Unraveling the causal relationships among the execution of process activities\nis a crucial element in predicting the consequences of process interventions\nand making informed decisions regarding process improvements. Process discovery\nalgorithms exploit time precedence as their main source of model derivation.\nHence, a causal view can supplement process discovery, being a new perspective\nin which relations reflect genuine cause-effect dependencies among the tasks.\nThis calls for faithful new techniques to discover the causal execution\ndependencies among the tasks in the process. To this end, our work offers a\nsystematic approach to the unveiling of the causal business process by\nleveraging an existing causal discovery algorithm over activity timing. In\naddition, this work delves into a set of conditions under which process mining\ndiscovery algorithms generate a model that is incongruent with the causal\nbusiness process model, and shows how the latter model can be methodologically\nemployed for a sound analysis of the process. Our methodology searches for such\ndiscrepancies between the two models in the context of three causal patterns,\nand derives a new view in which these inconsistencies are annotated over the\nmined process model. We demonstrate our methodology employing two open process\nmining algorithms, the IBM Process Mining tool, and the LiNGAM causal discovery\ntechnique. We apply it to a synthesized dataset and two open benchmark\ndatasets.\n", "date": "2023-10-23", "categories": []}
{"id": "2405.14496", "title": "Hybrid Top-Down Global Causal Discovery with Local Search for Linear and\n  Nonlinear Additive Noise Models", "abstract": "  Learning the unique directed acyclic graph corresponding to an unknown causal\nmodel is a challenging task. Methods based on functional causal models can\nidentify a unique graph, but either suffer from the curse of dimensionality or\nimpose strong parametric assumptions. To address these challenges, we propose a\nnovel hybrid approach for global causal discovery in observational data that\nleverages local causal substructures. We first present a topological sorting\nalgorithm that leverages ancestral relationships in linear structural causal\nmodels to establish a compact top-down hierarchical ordering, encoding more\ncausal information than linear orderings produced by existing methods. We\ndemonstrate that this approach generalizes to nonlinear settings with arbitrary\nnoise. We then introduce a nonparametric constraint-based algorithm that prunes\nspurious edges by searching for local conditioning sets, achieving greater\naccuracy than current methods. We provide theoretical guarantees for\ncorrectness and worst-case polynomial time complexities, with empirical\nvalidation on synthetic data.\n", "date": "2024-05-23", "categories": []}
{"id": "2501.06534", "title": "Dynamic Causal Structure Discovery and Causal Effect Estimation", "abstract": "  To represent the causal relationships between variables, a directed acyclic\ngraph (DAG) is widely utilized in many areas, such as social sciences,\nepidemics, and genetics. Many causal structure learning approaches are\ndeveloped to learn the hidden causal structure utilizing deep-learning\napproaches. However, these approaches have a hidden assumption that the causal\nrelationship remains unchanged over time, which may not hold in real life. In\nthis paper, we develop a new framework to model the dynamic causal graph where\nthe causal relations are allowed to be time-varying. We incorporate the basis\napproximation method into the score-based causal discovery approach to capture\nthe dynamic pattern of the causal graphs. Utilizing the autoregressive model\nstructure, we could capture both contemporaneous and time-lagged causal\nrelationships while allowing them to vary with time. We propose an algorithm\nthat could provide both past-time estimates and future-time predictions on the\ncausal graphs, and conduct simulations to demonstrate the usefulness of the\nproposed method. We also apply the proposed method for the covid-data analysis,\nand provide causal estimates on how policy restriction's effect changes.\n", "date": "2025-01-11", "categories": []}
{"id": "2501.05498", "title": "Generative Flow Networks: Theory and Applications to Structure Learning", "abstract": "  Without any assumptions about data generation, multiple causal models may\nexplain our observations equally well. To avoid selecting a single arbitrary\nmodel that could result in unsafe decisions if it does not match reality, it is\ntherefore essential to maintain a notion of epistemic uncertainty about our\npossible candidates. This thesis studies the problem of structure learning from\na Bayesian perspective, approximating the posterior distribution over the\nstructure of a causal model, represented as a directed acyclic graph (DAG),\ngiven data. It introduces Generative Flow Networks (GFlowNets), a novel class\nof probabilistic models designed for modeling distributions over discrete and\ncompositional objects such as graphs. They treat generation as a sequential\ndecision making problem, constructing samples of a target distribution defined\nup to a normalization constant piece by piece. In the first part of this\nthesis, we present the mathematical foundations of GFlowNets, their connections\nto existing domains of machine learning and statistics such as variational\ninference and reinforcement learning, and their extensions beyond discrete\nproblems. In the second part of this thesis, we show how GFlowNets can\napproximate the posterior distribution over DAG structures of causal Bayesian\nNetworks, along with the parameters of its causal mechanisms, given\nobservational and experimental data.\n", "date": "2025-01-09", "categories": []}
{"id": "2501.04724", "title": "Guiding Treatment Strategies: The Role of Adjuvant Anti-Her2 Neu Therapy\n  and Skin/Nipple Involvement in Local Recurrence-Free Survival in Breast\n  Cancer Patients", "abstract": "  This study explores how causal inference models, specifically the Linear\nNon-Gaussian Acyclic Model (LiNGAM), can extract causal relationships between\ndemographic factors, treatments, conditions, and outcomes from observational\npatient data, enabling insights beyond correlation. Unlike traditional\nrandomized controlled trials (RCTs), which establish causal relationships\nwithin narrowly defined populations, our method leverages broader observational\ndata, improving generalizability. Using over 40 features in the Duke MRI Breast\nCancer dataset, we found that Adjuvant Anti-Her2 Neu Therapy increased local\nrecurrence-free survival by 169 days, while Skin/Nipple involvement reduced it\nby 351 days. These findings highlight the therapy's importance for\nHer2-positive patients and the need for targeted interventions for high-risk\ncases, informing personalized treatment strategies.\n", "date": "2025-01-04", "categories": []}
{"id": "2412.20289", "title": "Causal Discovery on Dependent Binary Data", "abstract": "  The assumption of independence between observations (units) in a dataset is\nprevalent across various methodologies for learning causal graphical models.\nHowever, this assumption often finds itself in conflict with real-world data,\nposing challenges to accurate structure learning. We propose a\ndecorrelation-based approach for causal graph learning on dependent binary\ndata, where the local conditional distribution is defined by a latent utility\nmodel with dependent errors across units. We develop a pairwise maximum\nlikelihood method to estimate the covariance matrix for the dependence among\nthe units. Then, leveraging the estimated covariance matrix, we develop an\nEM-like iterative algorithm to generate and decorrelate samples of the latent\nutility variables, which serve as decorrelated data. Any standard causal\ndiscovery method can be applied on the decorrelated data to learn the\nunderlying causal graph. We demonstrate that the proposed decorrelation\napproach significantly improves the accuracy in causal graph learning, through\nnumerical experiments on both synthetic and real-world datasets.\n", "date": "2024-12-28", "categories": []}
{"id": "2409.12797", "title": "Efficient Identification of Direct Causal Parents via Invariance and\n  Minimum Error Testing", "abstract": "  Invariant causal prediction (ICP) is a popular technique for finding causal\nparents (direct causes) of a target via exploiting distribution shifts and\ninvariance testing (Peters et al., 2016). However, since ICP needs to run an\nexponential number of tests and fails to identify parents when distribution\nshifts only affect a few variables, applying ICP to practical large scale\nproblems is challenging. We propose MMSE-ICP and fastICP, two approaches which\nemploy an error inequality to address the identifiability problem of ICP. The\ninequality states that the minimum prediction error of the predictor using\ncausal parents is the smallest among all predictors which do not use\ndescendants. fastICP is an efficient approximation tailored for large problems\nas it exploits the inequality and a heuristic to run fewer tests. MMSE-ICP and\nfastICP not only outperform competitive baselines in many simulations but also\nachieve state-of-the-art result on a large scale real data benchmark.\n", "date": "2024-09-19", "categories": []}
{"id": "2409.17647", "title": "MECD: Unlocking Multi-Event Causal Discovery in Video Reasoning", "abstract": "  Video causal reasoning aims to achieve a high-level understanding of video\ncontent from a causal perspective. However, current video reasoning tasks are\nlimited in scope, primarily executed in a question-answering paradigm and\nfocusing on short videos containing only a single event and simple causal\nrelationships, lacking comprehensive and structured causality analysis for\nvideos with multiple events. To fill this gap, we introduce a new task and\ndataset, Multi-Event Causal Discovery (MECD). It aims to uncover the causal\nrelationships between events distributed chronologically across long videos.\nGiven visual segments and textual descriptions of events, MECD requires\nidentifying the causal associations between these events to derive a\ncomprehensive, structured event-level video causal diagram explaining why and\nhow the final result event occurred. To address MECD, we devise a novel\nframework inspired by the Granger Causality method, using an efficient\nmask-based event prediction model to perform an Event Granger Test, which\nestimates causality by comparing the predicted result event when premise events\nare masked versus unmasked. Furthermore, we integrate causal inference\ntechniques such as front-door adjustment and counterfactual inference to\naddress challenges in MECD like causality confounding and illusory causality.\nExperiments validate the effectiveness of our framework in providing causal\nrelationships in multi-event videos, outperforming GPT-4o and VideoLLaVA by\n5.7% and 4.1%, respectively.\n", "date": "2024-09-26", "categories": []}
{"id": "2410.10044", "title": "DAG-aware Transformer for Causal Effect Estimation", "abstract": "  Causal inference is a critical task across fields such as healthcare,\neconomics, and the social sciences. While recent advances in machine learning,\nespecially those based on the deep-learning architectures, have shown potential\nin estimating causal effects, existing approaches often fall short in handling\ncomplex causal structures and lack adaptability across various causal\nscenarios. In this paper, we present a novel transformer-based method for\ncausal inference that overcomes these challenges. The core innovation of our\nmodel lies in its integration of causal Directed Acyclic Graphs (DAGs) directly\ninto the attention mechanism, enabling it to accurately model the underlying\ncausal structure. This allows for flexible estimation of both average treatment\neffects (ATE) and conditional average treatment effects (CATE). Extensive\nexperiments on both synthetic and real-world datasets demonstrate that our\napproach surpasses existing methods in estimating causal effects across a wide\nrange of scenarios. The flexibility and robustness of our model make it a\nvaluable tool for researchers and practitioners tackling complex causal\ninference problems.\n", "date": "2024-10-13", "categories": []}
{"id": "2412.17508", "title": "An efficient search-and-score algorithm for ancestral graphs using\n  multivariate information scores", "abstract": "  We propose a greedy search-and-score algorithm for ancestral graphs, which\ninclude directed as well as bidirected edges, originating from unobserved\nlatent variables. The normalized likelihood score of ancestral graphs is\nestimated in terms of multivariate information over relevant ``ac-connected\nsubsets'' of vertices, C, that are connected through collider paths confined to\nthe ancestor set of C. For computational efficiency, the proposed two-step\nalgorithm relies on local information scores limited to the close surrounding\nvertices of each node (step 1) and edge (step 2). This computational strategy,\nalthough restricted to information contributions from ac-connected subsets\ncontaining up to two-collider paths, is shown to outperform state-of-the-art\ncausal discovery methods on challenging benchmark datasets.\n", "date": "2024-12-23", "categories": []}
{"id": "2412.19578", "title": "Graph-attention-based Casual Discovery with Trust Region-navigated\n  Clipping Policy Optimization", "abstract": "  In many domains of empirical sciences, discovering the causal structure\nwithin variables remains an indispensable task. Recently, to tackle with\nunoriented edges or latent assumptions violation suffered by conventional\nmethods, researchers formulated a reinforcement learning (RL) procedure for\ncausal discovery, and equipped REINFORCE algorithm to search for the\nbest-rewarded directed acyclic graph. The two keys to the overall performance\nof the procedure are the robustness of RL methods and the efficient encoding of\nvariables. However, on the one hand, REINFORCE is prone to local convergence\nand unstable performance during training. Neither trust region policy\noptimization, being computationally-expensive, nor proximal policy optimization\n(PPO), suffering from aggregate constraint deviation, is decent alternative for\ncombinatory optimization problems with considerable individual subactions. We\npropose a trust region-navigated clipping policy optimization method for causal\ndiscovery that guarantees both better search efficiency and steadiness in\npolicy optimization, in comparison with REINFORCE, PPO and our prioritized\nsampling-guided REINFORCE implementation. On the other hand, to boost the\nefficient encoding of variables, we propose a refined graph attention encoder\ncalled SDGAT that can grasp more feature information without priori\nneighbourhood information. With these improvements, the proposed method\noutperforms former RL method in both synthetic and benchmark datasets in terms\nof output results and optimization robustness.\n", "date": "2024-12-27", "categories": []}
{"id": "2311.17303", "title": "Enhancing the Performance of Neural Networks Through Causal Discovery\n  and Integration of Domain Knowledge", "abstract": "  In this paper, we develop a generic methodology to encode hierarchical\ncausality structure among observed variables into a neural network in order to\nimprove its predictive performance. The proposed methodology, called\ncausality-informed neural network (CINN), leverages three coherent steps to\nsystematically map the structural causal knowledge into the layer-to-layer\ndesign of neural network while strictly preserving the orientation of every\ncausal relationship. In the first step, CINN discovers causal relationships\nfrom observational data via directed acyclic graph (DAG) learning, where causal\ndiscovery is recast as a continuous optimization problem to avoid the\ncombinatorial nature. In the second step, the discovered hierarchical causality\nstructure among observed variables is systematically encoded into neural\nnetwork through a dedicated architecture and customized loss function. By\ncategorizing variables in the causal DAG as root, intermediate, and leaf nodes,\nthe hierarchical causal DAG is translated into CINN with a one-to-one\ncorrespondence between nodes in the causal DAG and units in the CINN while\nmaintaining the relative order among these nodes. Regarding the loss function,\nboth intermediate and leaf nodes in the DAG graph are treated as target outputs\nduring CINN training so as to drive co-learning of causal relationships among\ndifferent types of nodes. As multiple loss components emerge in CINN, we\nleverage the projection of conflicting gradients to mitigate gradient\ninterference among the multiple learning tasks. Computational experiments\nacross a broad spectrum of UCI data sets demonstrate substantial advantages of\nCINN in predictive performance over other state-of-the-art methods. In\naddition, an ablation study underscores the value of integrating structural and\nquantitative causal knowledge in enhancing the neural network's predictive\nperformance incrementally.\n", "date": "2023-11-29", "categories": []}
{"id": "2411.11590", "title": "Robust Causal Analysis of Linear Cyclic Systems With Hidden Confounders", "abstract": "  We live in a world full of complex systems which we need to improve our\nunderstanding of. To accomplish this, purely probabilistic investigations are\noften not enough. They are only the first step and must be followed by learning\nthe system's underlying mechanisms. This is what the discipline of causality is\nconcerned with. Many of those complex systems contain feedback loops which\nmeans that our methods have to allow for cyclic causal relations. Furthermore,\nsystems are rarely sufficiently isolated, which means that there are usually\nhidden confounders, i.e., unmeasured variables that each causally affects more\nthan one measured variable. Finally, data is often distorted by contaminating\nprocesses, and we need to apply methods that are robust against such\ndistortions. That's why we consider the robustness of LLC, see \\cite{llc}, one\nof the few causal analysis methods that can deal with cyclic models with hidden\nconfounders. Following a theoretical analysis of LLC's robustness properties,\nwe also provide robust extensions of LLC. To facilitate reproducibility and\nfurther research in this field, we make the source code publicly available.\n", "date": "2024-11-18", "categories": []}
{"id": "2405.14848", "title": "Local Causal Discovery for Structural Evidence of Direct Discrimination", "abstract": "  Identifying the causal pathways of unfairness is a critical objective for\nimproving policy design and algorithmic decision-making. Prior work in causal\nfairness analysis often requires knowledge of the causal graph, hindering\npractical applications in complex or low-knowledge domains. Moreover, global\ndiscovery methods that learn causal structure from data can display unstable\nperformance on finite samples, preventing robust fairness conclusions. To\nmitigate these challenges, we introduce local discovery for direct\ndiscrimination (LD3): a method that uncovers structural evidence of direct\nunfairness by identifying the causal parents of an outcome variable. LD3\nperforms a linear number of conditional independence tests relative to variable\nset size, and allows for latent confounding under the sufficient condition that\nall parents of the outcome are observed. We show that LD3 returns a valid\nadjustment set (VAS) under a new graphical criterion for the weighted\ncontrolled direct effect, a qualitative indicator of direct discrimination. LD3\nlimits unnecessary adjustment, providing interpretable VAS for assessing\nunfairness. We use LD3 to analyze causal fairness in two complex decision\nsystems: criminal recidivism prediction and liver transplant allocation. LD3\nwas more time-efficient and returned more plausible results on real-world data\nthan baselines, which took 46$\\times$ to 5870$\\times$ longer to execute.\n", "date": "2024-05-23", "categories": []}
{"id": "2412.15373", "title": "Granger Causality Detection with Kolmogorov-Arnold Networks", "abstract": "  Discovering causal relationships in time series data is central in many\nscientific areas, ranging from economics to climate science. Granger causality\nis a powerful tool for causality detection. However, its original formulation\nis limited by its linear form and only recently nonlinear machine-learning\ngeneralizations have been introduced. This study contributes to the definition\nof neural Granger causality models by investigating the application of\nKolmogorov-Arnold networks (KANs) in Granger causality detection and comparing\ntheir capabilities against multilayer perceptrons (MLP). In this work, we\ndevelop a framework called Granger Causality KAN (GC-KAN) along with a tailored\ntraining approach designed specifically for Granger causality detection. We\ntest this framework on both Vector Autoregressive (VAR) models and chaotic\nLorenz-96 systems, analysing the ability of KANs to sparsify input features by\nidentifying Granger causal relationships, providing a concise yet accurate\nmodel for Granger causality detection. Our findings show the potential of KANs\nto outperform MLPs in discerning interpretable Granger causal relationships,\nparticularly for the ability of identifying sparse Granger causality patterns\nin high-dimensional settings, and more generally, the potential of AI in\ncausality discovery for the dynamical laws in physical systems.\n", "date": "2024-12-19", "categories": []}
{"id": "2305.09565", "title": "Toward Falsifying Causal Graphs Using a Permutation-Based Test", "abstract": "  Understanding causal relationships among the variables of a system is\nparamount to explain and control its behavior. For many real-world systems,\nhowever, the true causal graph is not readily available and one must resort to\npredictions made by algorithms or domain experts. Therefore, metrics that\nquantitatively assess the goodness of a causal graph provide helpful checks\nbefore using it in downstream tasks. Existing metrics provide an\n$\\textit{absolute}$ number of inconsistencies between the graph and the\nobserved data, and without a baseline, practitioners are left to answer the\nhard question of how many such inconsistencies are acceptable or expected.\nHere, we propose a novel consistency metric by constructing a baseline through\nnode permutations. By comparing the number of inconsistencies with those on the\nbaseline, we derive an interpretable metric that captures whether the graph is\nsignificantly better than random. Evaluating on both simulated and real data\nsets from various domains, including biology and cloud monitoring, we\ndemonstrate that the true graph is not falsified by our metric, whereas the\nwrong graphs given by a hypothetical user are likely to be falsified.\n", "date": "2023-05-16", "categories": []}
{"id": "2210.07416", "title": "GLACIAL: Granger and Learning-based Causality Analysis for Longitudinal\n  Imaging Studies", "abstract": "  The Granger framework is useful for discovering causal relations in\ntime-varying signals. However, most Granger causality (GC) methods are\ndeveloped for densely sampled timeseries data. A substantially different\nsetting, particularly common in medical imaging, is the longitudinal study\ndesign, where multiple subjects are followed and sparsely observed over time.\nLongitudinal studies commonly track several biomarkers, which are likely\ngoverned by nonlinear dynamics that might have subject-specific idiosyncrasies\nand exhibit both direct and indirect causes. Furthermore, real-world\nlongitudinal data often suffer from widespread missingness. GC methods are not\nwell-suited to handle these issues. In this paper, we propose an approach named\nGLACIAL (Granger and LeArning-based CausalIty Analysis for Longitudinal\nstudies) to fill this methodological gap by marrying GC with a multi-task\nneural forecasting model. GLACIAL treats subjects as independent samples and\nuses the model's average prediction accuracy on hold-out subjects to probe\ncausal links. Input dropout and model interpolation are used to efficiently\nlearn nonlinear dynamic relationships between a large number of variables and\nto handle missing values respectively. Extensive simulations and experiments on\na real longitudinal medical imaging dataset show GLACIAL beating competitive\nbaselines and confirm its utility. Our code is available at\nhttps://github.com/mnhng/GLACIAL.\n", "date": "2022-10-13", "categories": []}
{"id": "2412.13952", "title": "Prompting Strategies for Enabling Large Language Models to Infer\n  Causation from Correlation", "abstract": "  The reasoning abilities of Large Language Models (LLMs) are attracting\nincreasing attention. In this work, we focus on causal reasoning and address\nthe task of establishing causal relationships based on correlation information,\na highly challenging problem on which several LLMs have shown poor performance.\nWe introduce a prompting strategy for this problem that breaks the original\ntask into fixed subquestions, with each subquestion corresponding to one step\nof a formal causal discovery algorithm, the PC algorithm. The proposed\nprompting strategy, PC-SubQ, guides the LLM to follow these algorithmic steps,\nby sequentially prompting it with one subquestion at a time, augmenting the\nnext subquestion's prompt with the answer to the previous one(s). We evaluate\nour approach on an existing causal benchmark, Corr2Cause: our experiments\nindicate a performance improvement across five LLMs when comparing PC-SubQ to\nbaseline prompting strategies. Results are robust to causal query\nperturbations, when modifying the variable names or paraphrasing the\nexpressions.\n", "date": "2024-12-18", "categories": []}
{"id": "2409.19377", "title": "Interpretable, multi-dimensional Evaluation Framework for Causal\n  Discovery from observational i.i.d. Data", "abstract": "  Nonlinear causal discovery from observational data imposes strict\nidentifiability assumptions on the formulation of structural equations utilized\nin the data generating process. The evaluation of structure learning methods\nunder assumption violations requires a rigorous and interpretable approach,\nwhich quantifies both the structural similarity of the estimation with the\nground truth and the capacity of the discovered graphs to be used for causal\ninference. Motivated by the lack of unified performance assessment framework,\nwe introduce an interpretable, six-dimensional evaluation metric, i.e.,\ndistance to optimal solution (DOS), which is specifically tailored to the field\nof causal discovery. Furthermore, this is the first research to assess the\nperformance of structure learning algorithms from seven different families on\nincreasing percentage of non-identifiable, nonlinear causal patterns, inspired\nby real-world processes. Our large-scale simulation study, which incorporates\nseven experimental factors, shows that besides causal order-based methods,\namortized causal discovery delivers results with comparatively high proximity\nto the optimal solution.\n", "date": "2024-09-28", "categories": []}
{"id": "2412.10509", "title": "Do Large Language Models Show Biases in Causal Learning?", "abstract": "  Causal learning is the cognitive process of developing the capability of\nmaking causal inferences based on available information, often guided by\nnormative principles. This process is prone to errors and biases, such as the\nillusion of causality, in which people perceive a causal relationship between\ntwo variables despite lacking supporting evidence. This cognitive bias has been\nproposed to underlie many societal problems, including social prejudice,\nstereotype formation, misinformation, and superstitious thinking. In this\nresearch, we investigate whether large language models (LLMs) develop causal\nillusions, both in real-world and controlled laboratory contexts of causal\nlearning and inference. To this end, we built a dataset of over 2K samples\nincluding purely correlational cases, situations with null contingency, and\ncases where temporal information excludes the possibility of causality by\nplacing the potential effect before the cause. We then prompted the models to\nmake statements or answer causal questions to evaluate their tendencies to\ninfer causation erroneously in these structured settings. Our findings show a\nstrong presence of causal illusion bias in LLMs. Specifically, in open-ended\ngeneration tasks involving spurious correlations, the models displayed bias at\nlevels comparable to, or even lower than, those observed in similar studies on\nhuman subjects. However, when faced with null-contingency scenarios or temporal\ncues that negate causal relationships, where it was required to respond on a\n0-100 scale, the models exhibited significantly higher bias. These findings\nsuggest that the models have not uniformly, consistently, or reliably\ninternalized the normative principles essential for accurate causal learning.\n", "date": "2024-12-13", "categories": []}
{"id": "2402.14027", "title": "Learning causation event conjunction sequences", "abstract": "  This is an examination of some methods that learn causations in event\nsequences. A causation is defined as a conjunction of one or more cause events\noccurring in an arbitrary order, with possible intervening non-causal events,\nthat lead to an effect. The methods include recurrent and non-recurrent\nartificial neural networks (ANNs), as well as a histogram-based algorithm. An\nattention recurrent ANN performed the best of the ANNs, while the histogram\nalgorithm was significantly superior to all the ANNs.\n", "date": "2024-02-17", "categories": []}
{"id": "2412.09843", "title": "Learning Structural Causal Models from Ordering: Identifiable Flow\n  Models", "abstract": "  In this study, we address causal inference when only observational data and a\nvalid causal ordering from the causal graph are available. We introduce a set\nof flow models that can recover component-wise, invertible transformation of\nexogenous variables. Our flow-based methods offer flexible model design while\nmaintaining causal consistency regardless of the number of discretization\nsteps. We propose design improvements that enable simultaneous learning of all\ncausal mechanisms and reduce abduction and prediction complexity to linear O(n)\nrelative to the number of layers, independent of the number of causal\nvariables. Empirically, we demonstrate that our method outperforms previous\nstate-of-the-art approaches and delivers consistent performance across a wide\nrange of structural causal models in answering observational, interventional,\nand counterfactual questions. Additionally, our method achieves a significant\nreduction in computational time compared to existing diffusion-based\ntechniques, making it practical for large structural causal models.\n", "date": "2024-12-13", "categories": []}
{"id": "2407.18607", "title": "Using GPT-4 to guide causal machine learning", "abstract": "  Since its introduction to the public, ChatGPT has had an unprecedented\nimpact. While some experts praised AI advancements and highlighted their\npotential risks, others have been critical about the accuracy and usefulness of\nLarge Language Models (LLMs). In this paper, we are interested in the ability\nof LLMs to identify causal relationships. We focus on the well-established\nGPT-4 (Turbo) and evaluate its performance under the most restrictive\nconditions, by isolating its ability to infer causal relationships based solely\non the variable labels without being given any other context by humans,\ndemonstrating the minimum level of effectiveness one can expect when it is\nprovided with label-only information. We show that questionnaire participants\njudge the GPT-4 graphs as the most accurate in the evaluated categories,\nclosely followed by knowledge graphs constructed by domain experts, with causal\nMachine Learning (ML) far behind. We use these results to highlight the\nimportant limitation of causal ML, which often produces causal graphs that\nviolate common sense, affecting trust in them. However, we show that pairing\nGPT-4 with causal ML overcomes this limitation, resulting in graphical\nstructures learnt from real data that align more closely with those identified\nby domain experts, compared to structures learnt by causal ML alone. Overall,\nour findings suggest that despite GPT-4 not being explicitly designed to reason\ncausally, it can still be a valuable tool for causal representation, as it\nimproves the causal discovery process of causal ML algorithms that are designed\nto do just that.\n", "date": "2024-07-26", "categories": []}
{"id": "2401.13009", "title": "Comparative Study of Causal Discovery Methods for Cyclic Models with\n  Hidden Confounders", "abstract": "  Nowadays, the need for causal discovery is ubiquitous. A better understanding\nof not just the stochastic dependencies between parts of a system, but also the\nactual cause-effect relations, is essential for all parts of science. Thus, the\nneed for reliable methods to detect causal directions is growing constantly. In\nthe last 50 years, many causal discovery algorithms have emerged, but most of\nthem are applicable only under the assumption that the systems have no feedback\nloops and that they are causally sufficient, i.e. that there are no unmeasured\nsubsystems that can affect multiple measured variables. This is unfortunate\nsince those restrictions can often not be presumed in practice. Feedback is an\nintegral feature of many processes, and real-world systems are rarely\ncompletely isolated and fully measured. Fortunately, in recent years, several\ntechniques, that can cope with cyclic, causally insufficient systems, have been\ndeveloped. And with multiple methods available, a practical application of\nthose algorithms now requires knowledge of the respective strengths and\nweaknesses. Here, we focus on the problem of causal discovery for sparse linear\nmodels which are allowed to have cycles and hidden confounders. We have\nprepared a comprehensive and thorough comparative study of four causal\ndiscovery techniques: two versions of the LLC method [10] and two variants of\nthe ASP-based algorithm [11]. The evaluation investigates the performance of\nthose techniques for various experiments with multiple interventional setups\nand different dataset sizes.\n", "date": "2024-01-23", "categories": []}
{"id": "2406.08666", "title": "Interventional Causal Discovery in a Mixture of DAGs", "abstract": "  Causal interactions among a group of variables are often modeled by a single\ncausal graph. In some domains, however, these interactions are best described\nby multiple co-existing causal graphs, e.g., in dynamical systems or genomics.\nThis paper addresses the hitherto unknown role of interventions in learning\ncausal interactions among variables governed by a mixture of causal systems,\neach modeled by one directed acyclic graph (DAG). Causal discovery from\nmixtures is fundamentally more challenging than single-DAG causal discovery.\nTwo major difficulties stem from (i)~an inherent uncertainty about the\nskeletons of the component DAGs that constitute the mixture and (ii)~possibly\ncyclic relationships across these component DAGs. This paper addresses these\nchallenges and aims to identify edges that exist in at least one component DAG\nof the mixture, referred to as the true edges. First, it establishes matching\nnecessary and sufficient conditions on the size of interventions required to\nidentify the true edges. Next, guided by the necessity results, an adaptive\nalgorithm is designed that learns all true edges using $O(n^2)$ interventions,\nwhere $n$ is the number of nodes. Remarkably, the size of the interventions is\noptimal if the underlying mixture model does not contain cycles across its\ncomponents. More generally, the gap between the intervention size used by the\nalgorithm and the optimal size is quantified. It is shown to be bounded by the\ncyclic complexity number of the mixture model, defined as the size of the\nminimal intervention that can break the cycles in the mixture, which is upper\nbounded by the number of cycles among the ancestors of a node.\n", "date": "2024-06-12", "categories": []}
{"id": "2412.01674", "title": "Causal Discovery by Interventions via Integer Programming", "abstract": "  Causal discovery is essential across various scientific fields to uncover\ncausal structures within data. Traditional methods relying on observational\ndata have limitations due to confounding variables. This paper presents an\noptimization-based approach using integer programming (IP) to design minimal\nintervention sets that ensure causal structure identifiability. Our method\nprovides exact and modular solutions that can be adjusted to different\nexperimental settings and constraints. We demonstrate its effectiveness through\ncomparative analysis across different settings, demonstrating its applicability\nand robustness.\n", "date": "2024-12-02", "categories": []}
{"id": "2310.15580", "title": "Identifiable Latent Polynomial Causal Models Through the Lens of Change", "abstract": "  Causal representation learning aims to unveil latent high-level causal\nrepresentations from observed low-level data. One of its primary tasks is to\nprovide reliable assurance of identifying these latent causal models, known as\nidentifiability. A recent breakthrough explores identifiability by leveraging\nthe change of causal influences among latent causal variables across multiple\nenvironments \\citep{liu2022identifying}. However, this progress rests on the\nassumption that the causal relationships among latent causal variables adhere\nstrictly to linear Gaussian models. In this paper, we extend the scope of\nlatent causal models to involve nonlinear causal relationships, represented by\npolynomial models, and general noise distributions conforming to the\nexponential family. Additionally, we investigate the necessity of imposing\nchanges on all causal parameters and present partial identifiability results\nwhen part of them remains unchanged. Further, we propose a novel empirical\nestimation method, grounded in our theoretical finding, that enables learning\nconsistent latent causal representations. Our experimental results, obtained\nfrom both synthetic and real-world data, validate our theoretical contributions\nconcerning identifiability and consistency.\n", "date": "2023-10-24", "categories": []}
{"id": "2411.19556", "title": "Differentiable Causal Discovery For Latent Hierarchical Causal Models", "abstract": "  Discovering causal structures with latent variables from observational data\nis a fundamental challenge in causal discovery. Existing methods often rely on\nconstraint-based, iterative discrete searches, limiting their scalability to\nlarge numbers of variables. Moreover, these methods frequently assume linearity\nor invertibility, restricting their applicability to real-world scenarios. We\npresent new theoretical results on the identifiability of nonlinear latent\nhierarchical causal models, relaxing previous assumptions in literature about\nthe deterministic nature of latent variables and exogenous noise. Building on\nthese insights, we develop a novel differentiable causal discovery algorithm\nthat efficiently estimates the structure of such models. To the best of our\nknowledge, this is the first work to propose a differentiable causal discovery\nmethod for nonlinear latent hierarchical models. Our approach outperforms\nexisting methods in both accuracy and scalability. We demonstrate its practical\nutility by learning interpretable hierarchical latent structures from\nhigh-dimensional image data and demonstrate its effectiveness on downstream\ntasks.\n", "date": "2024-11-29", "categories": []}
{"id": "2410.06163", "title": "Markov Equivalence and Consistency in Differentiable Structure Learning", "abstract": "  Existing approaches to differentiable structure learning of directed acyclic\ngraphs (DAGs) rely on strong identifiability assumptions in order to guarantee\nthat global minimizers of the acyclicity-constrained optimization problem\nidentifies the true DAG. Moreover, it has been observed empirically that the\noptimizer may exploit undesirable artifacts in the loss function. We explain\nand remedy these issues by studying the behavior of differentiable\nacyclicity-constrained programs under general likelihoods with multiple global\nminimizers. By carefully regularizing the likelihood, it is possible to\nidentify the sparsest model in the Markov equivalence class, even in the\nabsence of an identifiable parametrization. We first study the Gaussian case in\ndetail, showing how proper regularization of the likelihood defines a score\nthat identifies the sparsest model. Assuming faithfulness, it also recovers the\nMarkov equivalence class. These results are then generalized to general models\nand likelihoods, where the same claims hold. These theoretical results are\nvalidated empirically, showing how this can be done using standard\ngradient-based optimizers, thus paving the way for differentiable structure\nlearning under general models and losses.\n", "date": "2024-10-08", "categories": []}
{"id": "2411.17989", "title": "Regularized Multi-LLMs Collaboration for Enhanced Score-based Causal\n  Discovery", "abstract": "  As the significance of understanding the cause-and-effect relationships among\nvariables increases in the development of modern systems and algorithms,\nlearning causality from observational data has become a preferred and efficient\napproach over conducting randomized control trials. However, purely\nobservational data could be insufficient to reconstruct the true causal graph.\nConsequently, many researchers tried to utilise some form of prior knowledge to\nimprove causal discovery process. In this context, the impressive capabilities\nof large language models (LLMs) have emerged as a promising alternative to the\ncostly acquisition of prior expert knowledge. In this work, we further explore\nthe potential of using LLMs to enhance causal discovery approaches,\nparticularly focusing on score-based methods, and we propose a general\nframework to utilise the capacity of not only one but multiple LLMs to augment\nthe discovery process.\n", "date": "2024-11-27", "categories": []}
{"id": "2411.15888", "title": "Evaluating Large Language Models for Causal Modeling", "abstract": "  In this paper, we consider the process of transforming causal domain\nknowledge into a representation that aligns more closely with guidelines from\ncausal data science. To this end, we introduce two novel tasks related to\ndistilling causal domain knowledge into causal variables and detecting\ninteraction entities using LLMs. We have determined that contemporary LLMs are\nhelpful tools for conducting causal modeling tasks in collaboration with human\nexperts, as they can provide a wider perspective. Specifically, LLMs, such as\nGPT-4-turbo and Llama3-70b, perform better in distilling causal domain\nknowledge into causal variables compared to sparse expert models, such as\nMixtral-8x22b. On the contrary, sparse expert models such as Mixtral-8x22b\nstand out as the most effective in identifying interaction entities. Finally,\nwe highlight the dependency between the domain where the entities are generated\nand the performance of the chosen LLM for causal modeling.\n", "date": "2024-11-24", "categories": []}
{"id": "2411.12759", "title": "A Novel Approach to Eliminating Hallucinations in Large Language\n  Model-Assisted Causal Discovery", "abstract": "  The increasing use of large language models (LLMs) in causal discovery as a\nsubstitute for human domain experts highlights the need for optimal model\nselection. This paper presents the first hallucination survey of popular LLMs\nfor causal discovery. We show that hallucinations exist when using LLMs in\ncausal discovery so the choice of LLM is important. We propose using Retrieval\nAugmented Generation (RAG) to reduce hallucinations when quality data is\navailable. Additionally, we introduce a novel method employing multiple LLMs\nwith an arbiter in a debate to audit edges in causal graphs, achieving a\ncomparable reduction in hallucinations to RAG.\n", "date": "2024-11-16", "categories": []}
{"id": "2411.13264", "title": "Transformers with Sparse Attention for Granger Causality", "abstract": "  Temporal causal analysis means understanding the underlying causes behind\nobserved variables over time. Deep learning based methods such as transformers\nare increasingly used to capture temporal dynamics and causal relationships\nbeyond mere correlations. Recent works suggest self-attention weights of\ntransformers as a useful indicator of causal links. We leverage this to propose\na novel modification to the self-attention module to establish causal links\nbetween the variables of multivariate time-series data with varying lag\ndependencies. Our Sparse Attention Transformer captures causal relationships\nusing a two-fold approach - performing temporal attention first followed by\nattention between the variables across the time steps masking them individually\nto compute Granger Causality indices. The key novelty in our approach is the\nability of the model to assert importance and pick the most significant past\ntime instances for its prediction task against manually feeding a fixed time\nlag value. We demonstrate the effectiveness of our approach via extensive\nexperimentation on several synthetic benchmark datasets. Furthermore, we\ncompare the performance of our model with the traditional Vector Autoregression\nbased Granger Causality method that assumes fixed lag length.\n", "date": "2024-11-20", "categories": []}
{"id": "2411.01881", "title": "Causal Discovery and Classification Using Lempel-Ziv Complexity", "abstract": "  Inferring causal relationships in the decision-making processes of machine\nlearning algorithms is a crucial step toward achieving explainable Artificial\nIntelligence (AI). In this research, we introduce a novel causality measure and\na distance metric derived from Lempel-Ziv (LZ) complexity. We explore how the\nproposed causality measure can be used in decision trees by enabling splits\nbased on features that most strongly \\textit{cause} the outcome. We further\nevaluate the effectiveness of the causality-based decision tree and the\ndistance-based decision tree in comparison to a traditional decision tree using\nGini impurity. While the proposed methods demonstrate comparable classification\nperformance overall, the causality-based decision tree significantly\noutperforms both the distance-based decision tree and the Gini-based decision\ntree on datasets generated from causal models. This result indicates that the\nproposed approach can capture insights beyond those of classical decision\ntrees, especially in causally structured data. Based on the features used in\nthe LZ causal measure based decision tree, we introduce a causal strength for\neach features in the dataset so as to infer the predominant causal variables\nfor the occurrence of the outcome.\n", "date": "2024-11-04", "categories": []}
{"id": "2411.05625", "title": "Cross-validating causal discovery via Leave-One-Variable-Out", "abstract": "  We propose a new approach to falsify causal discovery algorithms without\nground truth, which is based on testing the causal model on a pair of variables\nthat has been dropped when learning the causal model. To this end, we use the\n\"Leave-One-Variable-Out (LOVO)\" prediction where $Y$ is inferred from $X$\nwithout any joint observations of $X$ and $Y$, given only training data from\n$X,Z_1,\\dots,Z_k$ and from $Z_1,\\dots,Z_k,Y$. We demonstrate that causal models\non the two subsets, in the form of Acyclic Directed Mixed Graphs (ADMGs), often\nentail conclusions on the dependencies between $X$ and $Y$, enabling this type\nof prediction. The prediction error can then be estimated since the joint\ndistribution $P(X, Y)$ is assumed to be available, and $X$ and $Y$ have only\nbeen omitted for the purpose of falsification. After presenting this graphical\nmethod, which is applicable to general causal discovery algorithms, we\nillustrate how to construct a LOVO predictor tailored towards algorithms\nrelying on specific a priori assumptions, such as linear additive noise models.\nSimulations indicate that the LOVO prediction error is indeed correlated with\nthe accuracy of the causal outputs, affirming the method's effectiveness.\n", "date": "2024-11-08", "categories": []}
{"id": "2411.04243", "title": "ION-C: Integration of Overlapping Networks via Constraints", "abstract": "  In many causal learning problems, variables of interest are often not all\nmeasured over the same observations, but are instead distributed across\nmultiple datasets with overlapping variables. Tillman et al. (2008) presented\nthe first algorithm for enumerating the minimal equivalence class of\nground-truth DAGs consistent with all input graphs by exploiting local\nindependence relations, called ION. In this paper, this problem is formulated\nas a more computationally efficient answer set programming (ASP) problem, which\nwe call ION-C, and solved with the ASP system clingo. The ION-C algorithm was\nrun on random synthetic graphs with varying sizes, densities, and degrees of\noverlap between subgraphs, with overlap having the largest impact on runtime,\nnumber of solution graphs, and agreement within the output set. To validate\nION-C on real-world data, we ran the algorithm on overlapping graphs learned\nfrom data from two successive iterations of the European Social Survey (ESS),\nusing a procedure for conducting joint independence tests to prevent\ninconsistencies in the input.\n", "date": "2024-11-06", "categories": []}
{"id": "2411.00213", "title": "Learning Mixtures of Unknown Causal Interventions", "abstract": "  The ability to conduct interventions plays a pivotal role in learning causal\nrelationships among variables, thus facilitating applications across diverse\nscientific disciplines such as genomics, economics, and machine learning.\nHowever, in many instances within these applications, the process of generating\ninterventional data is subject to noise: rather than data being sampled\ndirectly from the intended interventional distribution, interventions often\nyield data sampled from a blend of both intended and unintended interventional\ndistributions.\n  We consider the fundamental challenge of disentangling mixed interventional\nand observational data within linear Structural Equation Models (SEMs) with\nGaussian additive noise without the knowledge of the true causal graph. We\ndemonstrate that conducting interventions, whether do or soft, yields\ndistributions with sufficient diversity and properties conducive to efficiently\nrecovering each component within the mixture. Furthermore, we establish that\nthe sample complexity required to disentangle mixed data inversely correlates\nwith the extent of change induced by an intervention in the equations governing\nthe affected variable values. As a result, the causal graph can be identified\nup to its interventional Markov Equivalence Class, similar to scenarios where\nno noise influences the generation of interventional data. We further support\nour theoretical findings by conducting simulations wherein we perform causal\ndiscovery from such mixed data.\n", "date": "2024-10-31", "categories": []}
{"id": "2410.23862", "title": "$\\psi$DAG: Projected Stochastic Approximation Iteration for DAG\n  Structure Learning", "abstract": "  Learning the structure of Directed Acyclic Graphs (DAGs) presents a\nsignificant challenge due to the vast combinatorial search space of possible\ngraphs, which scales exponentially with the number of nodes. Recent\nadvancements have redefined this problem as a continuous optimization task by\nincorporating differentiable acyclicity constraints. These methods commonly\nrely on algebraic characterizations of DAGs, such as matrix exponentials, to\nenable the use of gradient-based optimization techniques. Despite these\ninnovations, existing methods often face optimization difficulties due to the\nhighly non-convex nature of DAG constraints and the per-iteration computational\ncomplexity. In this work, we present a novel framework for learning DAGs,\nemploying a Stochastic Approximation approach integrated with Stochastic\nGradient Descent (SGD)-based optimization techniques. Our framework introduces\nnew projection methods tailored to efficiently enforce DAG constraints,\nensuring that the algorithm converges to a feasible local minimum. With its low\niteration complexity, the proposed method is well-suited for handling\nlarge-scale problems with improved computational efficiency. We demonstrate the\neffectiveness and scalability of our framework through comprehensive\nexperimental evaluations, which confirm its superior performance across various\nsettings.\n", "date": "2024-10-31", "categories": []}
{"id": "2410.23155", "title": "QWO: Speeding Up Permutation-Based Causal Discovery in LiGAMs", "abstract": "  Causal discovery is essential for understanding relationships among variables\nof interest in many scientific domains. In this paper, we focus on\npermutation-based methods for learning causal graphs in Linear Gaussian Acyclic\nModels (LiGAMs), where the permutation encodes a causal ordering of the\nvariables. Existing methods in this setting are not scalable due to their high\ncomputational complexity. These methods are comprised of two main components:\n(i) constructing a specific DAG, $\\mathcal{G}^\\pi$, for a given permutation\n$\\pi$, which represents the best structure that can be learned from the\navailable data while adhering to $\\pi$, and (ii) searching over the space of\npermutations (i.e., causal orders) to minimize the number of edges in\n$\\mathcal{G}^\\pi$. We introduce QWO, a novel approach that significantly\nenhances the efficiency of computing $\\mathcal{G}^\\pi$ for a given permutation\n$\\pi$. QWO has a speed-up of $O(n^2)$ ($n$ is the number of variables) compared\nto the state-of-the-art BIC-based method, making it highly scalable. We show\nthat our method is theoretically sound and can be integrated into existing\nsearch strategies such as GRASP and hill-climbing-based methods to improve\ntheir performance.\n", "date": "2024-10-30", "categories": []}
{"id": "2312.17122", "title": "LLM4Causal: Democratized Causal Tools for Everyone via Large Language\n  Model", "abstract": "  Large Language Models (LLMs) have shown their success in language\nunderstanding and reasoning on general topics. However, their capability to\nperform inference based on user-specified structured data and knowledge in\ncorpus-rare concepts, such as causal decision-making is still limited. In this\nwork, we explore the possibility of fine-tuning an open-sourced LLM into\nLLM4Causal, which can identify the causal task, execute a corresponding\nfunction, and interpret its numerical results based on users' queries and the\nprovided dataset. Meanwhile, we propose a data generation process for more\ncontrollable GPT prompting and present two instruction-tuning datasets: (1)\nCausal-Retrieval-Bench for causal problem identification and input parameter\nextraction for causal function calling and (2) Causal-Interpret-Bench for\nin-context causal interpretation. By conducting end-to-end evaluations and two\nablation studies, we showed that LLM4Causal can deliver end-to-end solutions\nfor causal problems and provide easy-to-understand answers, which significantly\noutperforms the baselines.\n", "date": "2023-12-28", "categories": []}
{"id": "2410.19870", "title": "Causal Order Discovery based on Monotonic SCMs", "abstract": "  In this paper, we consider the problem of causal order discovery within the\nframework of monotonic Structural Causal Models (SCMs), which have gained\nattention for their potential to enable causal inference and causal discovery\nfrom observational data. While existing approaches either assume prior\nknowledge about the causal order or use complex optimization techniques to\nimpose sparsity in the Jacobian of Triangular Monotonic Increasing maps, our\nwork introduces a novel sequential procedure that directly identifies the\ncausal order by iteratively detecting the root variable. This method eliminates\nthe need for sparsity assumptions and the associated optimization challenges,\nenabling the identification of a unique SCM without the need for multiple\nindependence tests to break the Markov equivalence class. We demonstrate the\neffectiveness of our approach in sequentially finding the root variable,\ncomparing it to methods that maximize Jacobian sparsity.\n", "date": "2024-10-24", "categories": []}
{"id": "2410.19923", "title": "Language Agents Meet Causality -- Bridging LLMs and Causal World Models", "abstract": "  Large Language Models (LLMs) have recently shown great promise in planning\nand reasoning applications. These tasks demand robust systems, which arguably\nrequire a causal understanding of the environment. While LLMs can acquire and\nreflect common sense causal knowledge from their pretraining data, this\ninformation is often incomplete, incorrect, or inapplicable to a specific\nenvironment. In contrast, causal representation learning (CRL) focuses on\nidentifying the underlying causal structure within a given environment. We\npropose a framework that integrates CRLs with LLMs to enable causally-aware\nreasoning and planning. This framework learns a causal world model, with causal\nvariables linked to natural language expressions. This mapping provides LLMs\nwith a flexible interface to process and generate descriptions of actions and\nstates in text form. Effectively, the causal world model acts as a simulator\nthat the LLM can query and interact with. We evaluate the framework on causal\ninference and planning tasks across temporal scales and environmental\ncomplexities. Our experiments demonstrate the effectiveness of the approach,\nwith the causally-aware method outperforming LLM-based reasoners, especially\nfor longer planning horizons.\n", "date": "2024-10-25", "categories": []}
{"id": "2410.20089", "title": "Sample Efficient Bayesian Learning of Causal Graphs from Interventions", "abstract": "  Causal discovery is a fundamental problem with applications spanning various\nareas in science and engineering. It is well understood that solely using\nobservational data, one can only orient the causal graph up to its Markov\nequivalence class, necessitating interventional data to learn the complete\ncausal graph. Most works in the literature design causal discovery policies\nwith perfect interventions, i.e., they have access to infinite interventional\nsamples. This study considers a Bayesian approach for learning causal graphs\nwith limited interventional samples, mirroring real-world scenarios where such\nsamples are usually costly to obtain. By leveraging the recent result of\nWien\\\"obst et al. (2023) on uniform DAG sampling in polynomial time, we can\nefficiently enumerate all the cut configurations and their corresponding\ninterventional distributions of a target set, and further track their\nposteriors. Given any number of interventional samples, our proposed algorithm\nrandomly intervenes on a set of target vertices that cut all the edges in the\ngraph and returns a causal graph according to the posterior of each target set.\nWhen the number of interventional samples is large enough, we show\ntheoretically that our proposed algorithm will return the true causal graph\nwith high probability. We compare our algorithm against various baseline\nmethods on simulated datasets, demonstrating its superior accuracy measured by\nthe structural Hamming distance between the learned DAG and the ground truth.\nAdditionally, we present a case study showing how this algorithm could be\nmodified to answer more general causal questions without learning the whole\ngraph. As an example, we illustrate that our method can be used to estimate the\ncausal effect of a variable that cannot be intervened.\n", "date": "2024-10-26", "categories": []}
{"id": "2410.20405", "title": "Causal Modeling in Multi-Context Systems: Distinguishing Multiple\n  Context-Specific Causal Graphs which Account for Observational Support", "abstract": "  Causal structure learning with data from multiple contexts carries both\nopportunities and challenges. Opportunities arise from considering shared and\ncontext-specific causal graphs enabling to generalize and transfer causal\nknowledge across contexts. However, a challenge that is currently understudied\nin the literature is the impact of differing observational support between\ncontexts on the identifiability of causal graphs. Here we study in detail\nrecently introduced [6] causal graph objects that capture both causal\nmechanisms and data support, allowing for the analysis of a larger class of\ncontext-specific changes, characterizing distribution shifts more precisely. We\nthereby extend results on the identifiability of context-specific causal\nstructures and propose a framework to model context-specific independence (CSI)\nwithin structural causal models (SCMs) in a refined way that allows to explore\nscenarios where these graph objects differ. We demonstrate how this framework\ncan help explaining phenomena like anomalies or extreme events, where causal\nmechanisms change or appear to change under different conditions. Our results\ncontribute to the theoretical foundations for understanding causal relations in\nmulti-context systems, with implications for generalization, transfer learning,\nand anomaly detection. Future work may extend this approach to more complex\ndata types, such as time-series.\n", "date": "2024-10-27", "categories": []}
{"id": "2410.21141", "title": "LLM-initialized Differentiable Causal Discovery", "abstract": "  The discovery of causal relationships between random variables is an\nimportant yet challenging problem that has applications across many scientific\ndomains. Differentiable causal discovery (DCD) methods are effective in\nuncovering causal relationships from observational data; however, these\napproaches often suffer from limited interpretability and face challenges in\nincorporating domain-specific prior knowledge. In contrast, Large Language\nModels (LLMs)-based causal discovery approaches have recently been shown\ncapable of providing useful priors for causal discovery but struggle with\nformal causal reasoning. In this paper, we propose LLM-DCD, which uses an LLM\nto initialize the optimization of the maximum likelihood objective function of\nDCD approaches, thereby incorporating strong priors into the discovery method.\nTo achieve this initialization, we design our objective function to depend on\nan explicitly defined adjacency matrix of the causal graph as its only\nvariational parameter. Directly optimizing the explicitly defined adjacency\nmatrix provides a more interpretable approach to causal discovery.\nAdditionally, we demonstrate higher accuracy on key benchmarking datasets of\nour approach compared to state-of-the-art alternatives, and provide empirical\nevidence that the quality of the initialization directly impacts the quality of\nthe final output of our DCD approach. LLM-DCD opens up new opportunities for\ntraditional causal discovery methods like DCD to benefit from future\nimprovements in the causal reasoning capabilities of LLMs.\n", "date": "2024-10-28", "categories": []}
{"id": "2410.19469", "title": "Unified Causality Analysis Based on the Degrees of Freedom", "abstract": "  Temporally evolving systems are typically modeled by dynamic equations. A key\nchallenge in accurate modeling is understanding the causal relationships\nbetween subsystems, as well as identifying the presence and influence of\nunobserved hidden drivers on the observed dynamics. This paper presents a\nunified method capable of identifying fundamental causal relationships between\npairs of systems, whether deterministic or stochastic. Notably, the method also\nuncovers hidden common causes beyond the observed variables. By analyzing the\ndegrees of freedom in the system, our approach provides a more comprehensive\nunderstanding of both causal influence and hidden confounders. This unified\nframework is validated through theoretical models and simulations,\ndemonstrating its robustness and potential for broader application.\n", "date": "2024-10-25", "categories": []}
{"id": "2410.18147", "title": "MEC-IP: Efficient Discovery of Markov Equivalent Classes via Integer\n  Programming", "abstract": "  This paper presents a novel Integer Programming (IP) approach for discovering\nthe Markov Equivalent Class (MEC) of Bayesian Networks (BNs) through\nobservational data. The MEC-IP algorithm utilizes a unique clique-focusing\nstrategy and Extended Maximal Spanning Graphs (EMSG) to streamline the search\nfor MEC, thus overcoming the computational limitations inherent in other\nexisting algorithms. Our numerical results show that not only a remarkable\nreduction in computational time is achieved by our algorithm but also an\nimprovement in causal discovery accuracy is seen across diverse datasets. These\nfindings underscore this new algorithm's potential as a powerful tool for\nresearchers and practitioners in causal discovery and BNSL, offering a\nsignificant leap forward toward the efficient and accurate analysis of complex\ndata structures.\n", "date": "2024-10-22", "categories": []}
{"id": "2410.18396", "title": "Revisiting Differentiable Structure Learning: Inconsistency of $\\ell_1$\n  Penalty and Beyond", "abstract": "  Recent advances in differentiable structure learning have framed the\ncombinatorial problem of learning directed acyclic graphs as a continuous\noptimization problem. Various aspects, including data standardization, have\nbeen studied to identify factors that influence the empirical performance of\nthese methods. In this work, we investigate critical limitations in\ndifferentiable structure learning methods, focusing on settings where the true\nstructure can be identified up to Markov equivalence classes, particularly in\nthe linear Gaussian case. While Ng et al. (2024) highlighted potential\nnon-convexity issues in this setting, we demonstrate and explain why the use of\n$\\ell_1$-penalized likelihood in such cases is fundamentally inconsistent, even\nif the global optimum of the optimization problem can be found. To resolve this\nlimitation, we develop a hybrid differentiable structure learning method based\non $\\ell_0$-penalized likelihood with hard acyclicity constraint, where the\n$\\ell_0$ penalty can be approximated by different techniques including\nGumbel-Softmax. Specifically, we first estimate the underlying moral graph, and\nuse it to restrict the search space of the optimization problem, which helps\nalleviate the non-convexity issue. Experimental results show that the proposed\nmethod enhances empirical performance both before and after data\nstandardization, providing a more reliable path for future advancements in\ndifferentiable structure learning, especially for learning Markov equivalence\nclasses.\n", "date": "2024-10-24", "categories": []}
{"id": "2407.09632", "title": "Granger Causality in Extremes", "abstract": "  We introduce a rigorous mathematical framework for Granger causality in\nextremes, designed to identify causal links from extreme events in time series.\nGranger causality plays a pivotal role in uncovering directional relationships\namong time-varying variables. While this notion gains heightened importance\nduring extreme and highly volatile periods, state-of-the-art methods primarily\nfocus on causality within the body of the distribution, often overlooking\ncausal mechanisms that manifest only during extreme events. Our framework is\ndesigned to infer causality mainly from extreme events by leveraging the causal\ntail coefficient. We establish equivalences between causality in extremes and\nother causal concepts, including (classical) Granger causality, Sims causality,\nand structural causality. We prove other key properties of Granger causality in\nextremes and show that the framework is especially helpful under the presence\nof hidden confounders. We also propose a novel inference method for detecting\nthe presence of Granger causality in extremes from data. Our method is\nmodel-free, can handle non-linear and high-dimensional time series, outperforms\ncurrent state-of-the-art methods in all considered setups, both in performance\nand speed, and was found to uncover coherent effects when applied to financial\nand extreme weather observations.\n", "date": "2024-07-12", "categories": []}
{"id": "2410.14146", "title": "CausalChat: Interactive Causal Model Development and Refinement Using\n  Large Language Models", "abstract": "  Causal networks are widely used in many fields to model the complex\nrelationships between variables. A recent approach has sought to construct\ncausal networks by leveraging the wisdom of crowds through the collective\nparticipation of humans. While this can yield detailed causal networks that\nmodel the underlying phenomena quite well, it requires a large number of\nindividuals with domain understanding. We adopt a different approach:\nleveraging the causal knowledge that large language models, such as OpenAI's\nGPT-4, have learned by ingesting massive amounts of literature. Within a\ndedicated visual analytics interface, called CausalChat, users explore single\nvariables or variable pairs recursively to identify causal relations, latent\nvariables, confounders, and mediators, constructing detailed causal networks\nthrough conversation. Each probing interaction is translated into a tailored\nGPT-4 prompt and the response is conveyed through visual representations which\nare linked to the generated text for explanations. We demonstrate the\nfunctionality of CausalChat across diverse data contexts and conduct user\nstudies involving both domain experts and laypersons.\n", "date": "2024-10-18", "categories": []}
{"id": "2410.14436", "title": "Learning to refine domain knowledge for biological network inference", "abstract": "  Perturbation experiments allow biologists to discover causal relationships\nbetween variables of interest, but the sparsity and high dimensionality of\nthese data pose significant challenges for causal structure learning\nalgorithms. Biological knowledge graphs can bootstrap the inference of causal\nstructures in these situations, but since they compile vastly diverse\ninformation, they can bias predictions towards well-studied systems.\nAlternatively, amortized causal structure learning algorithms encode inductive\nbiases through data simulation and train supervised models to recapitulate\nthese synthetic graphs. However, realistically simulating biology is arguably\neven harder than understanding a specific system. In this work, we take\ninspiration from both strategies and propose an amortized algorithm for\nrefining domain knowledge, based on data observations. On real and synthetic\ndatasets, we show that our approach outperforms baselines in recovering ground\ntruth causal graphs and identifying errors in the prior knowledge with limited\ninterventional data.\n", "date": "2024-10-18", "categories": []}
{"id": "2311.07454", "title": "Causal Discovery under Latent Class Confounding", "abstract": "  An acyclic causal structure can be described with directed acyclic graph\n(DAG), where arrows indicate the possibility of direct causation. The task of\nlearning this structure from data is known as \"causal discovery.\" Diverse\npopulations or changing environments can sometimes give rise to data that is\nheterogeneous in the following sense: each population/environment is a \"source\"\nwhich idiosyncratically determines the forms of those direct causal effects.\nFrom this perspective, the source is a latent common cause for every observed\nvariable. While some methods for causal discovery are able to work around\nlatent confounding in special cases, especially when only few observables are\nconfounded, a global confounder is a difficult challenge. The only known ways\nto deal with latent global confounding involve assumptions that limit the\nstructural equations and/or noise functions. We demonstrate that globally\nconfounded causal structures can still be identifiable with arbitrary\nstructural equations and noise functions, so long as the number of latent\nclasses remains small relative to the size and sparsity of the underlying DAG.\n", "date": "2023-11-13", "categories": []}
{"id": "2301.07427", "title": "Boosting Synthetic Data Generation with Effective Nonlinear Causal\n  Discovery", "abstract": "  Synthetic data generation has been widely adopted in software testing, data\nprivacy, imbalanced learning, and artificial intelligence explanation. In all\nsuch contexts, it is crucial to generate plausible data samples. A common\nassumption of approaches widely used for data generation is the independence of\nthe features. However, typically, the variables of a dataset depend on one\nanother, and these dependencies are not considered in data generation leading\nto the creation of implausible records. The main problem is that dependencies\namong variables are typically unknown. In this paper, we design a synthetic\ndataset generator for tabular data that can discover nonlinear causalities\namong the variables and use them at generation time. State-of-the-art methods\nfor nonlinear causal discovery are typically inefficient. We boost them by\nrestricting the causal discovery among the features appearing in the frequent\npatterns efficiently retrieved by a pattern mining algorithm. We design a\nframework for generating synthetic datasets with known causalities to validate\nour proposal. Broad experimentation on many synthetic and real datasets with\nknown causalities shows the effectiveness of the proposed method.\n", "date": "2023-01-18", "categories": []}
{"id": "2410.02844", "title": "CAnDOIT: Causal Discovery with Observational and Interventional Data\n  from Time-Series", "abstract": "  The study of cause-and-effect is of the utmost importance in many branches of\nscience, but also for many practical applications of intelligent systems. In\nparticular, identifying causal relationships in situations that include hidden\nfactors is a major challenge for methods that rely solely on observational data\nfor building causal models. This paper proposes CAnDOIT, a causal discovery\nmethod to reconstruct causal models using both observational and interventional\ntime-series data. The use of interventional data in the causal analysis is\ncrucial for real-world applications, such as robotics, where the scenario is\nhighly complex and observational data alone are often insufficient to uncover\nthe correct causal structure. Validation of the method is performed initially\non randomly generated synthetic models and subsequently on a well-known\nbenchmark for causal structure learning in a robotic manipulation environment.\nThe experiments demonstrate that the approach can effectively handle data from\ninterventions and exploit them to enhance the accuracy of the causal analysis.\nA Python implementation of CAnDOIT has also been developed and is publicly\navailable on GitHub: https://github.com/lcastri/causalflow.\n", "date": "2024-10-03", "categories": []}
{"id": "2410.08787", "title": "Efficient Differentiable Discovery of Causal Order", "abstract": "  In the algorithm Intersort, Chevalley et al. (2024) proposed a score-based\nmethod to discover the causal order of variables in a Directed Acyclic Graph\n(DAG) model, leveraging interventional data to outperform existing methods.\nHowever, as a score-based method over the permutahedron, Intersort is\ncomputationally expensive and non-differentiable, limiting its ability to be\nutilised in problems involving large-scale datasets, such as those in genomics\nand climate models, or to be integrated into end-to-end gradient-based learning\nframeworks. We address this limitation by reformulating Intersort using\ndifferentiable sorting and ranking techniques. Our approach enables scalable\nand differentiable optimization of causal orderings, allowing the continuous\nscore function to be incorporated as a regularizer in downstream tasks.\nEmpirical results demonstrate that causal discovery algorithms benefit\nsignificantly from regularizing on the causal order, underscoring the\neffectiveness of our method. Our work opens the door to efficiently\nincorporating regularization for causal order into the training of\ndifferentiable models and thereby addresses a long-standing limitation of\npurely associational supervised learning.\n", "date": "2024-10-11", "categories": []}
{"id": "2410.05890", "title": "Ordering-Based Causal Discovery for Linear and Nonlinear Relations", "abstract": "  Identifying causal relations from purely observational data typically\nrequires additional assumptions on relations and/or noise. Most current methods\nrestrict their analysis to datasets that are assumed to have pure linear or\nnonlinear relations, which is often not reflective of real-world datasets that\ncontain a combination of both. This paper presents CaPS, an ordering-based\ncausal discovery algorithm that effectively handles linear and nonlinear\nrelations. CaPS introduces a novel identification criterion for topological\nordering and incorporates the concept of \"parent score\" during the\npost-processing optimization stage. These scores quantify the strength of the\naverage causal effect, helping to accelerate the pruning process and correct\ninaccurate predictions in the pruning step. Experimental results demonstrate\nthat our proposed solutions outperform state-of-the-art baselines on synthetic\ndata with varying ratios of linear and nonlinear relations. The results\nobtained from real-world data also support the competitiveness of CaPS. Code\nand datasets are available at https://github.com/E2real/CaPS.\n", "date": "2024-10-08", "categories": []}
{"id": "2410.06392", "title": "Counterfactual Causal Inference in Natural Language with Large Language\n  Models", "abstract": "  Causal structure discovery methods are commonly applied to structured data\nwhere the causal variables are known and where statistical testing can be used\nto assess the causal relationships. By contrast, recovering a causal structure\nfrom unstructured natural language data such as news articles contains numerous\nchallenges due to the absence of known variables or counterfactual data to\nestimate the causal links. Large Language Models (LLMs) have shown promising\nresults in this direction but also exhibit limitations. This work investigates\nLLM's abilities to build causal graphs from text documents and perform\ncounterfactual causal inference. We propose an end-to-end causal structure\ndiscovery and causal inference method from natural language: we first use an\nLLM to extract the instantiated causal variables from text data and build a\ncausal graph. We merge causal graphs from multiple data sources to represent\nthe most exhaustive set of causes possible. We then conduct counterfactual\ninference on the estimated graph. The causal graph conditioning allows\nreduction of LLM biases and better represents the causal estimands. We use our\nmethod to show that the limitations of LLMs in counterfactual causal reasoning\ncome from prediction errors and propose directions to mitigate them. We\ndemonstrate the applicability of our method on real-world news articles.\n", "date": "2024-10-08", "categories": []}
{"id": "2410.01221", "title": "Induced Covariance for Causal Discovery in Linear Sparse Structures", "abstract": "  Causal models seek to unravel the cause-effect relationships among variables\nfrom observed data, as opposed to mere mappings among them, as traditional\nregression models do. This paper introduces a novel causal discovery algorithm\ndesigned for settings in which variables exhibit linearly sparse relationships.\nIn such scenarios, the causal links represented by directed acyclic graphs\n(DAGs) can be encapsulated in a structural matrix. The proposed approach\nleverages the structural matrix's ability to reconstruct data and the\nstatistical properties it imposes on the data to identify the correct\nstructural matrix. This method does not rely on independence tests or graph\nfitting procedures, making it suitable for scenarios with limited training\ndata. Simulation results demonstrate that the proposed method outperforms the\nwell-known PC, GES, BIC exact search, and LINGAM-based methods in recovering\nlinearly sparse causal structures.\n", "date": "2024-10-02", "categories": []}
{"id": "2311.10228", "title": "Data-Driven Bayesian Network Models of Hurricane Evacuation Decision\n  Making", "abstract": "  Hurricanes cause significant economic and human costs, requiring individuals\nto make critical evacuation decisions under uncertainty and stress. To enhance\nthe understanding of this decision-making process, we propose using Bayesian\nNetworks (BNs) to model evacuation decisions during hurricanes. We collected\nquestionnaire data from two significant hurricane events: Hurricane Harvey and\nHurricane Irma. We employed a data-driven approach by first conducting variable\nselection using mutual information, followed by BN structure learning with two\nconstraint-based algorithms. The robustness of the learned structures was\nenhanced by model averaging based on bootstrap resampling. We examined and\ncompared the learned structures of both hurricanes, revealing potential causal\nrelationships among key predictors of evacuation, including risk perception,\ninformation received from media, suggestions from family and friends, and\nneighbors evacuating. Our findings highlight the significant role of social\ninfluence, providing valuable insights into the process of evacuation\ndecision-making. Our results demonstrate the applicability and effectiveness of\ndata-driven BN modeling in evacuation decision making.\n", "date": "2023-11-16", "categories": []}
{"id": "2409.19060", "title": "CURATE: Scaling-up Differentially Private Causal Graph Discovery", "abstract": "  Causal Graph Discovery (CGD) is the process of estimating the underlying\nprobabilistic graphical model that represents joint distribution of features of\na dataset. CGD-algorithms are broadly classified into two categories: (i)\nConstraint-based algorithms (outcome depends on conditional independence (CI)\ntests), (ii) Score-based algorithms (outcome depends on optimized\nscore-function). Since, sensitive features of observational data is prone to\nprivacy-leakage, Differential Privacy (DP) has been adopted to ensure user\nprivacy in CGD. Adding same amount of noise in this sequential-natured\nestimation process affects the predictive performance of the algorithms. As\ninitial CI tests in constraint-based algorithms and later iterations of the\noptimization process of score-based algorithms are crucial, they need to be\nmore accurate, less noisy. Based on this key observation, we present CURATE\n(CaUsal gRaph AdapTivE privacy), a DP-CGD framework with adaptive privacy\nbudgeting. In contrast to existing DP-CGD algorithms with uniform privacy\nbudgeting across all iterations, CURATE allows adaptive privacy budgeting by\nminimizing error probability (for constraint-based), maximizing iterations of\nthe optimization problem (for score-based) while keeping the cumulative leakage\nbounded. To validate our framework, we present a comprehensive set of\nexperiments on several datasets and show that CURATE achieves higher utility\ncompared to existing DP-CGD algorithms with less privacy-leakage.\n", "date": "2024-09-27", "categories": []}
{"id": "2409.20187", "title": "Choosing DAG Models Using Markov and Minimal Edge Count in the Absence\n  of Ground Truth", "abstract": "  We give a novel nonparametric pointwise consistent statistical test (the\nMarkov Checker) of the Markov condition for directed acyclic graph (DAG) or\ncompleted partially directed acyclic graph (CPDAG) models given a dataset. We\nalso introduce the Cross-Algorithm Frugality Search (CAFS) for rejecting DAG\nmodels that either do not pass the Markov Checker test or that are not edge\nminimal. Edge minimality has been used previously by Raskutti and Uhler as a\nnonparametric simplicity criterion, though CAFS readily generalizes to other\nsimplicity conditions. Reference to the ground truth is not necessary for CAFS,\nso it is useful for finding causal structure learning algorithms and tuning\nparameter settings that output causal models that are approximately true from a\ngiven data set. We provide a software tool for this analysis that is suitable\nfor even quite large or dense models, provided a suitably fast pointwise\nconsistent test of conditional independence is available. In addition, we show\nin simulation that the CAFS procedure can pick approximately correct models\nwithout knowing the ground truth.\n", "date": "2024-09-30", "categories": []}
{"id": "2404.06349", "title": "CausalBench: A Comprehensive Benchmark for Causal Learning Capability of\n  LLMs", "abstract": "  The ability to understand causality significantly impacts the competence of\nlarge language models (LLMs) in output explanation and counterfactual\nreasoning, as causality reveals the underlying data distribution. However, the\nlack of a comprehensive benchmark currently limits the evaluation of LLMs'\ncausal learning capabilities. To fill this gap, this paper develops CausalBench\nbased on data from the causal research community, enabling comparative\nevaluations of LLMs against traditional causal learning algorithms. To provide\na comprehensive investigation, we offer three tasks of varying difficulties,\nincluding correlation, causal skeleton, and causality identification.\nEvaluations of 19 leading LLMs reveal that, while closed-source LLMs show\npotential for simple causal relationships, they significantly lag behind\ntraditional algorithms on larger-scale networks ($>50$ nodes). Specifically,\nLLMs struggle with collider structures but excel at chain structures,\nespecially at long-chain causality analogous to Chains-of-Thought techniques.\nThis supports the current prompt approaches while suggesting directions to\nenhance LLMs' causal reasoning capability. Furthermore, CausalBench\nincorporates background knowledge and training data into prompts to thoroughly\nunlock LLMs' text-comprehension ability during evaluation, whose findings\nindicate that, LLM understand causality through semantic associations with\ndistinct entities, rather than directly from contextual information or\nnumerical distributions.\n", "date": "2024-04-09", "categories": []}
{"id": "2310.13387", "title": "Assumption violations in causal discovery and the robustness of score\n  matching", "abstract": "  When domain knowledge is limited and experimentation is restricted by\nethical, financial, or time constraints, practitioners turn to observational\ncausal discovery methods to recover the causal structure, exploiting the\nstatistical properties of their data. Because causal discovery without further\nassumptions is an ill-posed problem, each algorithm comes with its own set of\nusually untestable assumptions, some of which are hard to meet in real\ndatasets. Motivated by these considerations, this paper extensively benchmarks\nthe empirical performance of recent causal discovery methods on observational\ni.i.d. data generated under different background conditions, allowing for\nviolations of the critical assumptions required by each selected approach. Our\nexperimental findings show that score matching-based methods demonstrate\nsurprising performance in the false positive and false negative rate of the\ninferred graph in these challenging scenarios, and we provide theoretical\ninsights into their performance. This work is also the first effort to\nbenchmark the stability of causal discovery algorithms with respect to the\nvalues of their hyperparameters. Finally, we hope this paper will set a new\nstandard for the evaluation of causal discovery methods and can serve as an\naccessible entry point for practitioners interested in the field, highlighting\nthe empirical implications of different algorithm choices.\n", "date": "2023-10-20", "categories": []}
{"id": "2409.08419", "title": "Introducing CausalBench: A Flexible Benchmark Framework for Causal\n  Analysis and Machine Learning", "abstract": "  While witnessing the exceptional success of machine learning (ML)\ntechnologies in many applications, users are starting to notice a critical\nshortcoming of ML: correlation is a poor substitute for causation. The\nconventional way to discover causal relationships is to use randomized\ncontrolled experiments (RCT); in many situations, however, these are\nimpractical or sometimes unethical. Causal learning from observational data\noffers a promising alternative. While being relatively recent, causal learning\naims to go far beyond conventional machine learning, yet several major\nchallenges remain. Unfortunately, advances are hampered due to the lack of\nunified benchmark datasets, algorithms, metrics, and evaluation service\ninterfaces for causal learning. In this paper, we introduce {\\em CausalBench},\na transparent, fair, and easy-to-use evaluation platform, aiming to (a) enable\nthe advancement of research in causal learning by facilitating scientific\ncollaboration in novel algorithms, datasets, and metrics and (b) promote\nscientific objectivity, reproducibility, fairness, and awareness of bias in\ncausal learning research. CausalBench provides services for benchmarking data,\nalgorithms, models, and metrics, impacting the needs of a broad of scientific\nand engineering disciplines.\n", "date": "2024-09-12", "categories": []}
{"id": "2409.10271", "title": "Causal Discovery in Recommender Systems: Example and Discussion", "abstract": "  Causality is receiving increasing attention by the artificial intelligence\nand machine learning communities. This paper gives an example of modelling a\nrecommender system problem using causal graphs. Specifically, we approached the\ncausal discovery task to learn a causal graph by combining observational data\nfrom an open-source dataset with prior knowledge. The resulting causal graph\nshows that only a few variables effectively influence the analysed feedback\nsignals. This contrasts with the recent trend in the machine learning community\nto include more and more variables in massive models, such as neural networks.\n", "date": "2024-09-16", "categories": []}
{"id": "2409.07594", "title": "Automated Discovery of Pairwise Interactions from Unstructured Data", "abstract": "  Pairwise interactions between perturbations to a system can provide evidence\nfor the causal dependencies of the underlying underlying mechanisms of a\nsystem. When observations are low dimensional, hand crafted measurements,\ndetecting interactions amounts to simple statistical tests, but it is not\nobvious how to detect interactions between perturbations affecting latent\nvariables. We derive two interaction tests that are based on pairwise\ninterventions, and show how these tests can be integrated into an active\nlearning pipeline to efficiently discover pairwise interactions between\nperturbations. We illustrate the value of these tests in the context of\nbiology, where pairwise perturbation experiments are frequently used to reveal\ninteractions that are not observable from any single perturbation. Our tests\ncan be run on unstructured data, such as the pixels in an image, which enables\na more general notion of interaction than typical cell viability experiments,\nand can be run on cheaper experimental assays. We validate on several synthetic\nand real biological experiments that our tests are able to identify interacting\npairs effectively. We evaluate our approach on a real biological experiment\nwhere we knocked out 50 pairs of genes and measured the effect with microscopy\nimages. We show that we are able to recover significantly more known biological\ninteractions than random search and standard active learning baselines.\n", "date": "2024-09-11", "categories": []}
{"id": "2409.07880", "title": "Non-negative Weighted DAG Structure Learning", "abstract": "  We address the problem of learning the topology of directed acyclic graphs\n(DAGs) from nodal observations, which adhere to a linear structural equation\nmodel. Recent advances framed the combinatorial DAG structure learning task as\na continuous optimization problem, yet existing methods must contend with the\ncomplexities of non-convex optimization. To overcome this limitation, we assume\nthat the latent DAG contains only non-negative edge weights. Leveraging this\nadditional structure, we argue that cycles can be effectively characterized\n(and prevented) using a convex acyclicity function based on the log-determinant\nof the adjacency matrix. This convexity allows us to relax the task of learning\nthe non-negative weighted DAG as an abstract convex optimization problem. We\npropose a DAG recovery algorithm based on the method of multipliers, that is\nguaranteed to return a global minimizer. Furthermore, we prove that in the\ninfinite sample size regime, the convexity of our approach ensures the recovery\nof the true DAG structure. We empirically validate the performance of our\nalgorithm in several reproducible synthetic-data test cases, showing that it\noutperforms state-of-the-art alternatives.\n", "date": "2024-09-12", "categories": []}
{"id": "2310.05655", "title": "Causal structure learning with momentum: Sampling distributions over\n  Markov Equivalence Classes of DAGs", "abstract": "  In the context of inferring a Bayesian network structure (directed acyclic\ngraph, DAG for short), we devise a non-reversible continuous time Markov chain,\nthe ``Causal Zig-Zag sampler'', that targets a probability distribution over\nclasses of observationally equivalent (Markov equivalent) DAGs. The classes are\nrepresented as completed partially directed acyclic graphs (CPDAGs). The\nnon-reversible Markov chain relies on the operators used in Chickering's Greedy\nEquivalence Search (GES) and is endowed with a momentum variable, which\nimproves mixing significantly as we show empirically. The possible target\ndistributions include posterior distributions based on a prior over DAGs and a\nMarkov equivalent likelihood. We offer an efficient implementation wherein we\ndevelop new algorithms for listing, counting, uniformly sampling, and applying\npossible moves of the GES operators, all of which significantly improve upon\nthe state-of-the-art run-time.\n", "date": "2023-10-09", "categories": []}
{"id": "2406.02191", "title": "On the Recoverability of Causal Relations from Temporally Aggregated\n  I.I.D. Data", "abstract": "  We consider the effect of temporal aggregation on instantaneous\n(non-temporal) causal discovery in general setting. This is motivated by the\nobservation that the true causal time lag is often considerably shorter than\nthe observational interval. This discrepancy leads to high aggregation, causing\ntime-delay causality to vanish and instantaneous dependence to manifest.\nAlthough we expect such instantaneous dependence has consistency with the true\ncausal relation in certain sense to make the discovery results meaningful, it\nremains unclear what type of consistency we need and when will such consistency\nbe satisfied. We proposed functional consistency and conditional independence\nconsistency in formal way correspond functional causal model-based methods and\nconditional independence-based methods respectively and provide the conditions\nunder which these consistencies will hold. We show theoretically and\nexperimentally that causal discovery results may be seriously distorted by\naggregation especially in complete nonlinear case and we also find causal\nrelationship still recoverable from aggregated data if we have partial\nlinearity or appropriate prior. Our findings suggest community should take a\ncautious and meticulous approach when interpreting causal discovery results\nfrom such data and show why and when aggregation will distort the performance\nof causal discovery methods.\n", "date": "2024-06-04", "categories": []}
{"id": "2407.13054", "title": "Comprehensive Review and Empirical Evaluation of Causal Discovery\n  Algorithms for Numerical Data", "abstract": "  Causal analysis has become an essential component in understanding the\nunderlying causes of phenomena across various fields. Despite its significance,\nexisting literature on causal discovery algorithms is fragmented, with\ninconsistent methodologies, i.e., there is no universal classification standard\nfor existing methods, and a lack of comprehensive evaluations, i.e., data\ncharacteristics are often ignored to be jointly analyzed when benchmarking\nalgorithms. This study addresses these gaps by conducting an exhaustive review\nand empirical evaluation for causal discovery methods on numerical data, aiming\nto provide a clearer and more structured understanding of the field. Our\nresearch begins with a comprehensive literature review spanning over two\ndecades, analyzing over 200 academic articles and identifying more than 40\nrepresentative algorithms. This extensive analysis leads to the development of\na structured taxonomy tailored to the complexities of causal discovery,\ncategorizing methods into six main types. To address the lack of comprehensive\nevaluations, our study conducts an extensive empirical assessment of 29 causal\ndiscovery algorithms on multiple synthetic and real-world datasets. We\ncategorize synthetic datasets based on size, linearity, and noise distribution,\nemploying five evaluation metrics, and summarize the top-3 algorithm\nrecommendations, providing guidelines for users in various data scenarios. Our\nresults highlight a significant impact of dataset characteristics on algorithm\nperformance. Moreover, a metadata extraction strategy with an accuracy\nexceeding 80% is developed to assist users in algorithm selection on unknown\ndatasets. Based on these insights, we offer professional and practical\nguidelines to help users choose the most suitable causal discovery methods for\ntheir specific dataset.\n", "date": "2024-07-17", "categories": []}
{"id": "2404.05746", "title": "Causality for Earth Science -- A Review on Time-series and\n  Spatiotemporal Causality Methods", "abstract": "  This survey paper covers the breadth and depth of time-series and\nspatiotemporal causality methods, and their applications in Earth Science. More\nspecifically, the paper presents an overview of causal discovery and causal\ninference, explains the underlying causal assumptions, and enlists evaluation\ntechniques and key terminologies of the domain area. The paper elicits the\nvarious state-of-the-art methods introduced for time-series and spatiotemporal\ncausal analysis along with their strengths and limitations. The paper further\ndescribes the existing applications of several methods for answering specific\nEarth Science questions such as extreme weather events, sea level rise,\nteleconnections etc. This survey paper can serve as a primer for Data Science\nresearchers interested in data-driven causal study as we share a list of\nresources, such as Earth Science datasets (synthetic, simulated and\nobservational data) and open source tools for causal analysis. It will equally\nbenefit the Earth Science community interested in taking an AI-driven approach\nto study the causality of different dynamic and thermodynamic processes as we\npresent the open challenges and opportunities in performing causality-based\nEarth Science study.\n", "date": "2024-04-03", "categories": []}
{"id": "2401.05218", "title": "Invariant Causal Prediction with Local Models", "abstract": "  We consider the task of identifying the causal parents of a target variable\namong a set of candidates from observational data. Our main assumption is that\nthe candidate variables are observed in different environments which may, under\ncertain assumptions, be regarded as interventions on the observed system. We\nassume a linear relationship between target and candidates, which can be\ndifferent in each environment with the only restriction that the causal\nstructure is invariant across environments. Within our proposed setting we\nprovide sufficient conditions for identifiability of the causal parents and\nintroduce a practical method called L-ICP ($\\textbf{L}$ocalized\n$\\textbf{I}$nvariant $\\textbf{Ca}$usal $\\textbf{P}$rediction), which is based\non a hypothesis test for parent identification using a ratio of minimum and\nmaximum statistics. We then show in a simplified setting that the statistical\npower of L-ICP converges exponentially fast in the sample size, and finally we\nanalyze the behavior of L-ICP experimentally in more general settings.\n", "date": "2024-01-10", "categories": []}
{"id": "2407.04980", "title": "Enabling Causal Discovery in Post-Nonlinear Models with Normalizing\n  Flows", "abstract": "  Post-nonlinear (PNL) causal models stand out as a versatile and adaptable\nframework for modeling intricate causal relationships. However, accurately\ncapturing the invertibility constraint required in PNL models remains\nchallenging in existing studies. To address this problem, we introduce CAF-PoNo\n(Causal discovery via Normalizing Flows for Post-Nonlinear models), harnessing\nthe power of the normalizing flows architecture to enforce the crucial\ninvertibility constraint in PNL models. Through normalizing flows, our method\nprecisely reconstructs the hidden noise, which plays a vital role in\ncause-effect identification through statistical independence testing.\nFurthermore, the proposed approach exhibits remarkable extensibility, as it can\nbe seamlessly expanded to facilitate multivariate causal discovery via causal\norder identification, empowering us to efficiently unravel complex causal\nrelationships. Extensive experimental evaluations on both simulated and real\ndatasets consistently demonstrate that the proposed method outperforms several\nstate-of-the-art approaches in both bivariate and multivariate causal discovery\ntasks.\n", "date": "2024-07-06", "categories": []}
{"id": "2407.04992", "title": "Scalable Variational Causal Discovery Unconstrained by Acyclicity", "abstract": "  Bayesian causal discovery offers the power to quantify epistemic\nuncertainties among a broad range of structurally diverse causal theories\npotentially explaining the data, represented in forms of directed acyclic\ngraphs (DAGs). However, existing methods struggle with efficient DAG sampling\ndue to the complex acyclicity constraint. In this study, we propose a scalable\nBayesian approach to effectively learn the posterior distribution over causal\ngraphs given observational data thanks to the ability to generate DAGs without\nexplicitly enforcing acyclicity. Specifically, we introduce a novel\ndifferentiable DAG sampling method that can generate a valid acyclic causal\ngraph by mapping an unconstrained distribution of implicit topological orders\nto a distribution over DAGs. Given this efficient DAG sampling scheme, we are\nable to model the posterior distribution over causal graphs using a simple\nvariational distribution over a continuous domain, which can be learned via the\nvariational inference framework. Extensive empirical experiments on both\nsimulated and real datasets demonstrate the superior performance of the\nproposed model compared to several state-of-the-art baselines.\n", "date": "2024-07-06", "categories": []}
{"id": "2408.14101", "title": "Estimating Causal Effects from Learned Causal Networks", "abstract": "  The standard approach to answering an identifiable causal-effect query (e.g.,\n$P(Y|do(X)$) when given a causal diagram and observational data is to first\ngenerate an estimand, or probabilistic expression over the observable\nvariables, which is then evaluated using the observational data. In this paper,\nwe propose an alternative paradigm for answering causal-effect queries over\ndiscrete observable variables. We propose to instead learn the causal Bayesian\nnetwork and its confounding latent variables directly from the observational\ndata. Then, efficient probabilistic graphical model (PGM) algorithms can be\napplied to the learned model to answer queries. Perhaps surprisingly, we show\nthat this \\emph{model completion} learning approach can be more effective than\nestimand approaches, particularly for larger models in which the estimand\nexpressions become computationally difficult.\n  We illustrate our method's potential using a benchmark collection of Bayesian\nnetworks and synthetically generated causal models.\n", "date": "2024-08-26", "categories": []}
{"id": "2404.11341", "title": "The Causal Chambers: Real Physical Systems as a Testbed for AI\n  Methodology", "abstract": "  In some fields of AI, machine learning and statistics, the validation of new\nmethods and algorithms is often hindered by the scarcity of suitable real-world\ndatasets. Researchers must often turn to simulated data, which yields limited\ninformation about the applicability of the proposed methods to real problems.\nAs a step forward, we have constructed two devices that allow us to quickly and\ninexpensively produce large datasets from non-trivial but well-understood\nphysical systems. The devices, which we call causal chambers, are\ncomputer-controlled laboratories that allow us to manipulate and measure an\narray of variables from these physical systems, providing a rich testbed for\nalgorithms from a variety of fields. We illustrate potential applications\nthrough a series of case studies in fields such as causal discovery,\nout-of-distribution generalization, change point detection, independent\ncomponent analysis, and symbolic regression. For applications to causal\ninference, the chambers allow us to carefully perform interventions. We also\nprovide and empirically validate a causal model of each chamber, which can be\nused as ground truth for different tasks. All hardware and software is made\nopen source, and the datasets are publicly available at causalchamber.org or\nthrough the Python package causalchamber.\n", "date": "2024-04-17", "categories": []}
{"id": "2408.12669", "title": "Bayesian Network Modeling of Causal Influence within Cognitive Domains\n  and Clinical Dementia Severity Ratings for Western and Indian Cohorts", "abstract": "  This study investigates the causal relationships between Clinical Dementia\nRatings (CDR) and its six domain scores across two distinct aging datasets: the\nAlzheimer's Disease Neuroimaging Initiative (ADNI) and the Longitudinal Aging\nStudy of India (LASI). Using Directed Acyclic Graphs (DAGs) derived from\nBayesian network models, we analyze the dependencies among domain scores and\ntheir influence on the global CDR. Our approach leverages the PC algorithm to\nestimate the DAG structures for both datasets, revealing notable differences in\ncausal relationships and edge strengths between the Western and Indian\npopulations. The analysis highlights a stronger dependency of CDR scores on\nmemory functions in both datasets, but with significant variations in edge\nstrengths and node degrees. By contrasting these findings, we aim to elucidate\npopulation-specific differences and similarities in dementia progression,\nproviding insights that could inform targeted interventions and improve\nunderstanding of dementia across diverse demographic contexts.\n", "date": "2024-08-16", "categories": []}
{"id": "2408.11181", "title": "A Full DAG Score-Based Algorithm for Learning Causal Bayesian Networks\n  with Latent Confounders", "abstract": "  Causal Bayesian networks (CBN) are popular graphical probabilistic models\nthat encode causal relations among variables. Learning their graphical\nstructure from observational data has received a lot of attention in the\nliterature. When there exists no latent (unobserved) confounder, i.e., no\nunobserved direct common cause of some observed variables, learning algorithms\ncan be divided essentially into two classes: constraint-based and score-based\napproaches. The latter are often thought to be more robust than the former and\nto produce better results. However, to the best of our knowledge, when\nvariables are discrete, no score-based algorithm is capable of dealing with\nlatent confounders. This paper introduces the first fully score-based structure\nlearning algorithm searching the space of DAGs (directed acyclic graphs) that\nis capable of identifying the presence of some latent confounders. It is\njustified mathematically and experiments highlight its effectiveness.\n", "date": "2024-08-20", "categories": []}
{"id": "2208.05949", "title": "Valid Inference After Causal Discovery", "abstract": "  Causal discovery and causal effect estimation are two fundamental tasks in\ncausal inference. While many methods have been developed for each task\nindividually, statistical challenges arise when applying these methods jointly:\nestimating causal effects after running causal discovery algorithms on the same\ndata leads to \"double dipping,\" invalidating the coverage guarantees of\nclassical confidence intervals. To this end, we develop tools for valid\npost-causal-discovery inference. Across empirical studies, we show that a naive\ncombination of causal discovery and subsequent inference algorithms leads to\nhighly inflated miscoverage rates; on the other hand, applying our method\nprovides reliable coverage while achieving more accurate causal discovery than\ndata splitting.\n", "date": "2022-08-11", "categories": []}
{"id": "2305.00050", "title": "Causal Reasoning and Large Language Models: Opening a New Frontier for\n  Causality", "abstract": "  The causal capabilities of large language models (LLMs) are a matter of\nsignificant debate, with critical implications for the use of LLMs in\nsocietally impactful domains such as medicine, science, law, and policy. We\nconduct a \"behavorial\" study of LLMs to benchmark their capability in\ngenerating causal arguments. Across a wide range of tasks, we find that LLMs\ncan generate text corresponding to correct causal arguments with high\nprobability, surpassing the best-performing existing methods. Algorithms based\non GPT-3.5 and 4 outperform existing algorithms on a pairwise causal discovery\ntask (97%, 13 points gain), counterfactual reasoning task (92%, 20 points gain)\nand event causality (86% accuracy in determining necessary and sufficient\ncauses in vignettes). We perform robustness checks across tasks and show that\nthe capabilities cannot be explained by dataset memorization alone, especially\nsince LLMs generalize to novel datasets that were created after the training\ncutoff date.\n  That said, LLMs exhibit unpredictable failure modes, and we discuss the kinds\nof errors that may be improved and what are the fundamental limits of LLM-based\nanswers. Overall, by operating on the text metadata, LLMs bring capabilities so\nfar understood to be restricted to humans, such as using collected knowledge to\ngenerate causal graphs or identifying background causal context from natural\nlanguage. As a result, LLMs may be used by human domain experts to save effort\nin setting up a causal analysis, one of the biggest impediments to the\nwidespread adoption of causal methods. Given that LLMs ignore the actual data,\nour results also point to a fruitful research direction of developing\nalgorithms that combine LLMs with existing causal techniques. Code and datasets\nare available at https://github.com/py-why/pywhy-llm.\n", "date": "2023-04-28", "categories": []}
{"id": "2408.10976", "title": "Kernel-Based Differentiable Learning of Non-Parametric Directed Acyclic\n  Graphical Models", "abstract": "  Causal discovery amounts to learning a directed acyclic graph (DAG) that\nencodes a causal model. This model selection problem can be challenging due to\nits large combinatorial search space, particularly when dealing with\nnon-parametric causal models. Recent research has sought to bypass the\ncombinatorial search by reformulating causal discovery as a continuous\noptimization problem, employing constraints that ensure the acyclicity of the\ngraph. In non-parametric settings, existing approaches typically rely on\nfinite-dimensional approximations of the relationships between nodes, resulting\nin a score-based continuous optimization problem with a smooth acyclicity\nconstraint. In this work, we develop an alternative approximation method by\nutilizing reproducing kernel Hilbert spaces (RKHS) and applying general\nsparsity-inducing regularization terms based on partial derivatives. Within\nthis framework, we introduce an extended RKHS representer theorem. To enforce\nacyclicity, we advocate the log-determinant formulation of the acyclicity\nconstraint and show its stability. Finally, we assess the performance of our\nproposed RKHS-DAGMA procedure through simulations and illustrative data\nanalyses.\n", "date": "2024-08-20", "categories": []}
{"id": "2209.07028", "title": "Estimating large causal polytrees from small samples", "abstract": "  We consider the problem of estimating a large causal polytree from a\nrelatively small i.i.d. sample. This is motivated by the problem of determining\ncausal structure when the number of variables is very large compared to the\nsample size, such as in gene regulatory networks. We give an algorithm that\nrecovers the tree with high accuracy in such settings. The algorithm works\nunder essentially no distributional or modeling assumptions other than some\nmild non-degeneracy conditions.\n", "date": "2022-09-15", "categories": []}
{"id": "2304.02146", "title": "Structure Learning with Continuous Optimization: A Sober Look and Beyond", "abstract": "  This paper investigates in which cases continuous optimization for directed\nacyclic graph (DAG) structure learning can and cannot perform well and why this\nhappens, and suggests possible directions to make the search procedure more\nreliable. Reisach et al. (2021) suggested that the remarkable performance of\nseveral continuous structure learning approaches is primarily driven by a high\nagreement between the order of increasing marginal variances and the\ntopological order, and demonstrated that these approaches do not perform well\nafter data standardization. We analyze this phenomenon for continuous\napproaches assuming equal and non-equal noise variances, and show that the\nstatement may not hold in either case by providing counterexamples,\njustifications, and possible alternative explanations. We further demonstrate\nthat nonconvexity may be a main concern especially for the non-equal noise\nvariances formulation, while recent advances in continuous structure learning\nfail to achieve improvement in this case. Our findings suggest that future\nworks should take into account the non-equal noise variances formulation to\nhandle more general settings and for a more comprehensive empirical evaluation.\nLastly, we provide insights into other aspects of the search procedure,\nincluding thresholding and sparsity, and show that they play an important role\nin the final solutions.\n", "date": "2023-04-04", "categories": []}
{"id": "2408.07890", "title": "Local Causal Discovery with Background Knowledge", "abstract": "  Causality plays a pivotal role in various fields of study. Based on the\nframework of causal graphical models, previous works have proposed identifying\nwhether a variable is a cause or non-cause of a target in every Markov\nequivalent graph solely by learning a local structure. However, the presence of\nprior knowledge, often represented as a partially known causal graph, is common\nin many causal modeling applications. Leveraging this prior knowledge allows\nfor the further identification of causal relationships. In this paper, we first\npropose a method for learning the local structure using all types of causal\nbackground knowledge, including direct causal information, non-ancestral\ninformation and ancestral information. Then we introduce criteria for\nidentifying causal relationships based solely on the local structure in the\npresence of prior knowledge. We also apply out method to fair machine learning,\nand experiments involving local structure learning, causal relationship\nidentification, and fair machine learning demonstrate that our method is both\neffective and efficient.\n", "date": "2024-08-15", "categories": []}
{"id": "2402.05052", "title": "Causal Representation Learning from Multiple Distributions: A General\n  Setting", "abstract": "  In many problems, the measured variables (e.g., image pixels) are just\nmathematical functions of the latent causal variables (e.g., the underlying\nconcepts or objects). For the purpose of making predictions in changing\nenvironments or making proper changes to the system, it is helpful to recover\nthe latent causal variables $Z_i$ and their causal relations represented by\ngraph $\\mathcal{G}_Z$. This problem has recently been known as causal\nrepresentation learning. This paper is concerned with a general, completely\nnonparametric setting of causal representation learning from multiple\ndistributions (arising from heterogeneous data or nonstationary time series),\nwithout assuming hard interventions behind distribution changes. We aim to\ndevelop general solutions in this fundamental case; as a by product, this helps\nsee the unique benefit offered by other assumptions such as parametric causal\nmodels or hard interventions. We show that under the sparsity constraint on the\nrecovered graph over the latent variables and suitable sufficient change\nconditions on the causal influences, interestingly, one can recover the\nmoralized graph of the underlying directed acyclic graph, and the recovered\nlatent variables and their relations are related to the underlying causal model\nin a specific, nontrivial way. In some cases, most latent variables can even be\nrecovered up to component-wise transformations. Experimental results verify our\ntheoretical claims.\n", "date": "2024-02-07", "categories": []}
{"id": "2408.05584", "title": "Dynamical causality under invisible confounders", "abstract": "  Causality inference is prone to spurious causal interactions, due to the\nsubstantial confounders in a complex system. While many existing methods based\non the statistical methods or dynamical methods attempt to address\nmisidentification challenges, there remains a notable lack of effective methods\nto infer causality, in particular in the presence of invisible/unobservable\nconfounders. As a result, accurately inferring causation with invisible\nconfounders remains a largely unexplored and outstanding issue in data science\nand AI fields. In this work, we propose a method to overcome such challenges to\ninfer dynamical causality under invisible confounders (CIC method) and further\nreconstruct the invisible confounders from time-series data by developing an\northogonal decomposition theorem in a delay embedding space. The core of our\nCIC method lies in its ability to decompose the observed variables not in their\noriginal space but in their delay embedding space into the common and private\nsubspaces respectively, thereby quantifying causality between those variables\nboth theoretically and computationally. This theoretical foundation ensures the\ncausal detection for any high-dimensional system even with only two observed\nvariables under many invisible confounders, which is actually a long-standing\nproblem in the field. In addition to the invisible confounder problem, such a\ndecomposition actually makes the intertwined variables separable in the\nembedding space, thus also solving the non-separability problem of causal\ninference. Extensive validation of the CIC method is carried out using various\nreal datasets, and the experimental results demonstrates its effectiveness to\nreconstruct real biological networks even with unobserved confounders.\n", "date": "2024-08-10", "categories": []}
{"id": "2408.04819", "title": "Interventional Causal Structure Discovery over Graphical Models with\n  Convergence and Optimality Guarantees", "abstract": "  Learning causal structure from sampled data is a fundamental problem with\napplications in various fields, including healthcare, machine learning and\nartificial intelligence. Traditional methods predominantly rely on\nobservational data, but there exist limits regarding the identifiability of\ncausal structures with only observational data. Interventional data, on the\nother hand, helps establish a cause-and-effect relationship by breaking the\ninfluence of confounding variables. It remains to date under-explored to\ndevelop a mathematical framework that seamlessly integrates both observational\nand interventional data in causal structure learning. Furthermore, existing\nstudies often focus on centralized approaches, necessitating the transfer of\nentire datasets to a single server, which lead to considerable communication\noverhead and heightened risks to privacy. To tackle these challenges, we\ndevelop a bilevel polynomial optimization (Bloom) framework. Bloom not only\nprovides a powerful mathematical modeling framework, underpinned by theoretical\nsupport, for causal structure discovery from both interventional and\nobservational data, but also aspires to an efficient causal discovery algorithm\nwith convergence and optimality guarantees. We further extend Bloom to a\ndistributed setting to reduce the communication overhead and mitigate data\nprivacy risks. It is seen through experiments on both synthetic and real-world\ndatasets that Bloom markedly surpasses other leading learning algorithms.\n", "date": "2024-08-09", "categories": []}
{"id": "2408.04907", "title": "Causal Discovery of Linear Non-Gaussian Causal Models with Unobserved\n  Confounding", "abstract": "  We consider linear non-Gaussian structural equation models that involve\nlatent confounding. In this setting, the causal structure is identifiable, but,\nin general, it is not possible to identify the specific causal effects.\nInstead, a finite number of different causal effects result in the same\nobservational distribution. Most existing algorithms for identifying these\ncausal effects use overcomplete independent component analysis (ICA), which\noften suffers from convergence to local optima. Furthermore, the number of\nlatent variables must be known a priori. To address these issues, we propose an\nalgorithm that operates recursively rather than using overcomplete ICA. The\nalgorithm first infers a source, estimates the effect of the source and its\nlatent parents on their descendants, and then eliminates their influence from\nthe data. For both source identification and effect size estimation, we use\nrank conditions on matrices formed from higher-order cumulants. We prove\nasymptotic correctness under the mild assumption that locally, the number of\nlatent variables never exceeds the number of observed variables. Simulation\nstudies demonstrate that our method achieves comparable performance to\novercomplete ICA even though it does not know the number of latents in advance.\n", "date": "2024-08-09", "categories": []}
{"id": "2408.04254", "title": "Generating Fine-Grained Causality in Climate Time Series Data for\n  Forecasting and Anomaly Detection", "abstract": "  Understanding the causal interaction of time series variables can contribute\nto time series data analysis for many real-world applications, such as climate\nforecasting and extreme weather alerts. However, causal relationships are\ndifficult to be fully observed in real-world complex settings, such as\nspatial-temporal data from deployed sensor networks. Therefore, to capture\nfine-grained causal relations among spatial-temporal variables for further a\nmore accurate and reliable time series analysis, we first design a conceptual\nfine-grained causal model named TBN Granger Causality, which adds\ntime-respecting Bayesian Networks to the previous time-lagged Neural Granger\nCausality to offset the instantaneous effects. Second, we propose an end-to-end\ndeep generative model called TacSas, which discovers TBN Granger Causality in a\ngenerative manner to help forecast time series data and detect possible\nanomalies during the forecast. For evaluations, besides the causality discovery\nbenchmark Lorenz-96, we also test TacSas on climate benchmark ERA5 for climate\nforecasting and the extreme weather benchmark of NOAA for extreme weather\nalerts.\n", "date": "2024-08-08", "categories": []}
{"id": "2208.03703", "title": "Granger Causality using Neural Networks", "abstract": "  Dependence between nodes in a network is an important concept that pervades\nmany areas including finance, politics, sociology, genomics and the brain\nsciences. One way to characterize dependence between components of a\nmultivariate time series data is via Granger Causality (GC). Standard\ntraditional approaches to GC estimation / inference commonly assume linear\ndynamics, however such simplification does not hold in many real-world\napplications where signals are inherently non-linear. In such cases, imposing\nlinear models such as vector autoregressive (VAR) models can lead to\nmis-characterization of true Granger Causal interactions. To overcome this\nlimitation, Tank et al (IEEE Transactions on Pattern Analysis and Machine\nLearning, 2022) proposed a solution that uses neural networks with sparse\nregularization penalties. The regularization encourages learnable weights to be\nsparse, which enables inference on GC. This paper overcomes the limitations of\ncurrent methods by leveraging advances in machine learning and deep learning\nwhich have been demonstrated to learn hidden patterns in the data. We propose\nnovel classes of models that can handle underlying non-linearity in a\ncomputationally efficient manner, simultaneously providing GC and lag order\nselection. Firstly, we present the Learned Kernel VAR (LeKVAR) model that\nlearns kernel parameterized by a shared neural net followed by penalization on\nlearnable weights to discover GC structure. Secondly, we show one can directly\ndecouple lags and individual time series importance via decoupled penalties.\nThis is important as we want to select the lag order during the process of GC\nestimation. This decoupling acts as a filtering and can be extended to any DL\nmodel including Multi-Layer Perceptrons (MLP), Recurrent Neural Networks (RNN),\nLong Short Term Memory Networks (LSTM), Transformers etc, for simultaneous GC\nestimation and lag selection.\n", "date": "2022-08-07", "categories": []}
{"id": "2405.11250", "title": "Argumentative Causal Discovery", "abstract": "  Causal discovery amounts to unearthing causal relationships amongst features\nin data. It is a crucial companion to causal inference, necessary to build\nscientific knowledge without resorting to expensive or impossible randomised\ncontrol trials. In this paper, we explore how reasoning with symbolic\nrepresentations can support causal discovery. Specifically, we deploy\nassumption-based argumentation (ABA), a well-established and powerful knowledge\nrepresentation formalism, in combination with causality theories, to learn\ngraphs which reflect causal dependencies in the data. We prove that our method\nexhibits desirable properties, notably that, under natural conditions, it can\nretrieve ground-truth causal graphs. We also conduct experiments with an\nimplementation of our method in answer set programming (ASP) on four datasets\nfrom standard benchmarks in causal discovery, showing that our method compares\nwell against established baselines.\n", "date": "2024-05-18", "categories": []}
{"id": "2407.12254", "title": "COKE: Causal Discovery with Chronological Order and Expert Knowledge in\n  High Proportion of Missing Manufacturing Data", "abstract": "  Understanding causal relationships between machines is crucial for fault\ndiagnosis and optimization in manufacturing processes. Real-world datasets\nfrequently exhibit up to 90% missing data and high dimensionality from hundreds\nof sensors. These datasets also include domain-specific expert knowledge and\nchronological order information, reflecting the recording order across\ndifferent machines, which is pivotal for discerning causal relationships within\nthe manufacturing data. However, previous methods for handling missing data in\nscenarios akin to real-world conditions have not been able to effectively\nutilize expert knowledge. Conversely, prior methods that can incorporate expert\nknowledge struggle with datasets that exhibit missing values. Therefore, we\npropose COKE to construct causal graphs in manufacturing datasets by leveraging\nexpert knowledge and chronological order among sensors without imputing missing\ndata. Utilizing the characteristics of the recipe, we maximize the use of\nsamples with missing values, derive embeddings from intersections with an\ninitial graph that incorporates expert knowledge and chronological order, and\ncreate a sensor ordering graph. The graph-generating process has been optimized\nby an actor-critic architecture to obtain a final graph that has a maximum\nreward. Experimental evaluations in diverse settings of sensor quantities and\nmissing proportions demonstrate that our approach compared with the benchmark\nmethods shows an average improvement of 39.9% in the F1-score. Moreover, the\nF1-score improvement can reach 62.6% when considering the configuration similar\nto real-world datasets, and 85.0% in real-world semiconductor datasets. The\nsource code is available at https://github.com/OuTingYun/COKE.\n", "date": "2024-07-17", "categories": []}
{"id": "2408.00399", "title": "Unsupervised Pairwise Causal Discovery on Heterogeneous Data using\n  Mutual Information Measures", "abstract": "  A fundamental task in science is to determine the underlying causal relations\nbecause it is the knowledge of this functional structure what leads to the\ncorrect interpretation of an effect given the apparent associations in the\nobserved data. In this sense, Causal Discovery is a technique that tackles this\nchallenge by analyzing the statistical properties of the constituent variables.\nIn this work, we target the generalizability of the discovery method by\nfollowing a reductionist approach that only involves two variables, i.e., the\npairwise or bi-variate setting. We question the current (possibly misleading)\nbaseline results on the basis that they were obtained through supervised\nlearning, which is arguably contrary to this genuinely exploratory endeavor. In\nconsequence, we approach this problem in an unsupervised way, using robust\nMutual Information measures, and observing the impact of the different variable\ntypes, which is oftentimes ignored in the design of solutions. Thus, we provide\na novel set of standard unbiased results that can serve as a reference to guide\nfuture discovery tasks in completely unknown environments.\n", "date": "2024-08-01", "categories": []}
{"id": "2211.03374", "title": "Deep Causal Learning: Representation, Discovery and Inference", "abstract": "  Causal learning has garnered significant attention in recent years because it\nreveals the essential relationships that underpin phenomena and delineates the\nmechanisms by which the world evolves. Nevertheless, traditional causal\nlearning methods face numerous challenges and limitations, including\nhigh-dimensional, unstructured variables, combinatorial optimization problems,\nunobserved confounders, selection biases, and estimation inaccuracies. Deep\ncausal learning, which leverages deep neural networks, offers innovative\ninsights and solutions for addressing these challenges. Although numerous deep\nlearning-based methods for causal discovery and inference have been proposed,\nthere remains a dearth of reviews examining the underlying mechanisms by which\ndeep learning can enhance causal learning. In this article, we comprehensively\nreview how deep learning can contribute to causal learning by tackling\ntraditional challenges across three key dimensions: representation, discovery,\nand inference. We emphasize that deep causal learning is pivotal for advancing\nthe theoretical frontiers and broadening the practical applications of causal\nscience. We conclude by summarizing open issues and outlining potential\ndirections for future research.\n", "date": "2022-11-07", "categories": []}
{"id": "2407.18752", "title": "Knowledge Graph Structure as Prompt: Improving Small Language Models\n  Capabilities for Knowledge-based Causal Discovery", "abstract": "  Causal discovery aims to estimate causal structures among variables based on\nobservational data. Large Language Models (LLMs) offer a fresh perspective to\ntackle the causal discovery problem by reasoning on the metadata associated\nwith variables rather than their actual data values, an approach referred to as\nknowledge-based causal discovery. In this paper, we investigate the\ncapabilities of Small Language Models (SLMs, defined as LLMs with fewer than 1\nbillion parameters) with prompt-based learning for knowledge-based causal\ndiscovery. Specifically, we present KG Structure as Prompt, a novel approach\nfor integrating structural information from a knowledge graph, such as common\nneighbor nodes and metapaths, into prompt-based learning to enhance the\ncapabilities of SLMs. Experimental results on three types of biomedical and\nopen-domain datasets under few-shot settings demonstrate the effectiveness of\nour approach, surpassing most baselines and even conventional fine-tuning\napproaches trained on full datasets. Our findings further highlight the strong\ncapabilities of SLMs: in combination with knowledge graphs and prompt-based\nlearning, SLMs demonstrate the potential to surpass LLMs with larger number of\nparameters. Our code and datasets are available on GitHub.\n", "date": "2024-07-26", "categories": []}
{"id": "2407.20694", "title": "Detecting Causality in the Frequency Domain with Cross-Mapping Coherence", "abstract": "  Understanding causal relationships within a system is crucial for uncovering\nits underlying mechanisms. Causal discovery methods, which facilitate the\nconstruction of such models from time-series data, hold the potential to\nsignificantly advance scientific and engineering fields.\n  This study introduces the Cross-Mapping Coherence (CMC) method, designed to\nreveal causal connections in the frequency domain between time series. CMC\nbuilds upon nonlinear state-space reconstruction and extends the Convergent\nCross-Mapping algorithm to the frequency domain by utilizing coherence metrics\nfor evaluation. We tested the Cross-Mapping Coherence method using simulations\nof logistic maps, Lorenz systems, Kuramoto oscillators, and the Wilson-Cowan\nmodel of the visual cortex. CMC accurately identified the direction of causal\nconnections in all simulated scenarios. When applied to the Wilson-Cowan model,\nCMC yielded consistent results similar to spectral Granger causality.\n  Furthermore, CMC exhibits high sensitivity in detecting weak connections,\ndemonstrates sample efficiency, and maintains robustness in the presence of\nnoise.\n  In conclusion, the capability to determine directed causal influences across\ndifferent frequency bands allows CMC to provide valuable insights into the\ndynamics of complex, nonlinear systems.\n", "date": "2024-07-30", "categories": []}
{"id": "2404.09871", "title": "Explainable Online Unsupervised Anomaly Detection for Cyber-Physical\n  Systems via Causal Discovery from Time Series", "abstract": "  Online unsupervised detection of anomalies is crucial to guarantee the\ncorrect operation of cyber-physical systems and the safety of humans\ninteracting with them. State-of-the-art approaches based on deep learning via\nneural networks achieve outstanding performance at anomaly recognition,\nevaluating the discrepancy between a normal model of the system (with no\nanomalies) and the real-time stream of sensor time series. However, large\ntraining data and time are typically required, and explainability is still a\nchallenge to identify the root of the anomaly and implement predictive\nmaintainance. In this paper, we use causal discovery to learn a normal causal\ngraph of the system, and we evaluate the persistency of causal links during\nreal-time acquisition of sensor data to promptly detect anomalies. On two\nbenchmark anomaly detection datasets, we show that our method has higher\ntraining efficiency, outperforms the accuracy of state-of-the-art neural\narchitectures and correctly identifies the sources of >10 different anomalies.\nThe code is at https://github.com/Isla-lab/causal_anomaly_detection.\n", "date": "2024-04-15", "categories": []}
{"id": "2407.19118", "title": "Large Language Models as Co-Pilots for Causal Inference in Medical\n  Studies", "abstract": "  The validity of medical studies based on real-world clinical data, such as\nobservational studies, depends on critical assumptions necessary for drawing\ncausal conclusions about medical interventions. Many published studies are\nflawed because they violate these assumptions and entail biases such as\nresidual confounding, selection bias, and misalignment between treatment and\nmeasurement times. Although researchers are aware of these pitfalls, they\ncontinue to occur because anticipating and addressing them in the context of a\nspecific study can be challenging without a large, often unwieldy,\ninterdisciplinary team with extensive expertise. To address this expertise gap,\nwe explore the use of large language models (LLMs) as co-pilot tools to assist\nresearchers in identifying study design flaws that undermine the validity of\ncausal inferences. We propose a conceptual framework for LLMs as causal\nco-pilots that encode domain knowledge across various fields, engaging with\nresearchers in natural language interactions to provide contextualized\nassistance in study design. We provide illustrative examples of how LLMs can\nfunction as causal co-pilots, propose a structured framework for their\ngrounding in existing causal inference frameworks, and highlight the unique\nchallenges and opportunities in adapting LLMs for reliable use in\nepidemiological research.\n", "date": "2024-07-26", "categories": []}
{"id": "2306.17557", "title": "The most likely common cause", "abstract": "  The common cause principle for two random variables $A$ and $B$ is examined\nin the case of causal insufficiency, when their common cause $C$ is known to\nexist, but only the joint probability of $A$ and $B$ is observed. As a result,\n$C$ cannot be uniquely identified (the latent confounder problem). We show that\nthe generalized maximum likelihood method can be applied to this situation and\nallows identification of $C$ that is consistent with the common cause\nprinciple. It closely relates to the maximum entropy principle. Investigation\nof the two binary symmetric variables reveals a non-analytic behavior of\nconditional probabilities reminiscent of a second-order phase transition. This\noccurs during the transition from correlation to anti-correlation in the\nobserved probability distribution. The relation between the generalized\nlikelihood approach and alternative methods, such as predictive likelihood and\nthe minimum common cause entropy, is discussed. The consideration of the common\ncause for three observed variables (and one hidden cause) uncovers causal\nstructures that defy representation through directed acyclic graphs with the\nMarkov condition.\n", "date": "2023-06-30", "categories": []}
{"id": "2407.16388", "title": "Anwendung von Causal-Discovery-Algorithmen zur Root-Cause-Analyse in der\n  Fahrzeugmontage", "abstract": "  Root Cause Analysis (RCA) is a quality management method that aims to\nsystematically investigate and identify the cause-and-effect relationships of\nproblems and their underlying causes. Traditional methods are based on the\nanalysis of problems by subject matter experts. In modern production processes,\nlarge amounts of data are collected. For this reason, increasingly\ncomputer-aided and data-driven methods are used for RCA. One of these methods\nare Causal Discovery Algorithms (CDA). This publication demonstrates the\napplication of CDA on data from the assembly of a leading automotive\nmanufacturer. The algorithms used learn the causal structure between the\ncharacteristics of the manufactured vehicles, the ergonomics and the temporal\nscope of the involved assembly processes, and quality-relevant product features\nbased on representative data. This publication compares various CDAs in terms\nof their suitability in the context of quality management. For this purpose,\nthe causal structures learned by the algorithms as well as their runtime are\ncompared. This publication provides a contribution to quality management and\ndemonstrates how CDAs can be used for RCA in assembly processes.\n", "date": "2024-07-23", "categories": []}
{"id": "2407.15259", "title": "New Rules for Causal Identification with Background Knowledge", "abstract": "  Identifying causal relations is crucial for a variety of downstream tasks. In\nadditional to observational data, background knowledge (BK), which could be\nattained from human expertise or experiments, is usually introduced for\nuncovering causal relations. This raises an open problem that in the presence\nof latent variables, what causal relations are identifiable from observational\ndata and BK. In this paper, we propose two novel rules for incorporating BK,\nwhich offer a new perspective to the open problem. In addition, we show that\nthese rules are applicable in some typical causality tasks, such as determining\nthe set of possible causal effects with observational data. Our rule-based\napproach enhances the state-of-the-art method by circumventing a process of\nenumerating block sets that would otherwise take exponential complexity.\n", "date": "2024-07-21", "categories": []}
{"id": "2407.10132", "title": "Optimal Kernel Choice for Score Function-based Causal Discovery", "abstract": "  Score-based methods have demonstrated their effectiveness in discovering\ncausal relationships by scoring different causal structures based on their\ngoodness of fit to the data. Recently, Huang et al. proposed a generalized\nscore function that can handle general data distributions and causal\nrelationships by modeling the relations in reproducing kernel Hilbert space\n(RKHS). The selection of an appropriate kernel within this score function is\ncrucial for accurately characterizing causal relationships and ensuring precise\ncausal discovery. However, the current method involves manual heuristic\nselection of kernel parameters, making the process tedious and less likely to\nensure optimality. In this paper, we propose a kernel selection method within\nthe generalized score function that automatically selects the optimal kernel\nthat best fits the data. Specifically, we model the generative process of the\nvariables involved in each step of the causal graph search procedure as a\nmixture of independent noise variables. Based on this model, we derive an\nautomatic kernel selection method by maximizing the marginal likelihood of the\nvariables involved in each search step. We conduct experiments on both\nsynthetic data and real-world benchmarks, and the results demonstrate that our\nproposed method outperforms heuristic kernel selection methods.\n", "date": "2024-07-14", "categories": []}
{"id": "2405.02327", "title": "CausalLP: Learning causal relations with weighted knowledge graph link\n  prediction", "abstract": "  Causal networks are useful in a wide variety of applications, from medical\ndiagnosis to root-cause analysis in manufacturing. In practice, however, causal\nnetworks are often incomplete with missing causal relations. This paper\npresents a novel approach, called CausalLP, that formulates the issue of\nincomplete causal networks as a knowledge graph completion problem. More\nspecifically, the task of finding new causal relations in an incomplete causal\nnetwork is mapped to the task of knowledge graph link prediction. The use of\nknowledge graphs to represent causal relations enables the integration of\nexternal domain knowledge; and as an added complexity, the causal relations\nhave weights representing the strength of the causal association between\nentities in the knowledge graph. Two primary tasks are supported by CausalLP:\ncausal explanation and causal prediction. An evaluation of this approach uses a\nbenchmark dataset of simulated videos for causal reasoning, CLEVRER-Humans, and\ncompares the performance of multiple knowledge graph embedding algorithms. Two\ndistinct dataset splitting approaches are used for evaluation: (1) random-based\nsplit, which is the method typically employed to evaluate link prediction\nalgorithms, and (2) Markov-based split, a novel data split technique that\nutilizes the Markovian property of causal relations. Results show that using\nweighted causal relations improves causal link prediction over the baseline\nwithout weighted relations.\n", "date": "2024-04-23", "categories": []}
{"id": "2407.05869", "title": "PORCA: Root Cause Analysis with Partially Observed Data", "abstract": "  Root Cause Analysis (RCA) aims at identifying the underlying causes of system\nfaults by uncovering and analyzing the causal structure from complex systems.\nIt has been widely used in many application domains. Reliable diagnostic\nconclusions are of great importance in mitigating system failures and financial\nlosses. However, previous studies implicitly assume a full observation of the\nsystem, which neglect the effect of partial observation (i.e., missing nodes\nand latent malfunction). As a result, they fail in deriving reliable RCA\nresults. In this paper, we unveil the issues of unobserved confounders and\nheterogeneity in partial observation and come up with a new problem of root\ncause analysis with partially observed data. To achieve this, we propose PORCA,\na novel RCA framework which can explore reliable root causes under both\nunobserved confounders and unobserved heterogeneity. PORCA leverages magnified\nscore-based causal discovery to efficiently optimize acyclic directed mixed\ngraph under unobserved confounders. In addition, we also develop a\nheterogeneity-aware scheduling strategy to provide adaptive sample weights.\nExtensive experimental results on one synthetic and two real-world datasets\ndemonstrate the effectiveness and superiority of the proposed framework.\n", "date": "2024-07-08", "categories": []}
{"id": "2402.08616", "title": "Adjustment Identification Distance: A gadjid for Causal Structure\n  Learning", "abstract": "  Evaluating graphs learned by causal discovery algorithms is difficult: The\nnumber of edges that differ between two graphs does not reflect how the graphs\ndiffer with respect to the identifying formulas they suggest for causal\neffects. We introduce a framework for developing causal distances between\ngraphs which includes the structural intervention distance for directed acyclic\ngraphs as a special case. We use this framework to develop improved\nadjustment-based distances as well as extensions to completed partially\ndirected acyclic graphs and causal orders. We develop new reachability\nalgorithms to compute the distances efficiently and to prove their low\npolynomial time complexity. In our package gadjid (open source at\nhttps://github.com/CausalDisco/gadjid), we provide implementations of our\ndistances; they are orders of magnitude faster with proven lower time\ncomplexity than the structural intervention distance and thereby provide a\nsuccess metric for causal discovery that scales to graph sizes that were\npreviously prohibitive.\n", "date": "2024-02-13", "categories": []}
{"id": "2407.07291", "title": "Causal Discovery in Semi-Stationary Time Series", "abstract": "  Discovering causal relations from observational time series without making\nthe stationary assumption is a significant challenge. In practice, this\nchallenge is common in many areas, such as retail sales, transportation\nsystems, and medical science. Here, we consider this problem for a class of\nnon-stationary time series. The structural causal model (SCM) of this type of\ntime series, called the semi-stationary time series, exhibits that a finite\nnumber of different causal mechanisms occur sequentially and periodically\nacross time. This model holds considerable practical utility because it can\nrepresent periodicity, including common occurrences such as seasonality and\ndiurnal variation. We propose a constraint-based, non-parametric algorithm for\ndiscovering causal relations in this setting. The resulting algorithm,\nPCMCI$_{\\Omega}$, can capture the alternating and recurring changes in the\ncausal mechanisms and then identify the underlying causal graph with\nconditional independence (CI) tests. We show that this algorithm is sound in\nidentifying causal relations on discrete time series. We validate the algorithm\nwith extensive experiments on continuous and discrete simulated data. We also\napply our algorithm to a real-world climate dataset.\n", "date": "2024-07-10", "categories": []}
{"id": "2304.05493", "title": "Optimizing Data-driven Causal Discovery Using Knowledge-guided Search", "abstract": "  Learning causal relationships solely from observational data often fails to\nreveal the underlying causal mechanisms due to the vast search space of\npossible causal graphs, which can grow exponentially, especially for greedy\nalgorithms using score-based approaches. Leveraging prior causal information,\nsuch as the presence or absence of causal edges, can help restrict and guide\nthe score-based discovery process, leading to a more accurate search. In the\nhealthcare domain, prior knowledge is abundant from sources like medical\njournals, electronic health records (EHRs), and clinical intervention outcomes.\nThis study introduces a knowledge-guided causal structure search (KGS) approach\nthat utilizes observational data and structural priors (such as causal edges)\nas constraints to learn the causal graph. KGS leverages prior edge information\nbetween variables, including the presence of a directed edge, the absence of an\nedge, and the presence of an undirected edge. We extensively evaluate KGS in\nmultiple settings using synthetic and benchmark real-world datasets, as well as\nin a real-life healthcare application related to oxygen therapy treatment. To\nobtain causal priors, we use GPT-4 to retrieve relevant literature information.\nOur results show that structural priors of any type and amount enhance the\nsearch process, improving performance and optimizing causal discovery. This\nguided strategy ensures that the discovered edges align with established causal\nknowledge, enhancing the trustworthiness of findings while expediting the\nsearch process. It also enables a more focused exploration of causal\nmechanisms, potentially leading to more effective and personalized healthcare\nsolutions.\n", "date": "2023-04-11", "categories": []}
{"id": "2407.06015", "title": "Simulation-based Benchmarking for Causal Structure Learning in Gene\n  Perturbation Experiments", "abstract": "  Causal structure learning (CSL) refers to the task of learning causal\nrelationships from data. Advances in CSL now allow learning of causal graphs in\ndiverse application domains, which has the potential to facilitate data-driven\ncausal decision-making. Real-world CSL performance depends on a number of\n$\\textit{context-specific}$ factors, including context-specific data\ndistributions and non-linear dependencies, that are important in practical\nuse-cases. However, our understanding of how to assess and select CSL methods\nin specific contexts remains limited. To address this gap, we present\n$\\textit{CausalRegNet}$, a multiplicative effect structural causal model that\nallows for generating observational and interventional data incorporating\ncontext-specific properties, with a focus on the setting of gene perturbation\nexperiments. Using real-world gene perturbation data, we show that CausalRegNet\ngenerates accurate distributions and scales far better than current simulation\nframeworks. We illustrate the use of CausalRegNet in assessing CSL methods in\nthe context of interventional experiments in biology.\n", "date": "2024-07-08", "categories": []}
{"id": "2310.04218", "title": "A Fixed-Parameter Tractable Algorithm for Counting Markov Equivalence\n  Classes with the same Skeleton", "abstract": "  Causal DAGs (also known as Bayesian networks) are a popular tool for encoding\nconditional dependencies between random variables. In a causal DAG, the random\nvariables are modeled as vertices in the DAG, and it is stipulated that every\nrandom variable is independent of its ancestors conditioned on its parents. It\nis possible, however, for two different causal DAGs on the same set of random\nvariables to encode exactly the same set of conditional dependencies. Such\ncausal DAGs are said to be Markov equivalent, and equivalence classes of Markov\nequivalent DAGs are known as Markov Equivalent Classes (MECs). Beautiful\ncombinatorial characterizations of MECs have been developed in the past few\ndecades, and it is known, in particular that all DAGs in the same MEC must have\nthe same \"skeleton\" (underlying undirected graph) and v-structures (induced\nsubgraph of the form $a\\rightarrow b \\leftarrow c$).\n  These combinatorial characterizations also suggest several natural\nalgorithmic questions. One of these is: given an undirected graph $G$ as input,\nhow many distinct Markov equivalence classes have the skeleton $G$? Much work\nhas been devoted in the last few years to this and other closely related\nproblems. However, to the best of our knowledge, a polynomial time algorithm\nfor the problem remains unknown.\n  In this paper, we make progress towards this goal by giving a fixed parameter\ntractable algorithm for the above problem, with the parameters being the\ntreewidth and the maximum degree of the input graph $G$. The main technical\ningredient in our work is a construction we refer to as shadow, which lets us\ncreate a \"local description\" of long-range constraints imposed by the\ncombinatorial characterizations of MECs.\n", "date": "2023-10-06", "categories": []}
{"id": "2407.01686", "title": "Everything that can be learned about a causal structure with latent\n  variables by observational and interventional probing schemes", "abstract": "  What types of differences among causal structures with latent variables are\nimpossible to distinguish by statistical data obtained by probing each visible\nvariable? If the probing scheme is simply passive observation, then it is\nwell-known that many different causal structures can realize the same joint\nprobability distributions. Even for the simplest case of two visible variables,\nfor instance, one cannot distinguish between one variable being a causal parent\nof the other and the two variables sharing a latent common cause. However, it\nis possible to distinguish between these two causal structures if we have\nrecourse to more powerful probing schemes, such as the possibility of\nintervening on one of the variables and observing the other. Herein, we address\nthe question of which causal structures remain indistinguishable even given the\nmost informative types of probing schemes on the visible variables. We find\nthat two causal structures remain indistinguishable if and only if they are\nboth associated with the same mDAG structure (as defined by Evans (2016)). We\nalso consider the question of when one causal structure dominates another in\nthe sense that it can realize all of the joint probability distributions that\ncan be realized by the other using a given probing scheme. (Equivalence of\ncausal structures is the special case of mutual dominance.) Finally, we\ninvestigate to what extent one can weaken the probing schemes implemented on\nthe visible variables and still have the same discrimination power as a\nmaximally informative probing scheme.\n", "date": "2024-07-01", "categories": []}
{"id": "2406.17831", "title": "Empirical Bayes for Dynamic Bayesian Networks Using Generalized\n  Variational Inference", "abstract": "  In this work, we demonstrate the Empirical Bayes approach to learning a\nDynamic Bayesian Network. By starting with several point estimates of structure\nand weights, we can use a data-driven prior to subsequently obtain a model to\nquantify uncertainty. This approach uses a recent development of Generalized\nVariational Inference, and indicates the potential of sampling the uncertainty\nof a mixture of DAG structures as well as a parameter posterior.\n", "date": "2024-06-25", "categories": []}
{"id": "2311.10263", "title": "Stable Differentiable Causal Discovery", "abstract": "  Inferring causal relationships as directed acyclic graphs (DAGs) is an\nimportant but challenging problem. Differentiable Causal Discovery (DCD) is a\npromising approach to this problem, framing the search as a continuous\noptimization. But existing DCD methods are numerically unstable, with poor\nperformance beyond tens of variables. In this paper, we propose Stable\nDifferentiable Causal Discovery (SDCD), a new method that improves previous DCD\nmethods in two ways: (1) It employs an alternative constraint for acyclicity;\nthis constraint is more stable, both theoretically and empirically, and fast to\ncompute. (2) It uses a training procedure tailored for sparse causal graphs,\nwhich are common in real-world scenarios. We first derive SDCD and prove its\nstability and correctness. We then evaluate it with both observational and\ninterventional data and on both small-scale and large-scale settings. We find\nthat SDCD outperforms existing methods in both convergence speed and accuracy\nand can scale to thousands of variables. We provide code at\nhttps://github.com/azizilab/sdcd.\n", "date": "2023-11-17", "categories": []}
{"id": "2406.17228", "title": "Greedy equivalence search for nonparametric graphical models", "abstract": "  One of the hallmark achievements of the theory of graphical models and\nBayesian model selection is the celebrated greedy equivalence search (GES)\nalgorithm due to Chickering and Meek. GES is known to consistently estimate the\nstructure of directed acyclic graph (DAG) models in various special cases\nincluding Gaussian and discrete models, which are in particular curved\nexponential families. A general theory that covers general nonparametric DAG\nmodels, however, is missing. Here, we establish the consistency of greedy\nequivalence search for general families of DAG models that satisfy smoothness\nconditions on the Markov factorization, and hence may not be curved exponential\nfamilies, or even parametric. The proof leverages recent advances in\nnonparametric Bayes to construct a test for comparing misspecified DAG models\nthat avoids arguments based on the Laplace approximation. Nonetheless, when the\nLaplace approximation is valid and a consistent scoring function exists, we\nrecover the classical result. As a result, we obtain a general consistency\ntheorem for GES applied to general DAG models.\n", "date": "2024-06-25", "categories": []}
{"id": "2406.17698", "title": "Identifying Nonstationary Causal Structures with High-Order Markov\n  Switching Models", "abstract": "  Causal discovery in time series is a rapidly evolving field with a wide\nvariety of applications in other areas such as climate science and\nneuroscience. Traditional approaches assume a stationary causal graph, which\ncan be adapted to nonstationary time series with time-dependent effects or\nheterogeneous noise. In this work we address nonstationarity via\nregime-dependent causal structures. We first establish identifiability for\nhigh-order Markov Switching Models, which provide the foundations for\nidentifiable regime-dependent causal discovery. Our empirical studies\ndemonstrate the scalability of our proposed approach for high-order\nregime-dependent structure estimation, and we illustrate its applicability on\nbrain activity data.\n", "date": "2024-06-25", "categories": []}
{"id": "2310.06312", "title": "Discovering Mixtures of Structural Causal Models from Time Series Data", "abstract": "  Discovering causal relationships from time series data is significant in\nfields such as finance, climate science, and neuroscience. However,\ncontemporary techniques rely on the simplifying assumption that data originates\nfrom the same causal model, while in practice, data is heterogeneous and can\nstem from different causal models. In this work, we relax this assumption and\nperform causal discovery from time series data originating from a mixture of\ncausal models. We propose a general variational inference-based framework\ncalled MCD to infer the underlying causal models as well as the mixing\nprobability of each sample. Our approach employs an end-to-end training process\nthat maximizes an evidence-lower bound for the data likelihood. We present two\nvariants: MCD-Linear for linear relationships and independent noise, and\nMCD-Nonlinear for nonlinear causal relationships and history-dependent noise.\nWe demonstrate that our method surpasses state-of-the-art benchmarks in causal\ndiscovery tasks through extensive experimentation on synthetic and real-world\ndatasets, particularly when the data emanates from diverse underlying causal\ngraphs. Theoretically, we prove the identifiability of such a model under some\nmild assumptions.\n", "date": "2023-10-10", "categories": []}
{"id": "2405.11548", "title": "Adaptive Online Experimental Design for Causal Discovery", "abstract": "  Causal discovery aims to uncover cause-and-effect relationships encoded in\ncausal graphs by leveraging observational, interventional data, or their\ncombination. The majority of existing causal discovery methods are developed\nassuming infinite interventional data. We focus on data interventional\nefficiency and formalize causal discovery from the perspective of online\nlearning, inspired by pure exploration in bandit problems. A graph separating\nsystem, consisting of interventions that cut every edge of the graph at least\nonce, is sufficient for learning causal graphs when infinite interventional\ndata is available, even in the worst case. We propose a track-and-stop causal\ndiscovery algorithm that adaptively selects interventions from the graph\nseparating system via allocation matching and learns the causal graph based on\nsampling history. Given any desired confidence value, the algorithm determines\na termination condition and runs until it is met. We analyze the algorithm to\nestablish a problem-dependent upper bound on the expected number of required\ninterventional samples. Our proposed algorithm outperforms existing methods in\nsimulations across various randomly generated causal graphs. It achieves higher\naccuracy, measured by the structural hamming distance (SHD) between the learned\ncausal graph and the ground truth, with significantly fewer samples.\n", "date": "2024-05-19", "categories": []}
{"id": "2406.16605", "title": "CLEAR: Can Language Models Really Understand Causal Graphs?", "abstract": "  Causal reasoning is a cornerstone of how humans interpret the world. To model\nand reason about causality, causal graphs offer a concise yet effective\nsolution. Given the impressive advancements in language models, a crucial\nquestion arises: can they really understand causal graphs? To this end, we\npioneer an investigation into language models' understanding of causal graphs.\nSpecifically, we develop a framework to define causal graph understanding, by\nassessing language models' behaviors through four practical criteria derived\nfrom diverse disciplines (e.g., philosophy and psychology). We then develop\nCLEAR, a novel benchmark that defines three complexity levels and encompasses\n20 causal graph-based tasks across these levels. Finally, based on our\nframework and benchmark, we conduct extensive experiments on six leading\nlanguage models and summarize five empirical findings. Our results indicate\nthat while language models demonstrate a preliminary understanding of causal\ngraphs, significant potential for improvement remains. Our project website is\nat https://github.com/OpenCausaLab/CLEAR.\n", "date": "2024-06-24", "categories": []}
{"id": "2406.16708", "title": "CausalFormer: An Interpretable Transformer for Temporal Causal Discovery", "abstract": "  Temporal causal discovery is a crucial task aimed at uncovering the causal\nrelations within time series data. The latest temporal causal discovery methods\nusually train deep learning models on prediction tasks to uncover the causality\nbetween time series. They capture causal relations by analyzing the parameters\nof some components of the trained models, e.g., attention weights and\nconvolution weights. However, this is an incomplete mapping process from the\nmodel parameters to the causality and fails to investigate the other\ncomponents, e.g., fully connected layers and activation functions, that are\nalso significant for causal discovery. To facilitate the utilization of the\nwhole deep learning models in temporal causal discovery, we proposed an\ninterpretable transformer-based causal discovery model termed CausalFormer,\nwhich consists of the causality-aware transformer and the decomposition-based\ncausality detector. The causality-aware transformer learns the causal\nrepresentation of time series data using a prediction task with the designed\nmulti-kernel causal convolution which aggregates each input time series along\nthe temporal dimension under the temporal priority constraint. Then, the\ndecomposition-based causality detector interprets the global structure of the\ntrained causality-aware transformer with the proposed regression relevance\npropagation to identify potential causal relations and finally construct the\ncausal graph. Experiments on synthetic, simulated, and real datasets\ndemonstrate the state-of-the-art performance of CausalFormer on discovering\ntemporal causality. Our code is available at\nhttps://github.com/lingbai-kong/CausalFormer.\n", "date": "2024-06-24", "categories": []}
{"id": "2305.15936", "title": "Learning DAGs from Data with Few Root Causes", "abstract": "  We present a novel perspective and algorithm for learning directed acyclic\ngraphs (DAGs) from data generated by a linear structural equation model (SEM).\nFirst, we show that a linear SEM can be viewed as a linear transform that, in\nprior work, computes the data from a dense input vector of random valued root\ncauses (as we will call them) associated with the nodes. Instead, we consider\nthe case of (approximately) few root causes and also introduce noise in the\nmeasurement of the data. Intuitively, this means that the DAG data is produced\nby few data-generating events whose effect percolates through the DAG. We prove\nidentifiability in this new setting and show that the true DAG is the global\nminimizer of the $L^0$-norm of the vector of root causes. For data with few\nroot causes, with and without noise, we show superior performance compared to\nprior DAG learning methods.\n", "date": "2023-05-25", "categories": []}
{"id": "2406.13966", "title": "Causal Inference with Latent Variables: Recent Advances and Future\n  Prospectives", "abstract": "  Causality lays the foundation for the trajectory of our world. Causal\ninference (CI), which aims to infer intrinsic causal relations among variables\nof interest, has emerged as a crucial research topic. Nevertheless, the lack of\nobservation of important variables (e.g., confounders, mediators, exogenous\nvariables, etc.) severely compromises the reliability of CI methods. The issue\nmay arise from the inherent difficulty in measuring the variables.\nAdditionally, in observational studies where variables are passively recorded,\ncertain covariates might be inadvertently omitted by the experimenter.\nDepending on the type of unobserved variables and the specific CI task, various\nconsequences can be incurred if these latent variables are carelessly handled,\nsuch as biased estimation of causal effects, incomplete understanding of causal\nmechanisms, lack of individual-level causal consideration, etc. In this survey,\nwe provide a comprehensive review of recent developments in CI with latent\nvariables. We start by discussing traditional CI techniques when variables of\ninterest are assumed to be fully observed. Afterward, under the taxonomy of\ncircumvention and inference-based methods, we provide an in-depth discussion of\nvarious CI strategies to handle latent variables, covering the tasks of causal\neffect estimation, mediation analysis, counterfactual reasoning, and causal\ndiscovery. Furthermore, we generalize the discussion to graph data where\ninterference among units may exist. Finally, we offer fresh aspects for further\nadvancement of CI with latent variables, especially new opportunities in the\nera of large language models (LLMs).\n", "date": "2024-06-20", "categories": []}
{"id": "2402.15301", "title": "Causal Graph Discovery with Retrieval-Augmented Generation based Large\n  Language Models", "abstract": "  Causal graph recovery is traditionally done using statistical\nestimation-based methods or based on individual's knowledge about variables of\ninterests. They often suffer from data collection biases and limitations of\nindividuals' knowledge. The advance of large language models (LLMs) provides\nopportunities to address these problems. We propose a novel method that\nleverages LLMs to deduce causal relationships in general causal graph recovery\ntasks. This method leverages knowledge compressed in LLMs and knowledge LLMs\nextracted from scientific publication database as well as experiment data about\nfactors of interest to achieve this goal. Our method gives a prompting strategy\nto extract associational relationships among those factors and a mechanism to\nperform causality verification for these associations. Comparing to other\nLLM-based methods that directly instruct LLMs to do the highly complex causal\nreasoning, our method shows clear advantage on causal graph quality on\nbenchmark datasets. More importantly, as causality among some factors may\nchange as new research results emerge, our method show sensitivity to new\nevidence in the literature and can provide useful information for updating\ncausal graphs accordingly.\n", "date": "2024-02-23", "categories": []}
{"id": "2406.09177", "title": "Scalable and Flexible Causal Discovery with an Efficient Test for\n  Adjacency", "abstract": "  To make accurate predictions, understand mechanisms, and design interventions\nin systems of many variables, we wish to learn causal graphs from large scale\ndata. Unfortunately the space of all possible causal graphs is enormous so\nscalably and accurately searching for the best fit to the data is a challenge.\nIn principle we could substantially decrease the search space, or learn the\ngraph entirely, by testing the conditional independence of variables. However,\ndeciding if two variables are adjacent in a causal graph may require an\nexponential number of tests. Here we build a scalable and flexible method to\nevaluate if two variables are adjacent in a causal graph, the Differentiable\nAdjacency Test (DAT). DAT replaces an exponential number of tests with a\nprovably equivalent relaxed problem. It then solves this problem by training\ntwo neural networks. We build a graph learning method based on DAT, DAT-Graph,\nthat can also learn from data with interventions. DAT-Graph can learn graphs of\n1000 variables with state of the art accuracy. Using the graph learned by\nDAT-Graph, we also build models that make much more accurate predictions of the\neffects of interventions on large scale RNA sequencing data.\n", "date": "2024-06-13", "categories": []}
{"id": "2406.10419", "title": "Learning Flexible Time-windowed Granger Causality Integrating\n  Heterogeneous Interventional Time Series Data", "abstract": "  Granger causality, commonly used for inferring causal structures from time\nseries data, has been adopted in widespread applications across various fields\ndue to its intuitive explainability and high compatibility with emerging deep\nneural network prediction models. To alleviate challenges in better deciphering\ncausal structures unambiguously from time series, the use of interventional\ndata has become a practical approach. However, existing methods have yet to be\nexplored in the context of imperfect interventions with unknown targets, which\nare more common and often more beneficial in a wide range of real-world\napplications. Additionally, the identifiability issues of Granger causality\nwith unknown interventional targets in complex network models remain unsolved.\nOur work presents a theoretically-grounded method that infers Granger causal\nstructure and identifies unknown targets by leveraging heterogeneous\ninterventional time series data. We further illustrate that learning Granger\ncausal structure and recovering interventional targets can mutually promote\neach other. Comparative experiments demonstrate that our method outperforms\nseveral robust baseline methods in learning Granger causal structure from\ninterventional time series data.\n", "date": "2024-06-14", "categories": []}
{"id": "2406.10537", "title": "Scalable Differentiable Causal Discovery in the Presence of Latent\n  Confounders with Skeleton Posterior (Extended Version)", "abstract": "  Differentiable causal discovery has made significant advancements in the\nlearning of directed acyclic graphs. However, its application to real-world\ndatasets remains restricted due to the ubiquity of latent confounders and the\nrequirement to learn maximal ancestral graphs (MAGs). To date, existing\ndifferentiable MAG learning algorithms have been limited to small datasets and\nfailed to scale to larger ones (e.g., with more than 50 variables).\n  The key insight in this paper is that the causal skeleton, which is the\nundirected version of the causal graph, has potential for improving accuracy\nand reducing the search space of the optimization procedure, thereby enhancing\nthe performance of differentiable causal discovery. Therefore, we seek to\naddress a two-fold challenge to harness the potential of the causal skeleton\nfor differentiable causal discovery in the presence of latent confounders: (1)\nscalable and accurate estimation of skeleton and (2) universal integration of\nskeleton estimation with differentiable causal discovery.\n  To this end, we propose SPOT (Skeleton Posterior-guided OpTimization), a\ntwo-phase framework that harnesses skeleton posterior for differentiable causal\ndiscovery in the presence of latent confounders. On the contrary to a\n``point-estimation'', SPOT seeks to estimate the posterior distribution of\nskeletons given the dataset. It first formulates the posterior inference as an\ninstance of amortized inference problem and concretizes it with a supervised\ncausal learning (SCL)-enabled solution to estimate the skeleton posterior. To\nincorporate the skeleton posterior with differentiable causal discovery, SPOT\nthen features a skeleton posterior-guided stochastic optimization procedure to\nguide the optimization of MAGs. [abridged due to length limit]\n", "date": "2024-06-15", "categories": []}
{"id": "2406.10917", "title": "Bayesian Intervention Optimization for Causal Discovery", "abstract": "  Causal discovery is crucial for understanding complex systems and informing\ndecisions. While observational data can uncover causal relationships under\ncertain assumptions, it often falls short, making active interventions\nnecessary. Current methods, such as Bayesian and graph-theoretical approaches,\ndo not prioritize decision-making and often rely on ideal conditions or\ninformation gain, which is not directly related to hypothesis testing. We\npropose a novel Bayesian optimization-based method inspired by Bayes factors\nthat aims to maximize the probability of obtaining decisive and correct\nevidence. Our approach uses observational data to estimate causal models under\ndifferent hypotheses, evaluates potential interventions pre-experimentally, and\niteratively updates priors to refine interventions. We demonstrate the\neffectiveness of our method through various experiments. Our contributions\nprovide a robust framework for efficient causal discovery through active\ninterventions, enhancing the practical application of theoretical advancements.\n", "date": "2024-06-16", "categories": []}
{"id": "2406.09049", "title": "Efficiently Deciding Algebraic Equivalence of Bow-Free Acyclic Path\n  Diagrams", "abstract": "  For causal discovery in the presence of latent confounders, constraints\nbeyond conditional independences exist that can enable causal discovery\nalgorithms to distinguish more pairs of graphs. Such constraints are not\nwell-understood yet. In the setting of linear structural equation models\nwithout bows, we study algebraic constraints and argue that these provide the\nmost fine-grained resolution achievable. We propose efficient algorithms that\ndecide whether two graphs impose the same algebraic constraints, or whether the\nconstraints imposed by one graph are a subset of those imposed by another\ngraph.\n", "date": "2024-06-10", "categories": []}
{"id": "2406.09338", "title": "Learning the Influence Graph of a High-Dimensional Markov Process with\n  Memory", "abstract": "  Motivated by multiple applications in social networks, nervous systems, and\nfinancial risk analysis, we consider the problem of learning the underlying\n(directed) influence graph or causal graph of a high-dimensional multivariate\ndiscrete-time Markov process with memory. At any discrete time instant, each\nobserved variable of the multivariate process is a binary string of random\nlength, which is parameterized by an unobservable or hidden [0,1]-valued\nscalar. The hidden scalars corresponding to the variables evolve according to\ndiscrete-time linear stochastic dynamics dictated by the underlying influence\ngraph whose nodes are the variables. We extend an existing algorithm for\nlearning i.i.d. graphical models to this Markovian setting with memory and\nprove that it can learn the influence graph based on the binary observations\nusing logarithmic (in number of variables or nodes) samples when the degree of\nthe influence graph is bounded. The crucial analytical contribution of this\nwork is the derivation of the sample complexity result by upper and lower\nbounding the rate of convergence of the observed Markov process with memory to\nits stationary distribution in terms of the parameters of the influence graph.\n", "date": "2024-06-13", "categories": []}
{"id": "2406.06812", "title": "On Learning what to Learn: heterogeneous observations of dynamics and\n  establishing (possibly causal) relations among them", "abstract": "  Before we attempt to learn a function between two (sets of) observables of a\nphysical process, we must first decide what the inputs and what the outputs of\nthe desired function are going to be. Here we demonstrate two distinct,\ndata-driven ways of initially deciding ``the right quantities'' to relate\nthrough such a function, and then proceed to learn it. This is accomplished by\nprocessing multiple simultaneous heterogeneous data streams (ensembles of time\nseries) from observations of a physical system: multiple observation processes\nof the system. We thus determine (a) what subsets of observables are common\nbetween the observation processes (and therefore observable from each other,\nrelatable through a function); and (b) what information is unrelated to these\ncommon observables, and therefore particular to each observation process, and\nnot contributing to the desired function. Any data-driven function\napproximation technique can subsequently be used to learn the input-output\nrelation, from k-nearest neighbors and Geometric Harmonics to Gaussian\nProcesses and Neural Networks. Two particular ``twists'' of the approach are\ndiscussed. The first has to do with the identifiability of particular\nquantities of interest from the measurements. We now construct mappings from a\nsingle set of observations of one process to entire level sets of measurements\nof the process, consistent with this single set. The second attempts to relate\nour framework to a form of causality: if one of the observation processes\nmeasures ``now'', while the second observation process measures ``in the\nfuture'', the function to be learned among what is common across observation\nprocesses constitutes a dynamical model for the system evolution.\n", "date": "2024-06-10", "categories": []}
{"id": "2406.06829", "title": "Personalized Binomial DAGs Learning with Network Structured Covariates", "abstract": "  The causal dependence in data is often characterized by Directed Acyclic\nGraphical (DAG) models, widely used in many areas. Causal discovery aims to\nrecover the DAG structure using observational data. This paper focuses on\ncausal discovery with multi-variate count data. We are motivated by real-world\nweb visit data, recording individual user visits to multiple websites. Building\na causal diagram can help understand user behavior in transitioning between\nwebsites, inspiring operational strategy. A challenge in modeling is user\nheterogeneity, as users with different backgrounds exhibit varied behaviors.\nAdditionally, social network connections can result in similar behaviors among\nfriends. We introduce personalized Binomial DAG models to address heterogeneity\nand network dependency between observations, which are common in real-world\napplications. To learn the proposed DAG model, we develop an algorithm that\nembeds the network structure into a dimension-reduced covariate, learns each\nnode's neighborhood to reduce the DAG search space, and explores the\nvariance-mean relation to determine the ordering. Simulations show our\nalgorithm outperforms state-of-the-art competitors in heterogeneous data. We\ndemonstrate its practical usefulness on a real-world web visit dataset.\n", "date": "2024-06-10", "categories": []}
{"id": "2406.07020", "title": "Learning Discrete Latent Variable Structures with Tensor Rank Conditions", "abstract": "  Unobserved discrete data are ubiquitous in many scientific disciplines, and\nhow to learn the causal structure of these latent variables is crucial for\nuncovering data patterns. Most studies focus on the linear latent variable\nmodel or impose strict constraints on latent structures, which fail to address\ncases in discrete data involving non-linear relationships or complex latent\nstructures. To achieve this, we explore a tensor rank condition on contingency\ntables for an observed variable set $\\mathbf{X}_p$, showing that the rank is\ndetermined by the minimum support of a specific conditional set (not necessary\nin $\\mathbf{X}_p$) that d-separates all variables in $\\mathbf{X}_p$. By this,\none can locate the latent variable through probing the rank on different\nobserved variables set, and further identify the latent causal structure under\nsome structure assumptions. We present the corresponding identification\nalgorithm and conduct simulated experiments to verify the effectiveness of our\nmethod. In general, our results elegantly extend the identification boundary\nfor causal discovery with discrete latent variables and expand the application\nscope of causal discovery with latent variables.\n", "date": "2024-06-11", "categories": []}
{"id": "2406.07378", "title": "Large Language Models for Constrained-Based Causal Discovery", "abstract": "  Causality is essential for understanding complex systems, such as the\neconomy, the brain, and the climate. Constructing causal graphs often relies on\neither data-driven or expert-driven approaches, both fraught with challenges.\nThe former methods, like the celebrated PC algorithm, face issues with data\nrequirements and assumptions of causal sufficiency, while the latter demand\nsubstantial time and domain knowledge. This work explores the capabilities of\nLarge Language Models (LLMs) as an alternative to domain experts for causal\ngraph generation. We frame conditional independence queries as prompts to LLMs\nand employ the PC algorithm with the answers. The performance of the LLM-based\nconditional independence oracle on systems with known causal graphs shows a\nhigh degree of variability. We improve the performance through a proposed\nstatistical-inspired voting schema that allows some control over false-positive\nand false-negative rates. Inspecting the chain-of-thought argumentation, we\nfind causal reasoning to justify its answer to a probabilistic query. We show\nevidence that knowledge-based CIT could eventually become a complementary tool\nfor data-driven causal discovery.\n", "date": "2024-06-11", "categories": []}
{"id": "2308.06718", "title": "Generalized Independent Noise Condition for Estimating Causal Structure\n  with Latent Variables", "abstract": "  We investigate the task of learning causal structure in the presence of\nlatent variables, including locating latent variables and determining their\nquantity, and identifying causal relationships among both latent and observed\nvariables. To this end, we propose a Generalized Independent Noise (GIN)\ncondition for linear non-Gaussian acyclic causal models that incorporate latent\nvariables, which establishes the independence between a linear combination of\ncertain measured variables and some other measured variables. Specifically, for\ntwo observed random vectors $\\bf{Y}$ and $\\bf{Z}$, GIN holds if and only if\n$\\omega^{\\intercal}\\mathbf{Y}$ and $\\mathbf{Z}$ are independent, where $\\omega$\nis a non-zero parameter vector determined by the cross-covariance between\n$\\mathbf{Y}$ and $\\mathbf{Z}$. We then give necessary and sufficient graphical\ncriteria of the GIN condition in linear non-Gaussian acyclic models. Roughly\nspeaking, GIN implies the existence of a set $\\mathcal{S}$ such that\n$\\mathcal{S}$ is causally earlier (w.r.t. the causal ordering) than\n$\\mathbf{Y}$, and that every active (collider-free) path between $\\mathbf{Y}$\nand $\\mathbf{Z}$ must contain a node from $\\mathcal{S}$. Interestingly, we find\nthat the independent noise condition (i.e., if there is no confounder, causes\nare independent of the residual derived from regressing the effect on the\ncauses) can be seen as a special case of GIN. With such a connection between\nGIN and latent causal structures, we further leverage the proposed GIN\ncondition, together with a well-designed search procedure, to efficiently\nestimate Linear, Non-Gaussian Latent Hierarchical Models (LiNGLaHs), where\nlatent confounders may also be causally related and may even follow a\nhierarchical structure. We show that the causal structure of a LiNGLaH is\nidentifiable in light of GIN conditions. Experimental results show the\neffectiveness of the proposed method.\n", "date": "2023-08-13", "categories": []}
{"id": "2312.12844", "title": "Effective Causal Discovery under Identifiable Heteroscedastic Noise\n  Model", "abstract": "  Capturing the underlying structural causal relations represented by Directed\nAcyclic Graphs (DAGs) has been a fundamental task in various AI disciplines.\nCausal DAG learning via the continuous optimization framework has recently\nachieved promising performance in terms of both accuracy and efficiency.\nHowever, most methods make strong assumptions of homoscedastic noise, i.e.,\nexogenous noises have equal variances across variables, observations, or even\nboth. The noises in real data usually violate both assumptions due to the\nbiases introduced by different data collection processes. To address the issue\nof heteroscedastic noise, we introduce relaxed and implementable sufficient\nconditions, proving the identifiability of a general class of SEM subject to\nthese conditions. Based on the identifiable general SEM, we propose a novel\nformulation for DAG learning that accounts for the variation in noise variance\nacross variables and observations. We then propose an effective two-phase\niterative DAG learning algorithm to address the increasing optimization\ndifficulties and to learn a causal DAG from data with heteroscedastic variable\nnoise under varying variance. We show significant empirical gains of the\nproposed approaches over state-of-the-art methods on both synthetic data and\nreal data.\n", "date": "2023-12-20", "categories": []}
{"id": "2310.15709", "title": "Causal Representation Learning Made Identifiable by Grouping of\n  Observational Variables", "abstract": "  A topic of great current interest is Causal Representation Learning (CRL),\nwhose goal is to learn a causal model for hidden features in a data-driven\nmanner. Unfortunately, CRL is severely ill-posed since it is a combination of\nthe two notoriously ill-posed problems of representation learning and causal\ndiscovery. Yet, finding practical identifiability conditions that guarantee a\nunique solution is crucial for its practical applicability. Most approaches so\nfar have been based on assumptions on the latent causal mechanisms, such as\ntemporal causality, or existence of supervision or interventions; these can be\ntoo restrictive in actual applications. Here, we show identifiability based on\nnovel, weak constraints, which requires no temporal structure, intervention,\nnor weak supervision. The approach is based on assuming the observational\nmixing exhibits a suitable grouping of the observational variables. We also\npropose a novel self-supervised estimation framework consistent with the model,\nprove its statistical consistency, and experimentally show its superior CRL\nperformances compared to the state-of-the-art baselines. We further demonstrate\nits robustness against latent confounders and causal cycles.\n", "date": "2023-10-24", "categories": []}
{"id": "2406.04598", "title": "OCDB: Revisiting Causal Discovery with a Comprehensive Benchmark and\n  Evaluation Framework", "abstract": "  Large language models (LLMs) have excelled in various natural language\nprocessing tasks, but challenges in interpretability and trustworthiness\npersist, limiting their use in high-stakes fields. Causal discovery offers a\npromising approach to improve transparency and reliability. However, current\nevaluations are often one-sided and lack assessments focused on\ninterpretability performance. Additionally, these evaluations rely on synthetic\ndata and lack comprehensive assessments of real-world datasets. These lead to\npromising methods potentially being overlooked. To address these issues, we\npropose a flexible evaluation framework with metrics for evaluating differences\nin causal structures and causal effects, which are crucial attributes that help\nimprove the interpretability of LLMs. We introduce the Open Causal Discovery\nBenchmark (OCDB), based on real data, to promote fair comparisons and drive\noptimization of algorithms. Additionally, our new metrics account for\nundirected edges, enabling fair comparisons between Directed Acyclic Graphs\n(DAGs) and Completed Partially Directed Acyclic Graphs (CPDAGs). Experimental\nresults show significant shortcomings in existing algorithms' generalization\ncapabilities on real data, highlighting the potential for performance\nimprovement and the importance of our framework in advancing causal discovery\ntechniques.\n", "date": "2024-06-07", "categories": []}
{"id": "2405.16225", "title": "Local Causal Structure Learning in the Presence of Latent Variables", "abstract": "  Discovering causal relationships from observational data, particularly in the\npresence of latent variables, poses a challenging problem. While current local\nstructure learning methods have proven effective and efficient when the focus\nlies solely on the local relationships of a target variable, they operate under\nthe assumption of causal sufficiency. This assumption implies that all the\ncommon causes of the measured variables are observed, leaving no room for\nlatent variables. Such a premise can be easily violated in various real-world\napplications, resulting in inaccurate structures that may adversely impact\ndownstream tasks. In light of this, our paper delves into the primary\ninvestigation of locally identifying potential parents and children of a target\nfrom observational data that may include latent variables. Specifically, we\nharness the causal information from m-separation and V-structures to derive\ntheoretical consistency results, effectively bridging the gap between global\nand local structure learning. Together with the newly developed stop rules, we\npresent a principled method for determining whether a variable is a direct\ncause or effect of a target. Further, we theoretically demonstrate the\ncorrectness of our approach under the standard causal Markov and faithfulness\nconditions, with infinite samples. Experimental results on both synthetic and\nreal-world data validate the effectiveness and efficiency of our approach.\n", "date": "2024-05-25", "categories": []}
{"id": "2406.03209", "title": "Challenges and Considerations in the Evaluation of Bayesian Causal\n  Discovery", "abstract": "  Representing uncertainty in causal discovery is a crucial component for\nexperimental design, and more broadly, for safe and reliable causal decision\nmaking. Bayesian Causal Discovery (BCD) offers a principled approach to\nencapsulating this uncertainty. Unlike non-Bayesian causal discovery, which\nrelies on a single estimated causal graph and model parameters for assessment,\nevaluating BCD presents challenges due to the nature of its inferred quantity -\nthe posterior distribution. As a result, the research community has proposed\nvarious metrics to assess the quality of the approximate posterior. However,\nthere is, to date, no consensus on the most suitable metric(s) for evaluation.\nIn this work, we reexamine this question by dissecting various metrics and\nunderstanding their limitations. Through extensive empirical evaluation, we\nfind that many existing metrics fail to exhibit a strong correlation with the\nquality of approximation to the true posterior, especially in scenarios with\nlow sample sizes where BCD is most desirable. We highlight the suitability (or\nlack thereof) of these metrics under two distinct factors: the identifiability\nof the underlying causal model and the quantity of available data. Both factors\naffect the entropy of the true posterior, indicating that the current metrics\nare less fitting in settings of higher entropy. Our findings underline the\nimportance of a more nuanced evaluation of new methods by taking into account\nthe nature of the true posterior, as well as guide and motivate the development\nof new evaluation procedures for this challenge.\n", "date": "2024-06-05", "categories": []}
{"id": "2406.03212", "title": "Inferring the time-varying coupling of dynamical systems with temporal\n  convolutional autoencoders", "abstract": "  Most approaches for assessing causality in complex dynamical systems fail\nwhen the interactions between variables are inherently non-linear and\nnon-stationary. Here we introduce Temporal Autoencoders for Causal Inference\n(TACI), a methodology that combines a new surrogate data metric for assessing\ncausal interactions with a novel two-headed machine learning architecture to\nidentify and measure the direction and strength of time-varying causal\ninteractions. Through tests on both synthetic and real-world datasets, we\ndemonstrate TACI's ability to accurately quantify dynamic causal interactions\nacross a variety of systems. Our findings display the method's effectiveness\ncompared to existing approaches and also highlight our approach's potential to\nbuild a deeper understanding of the mechanisms that underlie time-varying\ninteractions in physical and biological systems.\n", "date": "2024-06-05", "categories": []}
{"id": "2406.01823", "title": "Causal Discovery with Fewer Conditional Independence Tests", "abstract": "  Many questions in science center around the fundamental problem of\nunderstanding causal relationships. However, most constraint-based causal\ndiscovery algorithms, including the well-celebrated PC algorithm, often incur\nan exponential number of conditional independence (CI) tests, posing\nlimitations in various applications. Addressing this, our work focuses on\ncharacterizing what can be learned about the underlying causal graph with a\nreduced number of CI tests. We show that it is possible to a learn a coarser\nrepresentation of the hidden causal graph with a polynomial number of tests.\nThis coarser representation, named Causal Consistent Partition Graph (CCPG),\ncomprises of a partition of the vertices and a directed graph defined over its\ncomponents. CCPG satisfies consistency of orientations and additional\nconstraints which favor finer partitions. Furthermore, it reduces to the\nunderlying causal graph when the causal graph is identifiable. As a\nconsequence, our results offer the first efficient algorithm for recovering the\ntrue causal graph with a polynomial number of tests, in special cases where the\ncausal graph is fully identifiable through observational data and potentially\nadditional interventions.\n", "date": "2024-06-03", "categories": []}
{"id": "2211.02763", "title": "Bayesian learning of Causal Structure and Mechanisms with GFlowNets and\n  Variational Bayes", "abstract": "  Bayesian causal structure learning aims to learn a posterior distribution\nover directed acyclic graphs (DAGs), and the mechanisms that define the\nrelationship between parent and child variables. By taking a Bayesian approach,\nit is possible to reason about the uncertainty of the causal model. The notion\nof modelling the uncertainty over models is particularly crucial for causal\nstructure learning since the model could be unidentifiable when given only a\nfinite amount of observational data. In this paper, we introduce a novel method\nto jointly learn the structure and mechanisms of the causal model using\nVariational Bayes, which we call Variational Bayes-DAG-GFlowNet (VBG). We\nextend the method of Bayesian causal structure learning using GFlowNets to\nlearn not only the posterior distribution over the structure, but also the\nparameters of a linear-Gaussian model. Our results on simulated data suggest\nthat VBG is competitive against several baselines in modelling the posterior\nover DAGs and mechanisms, while offering several advantages over existing\nmethods, including the guarantee to sample acyclic graphs, and the flexibility\nto generalize to non-linear causal mechanisms.\n", "date": "2022-11-04", "categories": []}
{"id": "2310.17816", "title": "Local Discovery by Partitioning: Polynomial-Time Causal Discovery Around\n  Exposure-Outcome Pairs", "abstract": "  Causal discovery is crucial for causal inference in observational studies, as\nit can enable the identification of valid adjustment sets (VAS) for unbiased\neffect estimation. However, global causal discovery is notoriously hard in the\nnonparametric setting, with exponential time and sample complexity in the worst\ncase. To address this, we propose local discovery by partitioning (LDP): a\nlocal causal discovery method that is tailored for downstream inference tasks\nwithout requiring parametric and pretreatment assumptions. LDP is a\nconstraint-based procedure that returns a VAS for an exposure-outcome pair\nunder latent confounding, given sufficient conditions. The total number of\nindependence tests performed is worst-case quadratic with respect to the\ncardinality of the variable set. Asymptotic theoretical guarantees are\nnumerically validated on synthetic graphs. Adjustment sets from LDP yield less\nbiased and more precise average treatment effect estimates than baseline\ndiscovery algorithms, with LDP outperforming on confounder recall, runtime, and\ntest count for VAS discovery. Notably, LDP ran at least 1300x faster than\nbaselines on a benchmark.\n", "date": "2023-10-25", "categories": []}
{"id": "2402.15255", "title": "Optimal Transport for Structure Learning Under Missing Data", "abstract": "  Causal discovery in the presence of missing data introduces a chicken-and-egg\ndilemma. While the goal is to recover the true causal structure, robust\nimputation requires considering the dependencies or, preferably, causal\nrelations among variables. Merely filling in missing values with existing\nimputation methods and subsequently applying structure learning on the complete\ndata is empirically shown to be sub-optimal. To address this problem, we\npropose a score-based algorithm for learning causal structures from missing\ndata based on optimal transport. This optimal transport viewpoint diverges from\nexisting score-based approaches that are dominantly based on expectation\nmaximization. We formulate structure learning as a density fitting problem,\nwhere the goal is to find the causal model that induces a distribution of\nminimum Wasserstein distance with the observed data distribution. Our framework\nis shown to recover the true causal graphs more effectively than competing\nmethods in most simulations and real-data settings. Empirical evidence also\nshows the superior scalability of our approach, along with the flexibility to\nincorporate any off-the-shelf causal discovery methods for complete data.\n", "date": "2024-02-23", "categories": []}
{"id": "2406.00394", "title": "Learning Causal Abstractions of Linear Structural Causal Models", "abstract": "  The need for modelling causal knowledge at different levels of granularity\narises in several settings. Causal Abstraction provides a framework for\nformalizing this problem by relating two Structural Causal Models at different\nlevels of detail. Despite increasing interest in applying causal abstraction,\ne.g. in the interpretability of large machine learning models, the graphical\nand parametrical conditions under which a causal model can abstract another are\nnot known. Furthermore, learning causal abstractions from data is still an open\nproblem. In this work, we tackle both issues for linear causal models with\nlinear abstraction functions. First, we characterize how the low-level\ncoefficients and the abstraction function determine the high-level coefficients\nand how the high-level model constrains the causal ordering of low-level\nvariables. Then, we apply our theoretical results to learn high-level and\nlow-level causal models and their abstraction function from observational data.\nIn particular, we introduce Abs-LiNGAM, a method that leverages the constraints\ninduced by the learned high-level model and the abstraction function to speedup\nthe recovery of the larger low-level model, under the assumption of\nnon-Gaussian noise terms. In simulated settings, we show the effectiveness of\nlearning causal abstractions from data and the potential of our method in\nimproving scalability of causal discovery.\n", "date": "2024-06-01", "categories": []}
{"id": "2405.06902", "title": "Causal Inference from Slowly Varying Nonstationary Processes", "abstract": "  Causal inference from observational data following the restricted structural\ncausal models (SCM) framework hinges largely on the asymmetry between cause and\neffect from the data generating mechanisms, such as non-Gaussianity or\nnon-linearity. This methodology can be adapted to stationary time series, yet\ninferring causal relationships from nonstationary time series remains a\nchallenging task. In this work, we propose a new class of restricted SCM, via a\ntime-varying filter and stationary noise, and exploit the asymmetry from\nnonstationarity for causal identification in both bivariate and network\nsettings. We propose efficient procedures by leveraging powerful estimates of\nthe bivariate evolutionary spectra for slowly varying processes. Various\nsynthetic and real datasets that involve high-order and non-smooth filters are\nevaluated to demonstrate the effectiveness of our proposed methodology.\n", "date": "2024-05-11", "categories": []}
{"id": "2306.02931", "title": "Bivariate Causal Discovery using Bayesian Model Selection", "abstract": "  Much of the causal discovery literature prioritises guaranteeing the\nidentifiability of causal direction in statistical models. For structures\nwithin a Markov equivalence class, this requires strong assumptions which may\nnot hold in real-world datasets, ultimately limiting the usability of these\nmethods. Building on previous attempts, we show how to incorporate causal\nassumptions within the Bayesian framework. Identifying causal direction then\nbecomes a Bayesian model selection problem. This enables us to construct models\nwith realistic assumptions, and consequently allows for the differentiation\nbetween Markov equivalent causal structures. We analyse why Bayesian model\nselection works in situations where methods based on maximum likelihood fail.\nTo demonstrate our approach, we construct a Bayesian non-parametric model that\ncan flexibly model the joint distribution. We then outperform previous methods\non a wide range of benchmark datasets with varying data generating assumptions.\n", "date": "2023-06-05", "categories": []}
{"id": "2404.14786", "title": "RealTCD: Temporal Causal Discovery from Interventional Data with Large\n  Language Model", "abstract": "  In the field of Artificial Intelligence for Information Technology\nOperations, causal discovery is pivotal for operation and maintenance of graph\nconstruction, facilitating downstream industrial tasks such as root cause\nanalysis. Temporal causal discovery, as an emerging method, aims to identify\ntemporal causal relationships between variables directly from observations by\nutilizing interventional data. However, existing methods mainly focus on\nsynthetic datasets with heavy reliance on intervention targets and ignore the\ntextual information hidden in real-world systems, failing to conduct causal\ndiscovery for real industrial scenarios. To tackle this problem, in this paper\nwe propose to investigate temporal causal discovery in industrial scenarios,\nwhich faces two critical challenges: 1) how to discover causal relationships\nwithout the interventional targets that are costly to obtain in practice, and\n2) how to discover causal relations via leveraging the textual information in\nsystems which can be complex yet abundant in industrial contexts. To address\nthese challenges, we propose the RealTCD framework, which is able to leverage\ndomain knowledge to discover temporal causal relationships without\ninterventional targets. Specifically, we first develop a score-based temporal\ncausal discovery method capable of discovering causal relations for root cause\nanalysis without relying on interventional targets through strategic masking\nand regularization. Furthermore, by employing Large Language Models (LLMs) to\nhandle texts and integrate domain knowledge, we introduce LLM-guided\nmeta-initialization to extract the meta-knowledge from textual information\nhidden in systems to boost the quality of discovery. We conduct extensive\nexperiments on simulation and real-world datasets to show the superiority of\nour proposed RealTCD framework over existing baselines in discovering temporal\ncausal structures.\n", "date": "2024-04-23", "categories": []}
{"id": "2405.16718", "title": "Amortized Active Causal Induction with Deep Reinforcement Learning", "abstract": "  We present Causal Amortized Active Structure Learning (CAASL), an active\nintervention design policy that can select interventions that are adaptive,\nreal-time and that does not require access to the likelihood. This policy, an\namortized network based on the transformer, is trained with reinforcement\nlearning on a simulator of the design environment, and a reward function that\nmeasures how close the true causal graph is to a causal graph posterior\ninferred from the gathered data. On synthetic data and a single-cell gene\nexpression simulator, we demonstrate empirically that the data acquired through\nour policy results in a better estimate of the underlying causal graph than\nalternative strategies. Our design policy successfully achieves amortized\nintervention design on the distribution of the training environment while also\ngeneralizing well to distribution shifts in test-time design environments.\nFurther, our policy also demonstrates excellent zero-shot generalization to\ndesign environments with dimensionality higher than that during training, and\nto intervention types that it has not been trained on.\n", "date": "2024-05-26", "categories": []}
{"id": "2311.07259", "title": "Towards Bounding Causal Effects under Markov Equivalence", "abstract": "  Predicting the effect of unseen interventions is a fundamental research\nquestion across the data sciences. It is well established that in general such\nquestions cannot be answered definitively from observational data. This\nrealization has fuelled a growing literature introducing various identifying\nassumptions, for example in the form of a causal diagram among relevant\nvariables. In practice, this paradigm is still too rigid for many practical\napplications as it is generally not possible to confidently delineate the true\ncausal diagram. In this paper, we consider the derivation of bounds on causal\neffects given only observational data. We propose to take as input a less\ninformative structure known as a Partial Ancestral Graph, which represents a\nMarkov equivalence class of causal diagrams and is learnable from data. In this\nmore ``data-driven'' setting, we provide a systematic algorithm to derive\nbounds on causal effects that exploit the invariant properties of the\nequivalence class, and that can be computed analytically. We demonstrate our\nmethod with synthetic and real data examples.\n", "date": "2023-11-13", "categories": []}
{"id": "2402.03614", "title": "Bayesian Vector AutoRegression with Factorised Granger-Causal Graphs", "abstract": "  We study the problem of automatically discovering Granger causal relations\nfrom observational multivariate time-series data.Vector autoregressive (VAR)\nmodels have been time-tested for this problem, including Bayesian variants and\nmore recent developments using deep neural networks. Most existing VAR methods\nfor Granger causality use sparsity-inducing penalties/priors or post-hoc\nthresholds to interpret their coefficients as Granger causal graphs. Instead,\nwe propose a new Bayesian VAR model with a hierarchical factorised prior\ndistribution over binary Granger causal graphs, separately from the VAR\ncoefficients. We develop an efficient algorithm to infer the posterior over\nbinary Granger causal graphs. Comprehensive experiments on synthetic,\nsemi-synthetic, and climate data show that our method is more uncertainty\naware, has less hyperparameters, and achieves better performance than competing\napproaches, especially in low-data regimes where there are less observations.\n", "date": "2024-02-06", "categories": []}
{"id": "2405.15358", "title": "Coordinated Multi-Neighborhood Learning on a Directed Acyclic Graph", "abstract": "  Learning the structure of causal directed acyclic graphs (DAGs) is useful in\nmany areas of machine learning and artificial intelligence, with wide\napplications. However, in the high-dimensional setting, it is challenging to\nobtain good empirical and theoretical results without strong and often\nrestrictive assumptions. Additionally, it is questionable whether all of the\nvariables purported to be included in the network are observable. It is of\ninterest then to restrict consideration to a subset of the variables for\nrelevant and reliable inferences. In fact, researchers in various disciplines\ncan usually select a set of target nodes in the network for causal discovery.\nThis paper develops a new constraint-based method for estimating the local\nstructure around multiple user-specified target nodes, enabling coordination in\nstructure learning between neighborhoods. Our method facilitates causal\ndiscovery without learning the entire DAG structure. We establish consistency\nresults for our algorithm with respect to the local neighborhood structure of\nthe target nodes in the true graph. Experimental results on synthetic and\nreal-world data show that our algorithm is more accurate in learning the\nneighborhood structures with much less computational cost than standard methods\nthat estimate the entire DAG. An R package implementing our methods may be\naccessed at https://github.com/stephenvsmith/CML.\n", "date": "2024-05-24", "categories": []}
{"id": "2405.13100", "title": "Better Simulations for Validating Causal Discovery with the\n  DAG-Adaptation of the Onion Method", "abstract": "  The number of artificial intelligence algorithms for learning causal models\nfrom data is growing rapidly. Most ``causal discovery'' or ``causal structure\nlearning'' algorithms are primarily validated through simulation studies.\nHowever, no widely accepted simulation standards exist and publications often\nreport conflicting performance statistics -- even when only considering\npublications that simulate data from linear models. In response, several\nmanuscripts have criticized a popular simulation design for validating\nalgorithms in the linear case.\n  We propose a new simulation design for generating linear models for directed\nacyclic graphs (DAGs): the DAG-adaptation of the Onion (DaO) method. DaO\nsimulations are fundamentally different from existing simulations because they\nprioritize the distribution of correlation matrices rather than the\ndistribution of linear effects. Specifically, the DaO method uniformly samples\nthe space of all correlation matrices consistent with (i.e. Markov to) a DAG.\nWe also discuss how to sample DAGs and present methods for generating DAGs with\nscale-free in-degree or out-degree. We compare the DaO method against two\nalternative simulation designs and provide implementations of the DaO method in\nPython and R: https://github.com/bja43/DaO_simulation. We advocate for others\nto adopt DaO simulations as a fair universal benchmark.\n", "date": "2024-05-21", "categories": []}
{"id": "2405.13551", "title": "Large Language Models are Effective Priors for Causal Graph Discovery", "abstract": "  Causal structure discovery from observations can be improved by integrating\nbackground knowledge provided by an expert to reduce the hypothesis space.\nRecently, Large Language Models (LLMs) have begun to be considered as sources\nof prior information given the low cost of querying them relative to a human\nexpert. In this work, firstly, we propose a set of metrics for assessing LLM\njudgments for causal graph discovery independently of the downstream algorithm.\nSecondly, we systematically study a set of prompting designs that allows the\nmodel to specify priors about the structure of the causal graph. Finally, we\npresent a general methodology for the integration of LLM priors in graph\ndiscovery algorithms, finding that they help improve performance on\ncommon-sense benchmarks and especially when used for assessing edge\ndirectionality. Our work highlights the potential as well as the shortcomings\nof the use of LLMs in this problem space.\n", "date": "2024-05-22", "categories": []}
{"id": "2405.08699", "title": "Weakly-supervised causal discovery based on fuzzy knowledge and complex\n  data complementarity", "abstract": "  Causal discovery based on observational data is important for deciphering the\ncausal mechanism behind complex systems. However, the effectiveness of existing\ncausal discovery methods is limited due to inferior prior knowledge, domain\ninconsistencies, and the challenges of high-dimensional datasets with small\nsample sizes. To address this gap, we propose a novel weakly-supervised fuzzy\nknowledge and data co-driven causal discovery method named KEEL. KEEL adopts a\nfuzzy causal knowledge schema to encapsulate diverse types of fuzzy knowledge,\nand forms corresponding weakened constraints. This schema not only lessens the\ndependency on expertise but also allows various types of limited and\nerror-prone fuzzy knowledge to guide causal discovery. It can enhance the\ngeneralization and robustness of causal discovery, especially in\nhigh-dimensional and small-sample scenarios. In addition, we integrate the\nextended linear causal model (ELCM) into KEEL for dealing with the\nmulti-distribution and incomplete data. Extensive experiments with different\ndatasets demonstrate the superiority of KEEL over several state-of-the-art\nmethods in accuracy, robustness and computational efficiency. For causal\ndiscovery in real protein signal transduction processes, KEEL outperforms the\nbenchmark method with limited data. In summary, KEEL is effective to tackle the\ncausal discovery tasks with higher accuracy while alleviating the requirement\nfor extensive domain expertise.\n", "date": "2024-05-14", "categories": []}
{"id": "2405.08779", "title": "Jacobian Regularizer-based Neural Granger Causality", "abstract": "  With the advancement of neural networks, diverse methods for neural Granger\ncausality have emerged, which demonstrate proficiency in handling complex data,\nand nonlinear relationships. However, the existing framework of neural Granger\ncausality has several limitations. It requires the construction of separate\npredictive models for each target variable, and the relationship depends on the\nsparsity on the weights of the first layer, resulting in challenges in\neffectively modeling complex relationships between variables as well as\nunsatisfied estimation accuracy of Granger causality. Moreover, most of them\ncannot grasp full-time Granger causality. To address these drawbacks, we\npropose a Jacobian Regularizer-based Neural Granger Causality (JRNGC) approach,\na straightforward yet highly effective method for learning multivariate summary\nGranger causality and full-time Granger causality by constructing a single\nmodel for all target variables. Specifically, our method eliminates the\nsparsity constraints of weights by leveraging an input-output Jacobian matrix\nregularizer, which can be subsequently represented as the weighted causal\nmatrix in the post-hoc analysis. Extensive experiments show that our proposed\napproach achieves competitive performance with the state-of-the-art methods for\nlearning summary Granger causality and full-time Granger causality while\nmaintaining lower model complexity and high scalability.\n", "date": "2024-05-14", "categories": []}
{"id": "2405.07220", "title": "On Discovery of Local Independence over Continuous Variables via Neural\n  Contextual Decomposition", "abstract": "  Conditional independence provides a way to understand causal relationships\namong the variables of interest. An underlying system may exhibit more\nfine-grained causal relationships especially between a variable and its\nparents, which will be called the local independence relationships. One of the\nmost widely studied local relationships is Context-Specific Independence (CSI),\nwhich holds in a specific assignment of conditioned variables. However, its\napplicability is often limited since it does not allow continuous variables:\ndata conditioned to the specific value of a continuous variable contains few\ninstances, if not none, making it infeasible to test independence. In this\nwork, we define and characterize the local independence relationship that holds\nin a specific set of joint assignments of parental variables, which we call\ncontext-set specific independence (CSSI). We then provide a canonical\nrepresentation of CSSI and prove its fundamental properties. Based on our\ntheoretical findings, we cast the problem of discovering multiple CSSI\nrelationships in a system as finding a partition of the joint outcome space.\nFinally, we propose a novel method, coined neural contextual decomposition\n(NCD), which learns such partition by imposing each set to induce CSSI via\nmodeling a conditional distribution. We empirically demonstrate that the\nproposed method successfully discovers the ground truth local independence\nrelationships in both synthetic dataset and complex system reflecting the\nreal-world physical dynamics.\n", "date": "2024-05-12", "categories": []}
{"id": "2311.03309", "title": "Neural Structure Learning with Stochastic Differential Equations", "abstract": "  Discovering the underlying relationships among variables from temporal\nobservations has been a longstanding challenge in numerous scientific\ndisciplines, including biology, finance, and climate science. The dynamics of\nsuch systems are often best described using continuous-time stochastic\nprocesses. Unfortunately, most existing structure learning approaches assume\nthat the underlying process evolves in discrete-time and/or observations occur\nat regular time intervals. These mismatched assumptions can often lead to\nincorrect learned structures and models. In this work, we introduce a novel\nstructure learning method, SCOTCH, which combines neural stochastic\ndifferential equations (SDE) with variational inference to infer a posterior\ndistribution over possible structures. This continuous-time approach can\nnaturally handle both learning from and predicting observations at arbitrary\ntime points. Theoretically, we establish sufficient conditions for an SDE and\nSCOTCH to be structurally identifiable, and prove its consistency under\ninfinite data limits. Empirically, we demonstrate that our approach leads to\nimproved structure learning performance on both synthetic and real-world\ndatasets compared to relevant baselines under regular and irregular sampling\nintervals.\n", "date": "2023-11-06", "categories": []}
{"id": "2311.04037", "title": "Causal Discovery Under Local Privacy", "abstract": "  Differential privacy is a widely adopted framework designed to safeguard the\nsensitive information of data providers within a data set. It is based on the\napplication of controlled noise at the interface between the server that stores\nand processes the data, and the data consumers. Local differential privacy is a\nvariant that allows data providers to apply the privatization mechanism\nthemselves on their data individually. Therefore it provides protection also in\ncontexts in which the server, or even the data collector, cannot be trusted.\nThe introduction of noise, however, inevitably affects the utility of the data,\nparticularly by distorting the correlations between individual data components.\nThis distortion can prove detrimental to tasks such as causal discovery. In\nthis paper, we consider various well-known locally differentially private\nmechanisms and compare the trade-off between the privacy they provide, and the\naccuracy of the causal structure produced by algorithms for causal learning\nwhen applied to data obfuscated by these mechanisms. Our analysis yields\nvaluable insights for selecting appropriate local differentially private\nprotocols for causal discovery tasks. We foresee that our findings will aid\nresearchers and practitioners in conducting locally private causal discovery.\n", "date": "2023-11-07", "categories": []}
{"id": "2305.05281", "title": "Causal Discovery via Conditional Independence Testing with Proxy\n  Variables", "abstract": "  Distinguishing causal connections from correlations is important in many\nscenarios. However, the presence of unobserved variables, such as the latent\nconfounder, can introduce bias in conditional independence testing commonly\nemployed in constraint-based causal discovery for identifying causal relations.\nTo address this issue, existing methods introduced proxy variables to adjust\nfor the bias caused by unobserveness. However, these methods were either\nlimited to categorical variables or relied on strong parametric assumptions for\nidentification. In this paper, we propose a novel hypothesis-testing procedure\nthat can effectively examine the existence of the causal relationship over\ncontinuous variables, without any parametric constraint. Our procedure is based\non discretization, which under completeness conditions, is able to\nasymptotically establish a linear equation whose coefficient vector is\nidentifiable under the causal null hypothesis. Based on this, we introduce our\ntest statistic and demonstrate its asymptotic level and power. We validate the\neffectiveness of our procedure using both synthetic and real-world data.\n", "date": "2023-05-09", "categories": []}
{"id": "2306.08765", "title": "Causal Discovery from Time Series with Hybrids of Constraint-Based and\n  Noise-Based Algorithms", "abstract": "  Constraint-based methods and noise-based methods are two distinct families of\nmethods proposed for uncovering causal graphs from observational data. However,\nboth operate under strong assumptions that may be challenging to validate or\ncould be violated in real-world scenarios. In response to these challenges,\nthere is a growing interest in hybrid methods that amalgamate principles from\nboth methods, showing robustness to assumption violations. This paper\nintroduces a novel comprehensive framework for hybridizing constraint-based and\nnoise-based methods designed to uncover causal graphs from observational time\nseries. The framework is structured into two classes. The first class employs a\nnoise-based strategy to identify a super graph, containing the true graph,\nfollowed by a constraint-based strategy to eliminate unnecessary edges. In the\nsecond class, a constraint-based strategy is applied to identify a skeleton,\nwhich is then oriented using a noise-based strategy. The paper provides\ntheoretical guarantees for each class under the condition that all assumptions\nare satisfied, and it outlines some properties when assumptions are violated.\nTo validate the efficacy of the framework, two algorithms from each class are\nexperimentally tested on simulated data, realistic ecological data, and real\ndatasets sourced from diverse applications. Notably, two novel datasets related\nto Information Technology monitoring are introduced within the set of\nconsidered real datasets. The experimental results underscore the robustness\nand effectiveness of the hybrid approaches across a broad spectrum of datasets.\n", "date": "2023-06-14", "categories": []}
{"id": "2404.16326", "title": "NeuroKoopman Dynamic Causal Discovery", "abstract": "  In many real-world applications where the system dynamics has an underlying\ninterdependency among its variables (such as power grid, economics,\nneuroscience, omics networks, environmental ecosystems, and others), one is\noften interested in knowing whether the past values of one time series\ninfluences the future of another, known as Granger causality, and the\nassociated underlying dynamics. This paper introduces a Koopman-inspired\nframework that leverages neural networks for data-driven learning of the\nKoopman bases, termed NeuroKoopman Dynamic Causal Discovery (NKDCD), for\nreliably inferring the Granger causality along with the underlying nonlinear\ndynamics. NKDCD employs an autoencoder architecture that lifts the nonlinear\ndynamics to a higher dimension using data-learned bases, where the lifted time\nseries can be reliably modeled linearly. The lifting function, the linear\nGranger causality lag matrices, and the projection function (from lifted space\nto base space) are all represented as multilayer perceptrons and are all\nlearned simultaneously in one go. NKDCD also utilizes sparsity-inducing\npenalties on the weights of the lag matrices, encouraging the model to select\nonly the needed causal dependencies within the data. Through extensive testing\non practically applicable datasets, it is shown that the NKDCD outperforms the\nexisting nonlinear Granger causality discovery approaches.\n", "date": "2024-04-25", "categories": []}
{"id": "2404.16361", "title": "Evolutionary Causal Discovery with Relative Impact Stratification for\n  Interpretable Data Analysis", "abstract": "  This study proposes Evolutionary Causal Discovery (ECD) for causal discovery\nthat tailors response variables, predictor variables, and corresponding\noperators to research datasets. Utilizing genetic programming for variable\nrelationship parsing, the method proceeds with the Relative Impact\nStratification (RIS) algorithm to assess the relative impact of predictor\nvariables on the response variable, facilitating expression simplification and\nenhancing the interpretability of variable relationships. ECD proposes an\nexpression tree to visualize the RIS results, offering a differentiated\ndepiction of unknown causal relationships compared to conventional causal\ndiscovery. The ECD method represents an evolution and augmentation of existing\ncausal discovery methods, providing an interpretable approach for analyzing\nvariable relationships in complex systems, particularly in healthcare settings\nwith Electronic Health Record (EHR) data. Experiments on both synthetic and\nreal-world EHR datasets demonstrate the efficacy of ECD in uncovering patterns\nand mechanisms among variables, maintaining high accuracy and stability across\ndifferent noise levels. On the real-world EHR dataset, ECD reveals the\nintricate relationships between the response variable and other predictive\nvariables, aligning with the results of structural equation modeling and\nshapley additive explanations analyses.\n", "date": "2024-04-25", "categories": []}
{"id": "2404.14460", "title": "Inference of Causal Networks using a Topological Threshold", "abstract": "  We propose a constraint-based algorithm, which automatically determines\ncausal relevance thresholds, to infer causal networks from data. We call these\ntopological thresholds. We present two methods for determining the threshold:\nthe first seeks a set of edges that leaves no disconnected nodes in the\nnetwork; the second seeks a causal large connected component in the data.\n  We tested these methods both for discrete synthetic and real data, and\ncompared the results with those obtained for the PC algorithm, which we took as\nthe benchmark. We show that this novel algorithm is generally faster and more\naccurate than the PC algorithm.\n  The algorithm for determining the thresholds requires choosing a measure of\ncausality. We tested our methods for Fisher Correlations, commonly used in PC\nalgorithm (for instance in \\cite{kalisch2005}), and further proposed a discrete\nand asymmetric measure of causality, that we called Net Influence, which\nprovided very good results when inferring causal networks from discrete data.\nThis metric allows for inferring directionality of the edges in the process of\napplying the thresholds, speeding up the inference of causal DAGs.\n", "date": "2024-04-21", "categories": []}
{"id": "2307.16405", "title": "Causal-learn: Causal Discovery in Python", "abstract": "  Causal discovery aims at revealing causal relations from observational data,\nwhich is a fundamental task in science and engineering. We describe\n$\\textit{causal-learn}$, an open-source Python library for causal discovery.\nThis library focuses on bringing a comprehensive collection of causal discovery\nmethods to both practitioners and researchers. It provides easy-to-use APIs for\nnon-specialists, modular building blocks for developers, detailed documentation\nfor learners, and comprehensive methods for all. Different from previous\npackages in R or Java, $\\textit{causal-learn}$ is fully developed in Python,\nwhich could be more in tune with the recent preference shift in programming\nlanguages within related communities. The library is available at\nhttps://github.com/py-why/causal-learn.\n", "date": "2023-07-31", "categories": []}
{"id": "2309.02027", "title": "Granger Causal Inference in Multivariate Hawkes Processes by Minimum\n  Message Length", "abstract": "  Multivariate Hawkes processes (MHPs) are versatile probabilistic tools used\nto model various real-life phenomena: earthquakes, operations on stock markets,\nneuronal activity, virus propagation and many others. In this paper, we focus\non MHPs with exponential decay kernels and estimate connectivity graphs, which\nrepresent the Granger causal relations between their components. We approach\nthis inference problem by proposing an optimization criterion and model\nselection algorithm based on the minimum message length (MML) principle. MML\ncompares Granger causal models using the Occam's razor principle in the\nfollowing way: even when models have a comparable goodness-of-fit to the\nobserved data, the one generating the most concise explanation of the data is\npreferred. While most of the state-of-art methods using lasso-type penalization\ntend to overfitting in scenarios with short time horizons, the proposed\nMML-based method achieves high F1 scores in these settings. We conduct a\nnumerical study comparing the proposed algorithm to other related classical and\nstate-of-art methods, where we achieve the highest F1 scores in specific sparse\ngraph settings. We illustrate the proposed method also on G7 sovereign bond\ndata and obtain causal connections, which are in agreement with the expert\nknowledge available in the literature.\n", "date": "2023-09-05", "categories": []}
{"id": "2302.08070", "title": "Local Causal Discovery for Estimating Causal Effects", "abstract": "  Even when the causal graph underlying our data is unknown, we can use\nobservational data to narrow down the possible values that an average treatment\neffect (ATE) can take by (1) identifying the graph up to a Markov equivalence\nclass; and (2) estimating that ATE for each graph in the class. While the PC\nalgorithm can identify this class under strong faithfulness assumptions, it can\nbe computationally prohibitive. Fortunately, only the local graph structure\naround the treatment is required to identify the set of possible ATE values, a\nfact exploited by local discovery algorithms to improve computational\nefficiency. In this paper, we introduce Local Discovery using Eager Collider\nChecks (LDECC), a new local causal discovery algorithm that leverages\nunshielded colliders to orient the treatment's parents differently from\nexisting methods. We show that there exist graphs where LDECC exponentially\noutperforms existing local discovery algorithms and vice versa. Moreover, we\nshow that LDECC and existing algorithms rely on different faithfulness\nassumptions, leveraging this insight to weaken the assumptions for identifying\nthe set of possible ATE values.\n", "date": "2023-02-16", "categories": []}
{"id": "2404.04224", "title": "Active Causal Learning for Decoding Chemical Complexities with Targeted\n  Interventions", "abstract": "  Predicting and enhancing inherent properties based on molecular structures is\nparamount to design tasks in medicine, materials science, and environmental\nmanagement. Most of the current machine learning and deep learning approaches\nhave become standard for predictions, but they face challenges when applied\nacross different datasets due to reliance on correlations between molecular\nrepresentation and target properties. These approaches typically depend on\nlarge datasets to capture the diversity within the chemical space, facilitating\na more accurate approximation, interpolation, or extrapolation of the chemical\nbehavior of molecules. In our research, we introduce an active learning\napproach that discerns underlying cause-effect relationships through strategic\nsampling with the use of a graph loss function. This method identifies the\nsmallest subset of the dataset capable of encoding the most information\nrepresentative of a much larger chemical space. The identified causal relations\nare then leveraged to conduct systematic interventions, optimizing the design\ntask within a chemical space that the models have not encountered previously.\nWhile our implementation focused on the QM9 quantum-chemical dataset for a\nspecific design task-finding molecules with a large dipole moment-our active\ncausal learning approach, driven by intelligent sampling and interventions,\nholds potential for broader applications in molecular, materials design and\ndiscovery.\n", "date": "2024-04-05", "categories": []}
{"id": "2211.13715", "title": "Trust Your $\\nabla$: Gradient-based Intervention Targeting for Causal\n  Discovery", "abstract": "  Inferring causal structure from data is a challenging task of fundamental\nimportance in science. Observational data are often insufficient to identify a\nsystem's causal structure uniquely. While conducting interventions (i.e.,\nexperiments) can improve the identifiability, such samples are usually\nchallenging and expensive to obtain. Hence, experimental design approaches for\ncausal discovery aim to minimize the number of interventions by estimating the\nmost informative intervention target. In this work, we propose a novel\nGradient-based Intervention Targeting method, abbreviated GIT, that 'trusts'\nthe gradient estimator of a gradient-based causal discovery framework to\nprovide signals for the intervention acquisition function. We provide extensive\nexperiments in simulated and real-world datasets and demonstrate that GIT\nperforms on par with competitive baselines, surpassing them in the low-data\nregime.\n", "date": "2022-11-24", "categories": []}
{"id": "2404.01466", "title": "TS-CausalNN: Learning Temporal Causal Relations from Non-linear\n  Non-stationary Time Series Data", "abstract": "  The growing availability and importance of time series data across various\ndomains, including environmental science, epidemiology, and economics, has led\nto an increasing need for time-series causal discovery methods that can\nidentify the intricate relationships in the non-stationary, non-linear, and\noften noisy real world data. However, the majority of current time series\ncausal discovery methods assume stationarity and linear relations in data,\nmaking them infeasible for the task. Further, the recent deep learning-based\nmethods rely on the traditional causal structure learning approaches making\nthem computationally expensive. In this paper, we propose a Time-Series Causal\nNeural Network (TS-CausalNN) - a deep learning technique to discover\ncontemporaneous and lagged causal relations simultaneously. Our proposed\narchitecture comprises (i) convolutional blocks comprising parallel custom\ncausal layers, (ii) acyclicity constraint, and (iii) optimization techniques\nusing the augmented Lagrangian approach. In addition to the simple parallel\ndesign, an advantage of the proposed model is that it naturally handles the\nnon-stationarity and non-linearity of the data. Through experiments on multiple\nsynthetic and real world datasets, we demonstrate the empirical proficiency of\nour proposed approach as compared to several state-of-the-art methods. The\ninferred graphs for the real world dataset are in good agreement with the\ndomain understanding.\n", "date": "2024-04-01", "categories": []}
{"id": "2308.16859", "title": "Information Theoretically Optimal Sample Complexity of Learning\n  Dynamical Directed Acyclic Graphs", "abstract": "  In this article, the optimal sample complexity of learning the underlying\ninteractions or dependencies of a Linear Dynamical System (LDS) over a Directed\nAcyclic Graph (DAG) is studied. We call such a DAG underlying an LDS as\ndynamical DAG (DDAG). In particular, we consider a DDAG where the nodal\ndynamics are driven by unobserved exogenous noise sources that are wide-sense\nstationary (WSS) in time but are mutually uncorrelated, and have the same\n{power spectral density (PSD)}. Inspired by the static DAG setting, a metric\nand an algorithm based on the PSD matrix of the observed time series are\nproposed to reconstruct the DDAG. It is shown that the optimal sample\ncomplexity (or length of state trajectory) needed to learn the DDAG is\n$n=\\Theta(q\\log(p/q))$, where $p$ is the number of nodes and $q$ is the maximum\nnumber of parents per node. To prove the sample complexity upper bound, a\nconcentration bound for the PSD estimation is derived, under two different\nsampling strategies. A matching min-max lower bound using generalized Fano's\ninequality also is provided, thus showing the order optimality of the proposed\nalgorithm.\n", "date": "2023-08-31", "categories": []}
{"id": "2403.18994", "title": "Causal-StoNet: Causal Inference for High-Dimensional Complex Data", "abstract": "  With the advancement of data science, the collection of increasingly complex\ndatasets has become commonplace. In such datasets, the data dimension can be\nextremely high, and the underlying data generation process can be unknown and\nhighly nonlinear. As a result, the task of making causal inference with\nhigh-dimensional complex data has become a fundamental problem in many\ndisciplines, such as medicine, econometrics, and social science. However, the\nexisting methods for causal inference are frequently developed under the\nassumption that the data dimension is low or that the underlying data\ngeneration process is linear or approximately linear. To address these\nchallenges, this paper proposes a novel causal inference approach for dealing\nwith high-dimensional complex data. The proposed approach is based on deep\nlearning techniques, including sparse deep learning theory and stochastic\nneural networks, that have been developed in recent literature. By using these\ntechniques, the proposed approach can address both the high dimensionality and\nunknown data generation process in a coherent way. Furthermore, the proposed\napproach can also be used when missing values are present in the datasets.\nExtensive numerical studies indicate that the proposed approach outperforms\nexisting ones.\n", "date": "2024-03-27", "categories": []}
{"id": "2403.15500", "title": "Gene Regulatory Network Inference in the Presence of Dropouts: a Causal\n  View", "abstract": "  Gene regulatory network inference (GRNI) is a challenging problem,\nparticularly owing to the presence of zeros in single-cell RNA sequencing data:\nsome are biological zeros representing no gene expression, while some others\nare technical zeros arising from the sequencing procedure (aka dropouts), which\nmay bias GRNI by distorting the joint distribution of the measured gene\nexpressions. Existing approaches typically handle dropout error via imputation,\nwhich may introduce spurious relations as the true joint distribution is\ngenerally unidentifiable. To tackle this issue, we introduce a causal graphical\nmodel to characterize the dropout mechanism, namely, Causal Dropout Model. We\nprovide a simple yet effective theoretical result: interestingly, the\nconditional independence (CI) relations in the data with dropouts, after\ndeleting the samples with zero values (regardless if technical or not) for the\nconditioned variables, are asymptotically identical to the CI relations in the\noriginal data without dropouts. This particular test-wise deletion procedure,\nin which we perform CI tests on the samples without zeros for the conditioned\nvariables, can be seamlessly integrated with existing structure learning\napproaches including constraint-based and greedy score-based methods, thus\ngiving rise to a principled framework for GRNI in the presence of dropouts. We\nfurther show that the causal dropout model can be validated from data, and many\nexisting statistical models to handle dropouts fit into our model as specific\nparametric instances. Empirical evaluation on synthetic, curated, and\nreal-world experimental transcriptomic data comprehensively demonstrate the\nefficacy of our method.\n", "date": "2024-03-21", "categories": []}
{"id": "2403.16031", "title": "Learning Directed Acyclic Graphs from Partial Orderings", "abstract": "  Directed acyclic graphs (DAGs) are commonly used to model causal\nrelationships among random variables. In general, learning the DAG structure is\nboth computationally and statistically challenging. Moreover, without\nadditional information, the direction of edges may not be estimable from\nobservational data. In contrast, given a complete causal ordering of the\nvariables, the problem can be solved efficiently, even in high dimensions. In\nthis paper, we consider the intermediate problem of learning DAGs when a\npartial causal ordering of variables is available. We propose a general\nestimation framework for leveraging the partial ordering and present efficient\nestimation algorithms for low- and high-dimensional problems. The advantages of\nthe proposed framework are illustrated via numerical studies.\n", "date": "2024-03-24", "categories": []}
{"id": "2403.16523", "title": "Causal Discovery from Poisson Branching Structural Causal Model Using\n  High-Order Cumulant with Path Analysis", "abstract": "  Count data naturally arise in many fields, such as finance, neuroscience, and\nepidemiology, and discovering causal structure among count data is a crucial\ntask in various scientific and industrial scenarios. One of the most common\ncharacteristics of count data is the inherent branching structure described by\na binomial thinning operator and an independent Poisson distribution that\ncaptures both branching and noise. For instance, in a population count\nscenario, mortality and immigration contribute to the count, where survival\nfollows a Bernoulli distribution, and immigration follows a Poisson\ndistribution. However, causal discovery from such data is challenging due to\nthe non-identifiability issue: a single causal pair is Markov equivalent, i.e.,\n$X\\rightarrow Y$ and $Y\\rightarrow X$ are distributed equivalent. Fortunately,\nin this work, we found that the causal order from $X$ to its child $Y$ is\nidentifiable if $X$ is a root vertex and has at least two directed paths to\n$Y$, or the ancestor of $X$ with the most directed path to $X$ has a directed\npath to $Y$ without passing $X$. Specifically, we propose a Poisson Branching\nStructure Causal Model (PB-SCM) and perform a path analysis on PB-SCM using\nhigh-order cumulants. Theoretical results establish the connection between the\npath and cumulant and demonstrate that the path information can be obtained\nfrom the cumulant. With the path information, causal order is identifiable\nunder some graphical conditions. A practical algorithm for learning causal\nstructure under PB-SCM is proposed and the experiments demonstrate and verify\nthe effectiveness of the proposed method.\n", "date": "2024-03-25", "categories": []}
{"id": "2403.14843", "title": "Local Causal Discovery with Linear non-Gaussian Cyclic Models", "abstract": "  Local causal discovery is of great practical significance, as there are often\nsituations where the discovery of the global causal structure is unnecessary,\nand the interest lies solely on a single target variable. Most existing local\nmethods utilize conditional independence relations, providing only a partially\ndirected graph, and assume acyclicity for the ground-truth structure, even\nthough real-world scenarios often involve cycles like feedback mechanisms. In\nthis work, we present a general, unified local causal discovery method with\nlinear non-Gaussian models, whether they are cyclic or acyclic. We extend the\napplication of independent component analysis from the global context to\nindependent subspace analysis, enabling the exact identification of the\nequivalent local directed structures and causal strengths from the Markov\nblanket of the target variable. We also propose an alternative regression-based\nmethod in the particular acyclic scenarios. Our identifiability results are\nempirically validated using both synthetic and real-world datasets.\n", "date": "2024-03-21", "categories": []}
{"id": "2402.16068", "title": "ROS-Causal: A ROS-based Causal Analysis Framework for Human-Robot\n  Interaction Applications", "abstract": "  Deploying robots in human-shared spaces requires understanding interactions\namong nearby agents and objects. Modelling cause-and-effect relations through\ncausal inference aids in predicting human behaviours and anticipating robot\ninterventions. However, a critical challenge arises as existing causal\ndiscovery methods currently lack an implementation inside the ROS ecosystem,\nthe standard de facto in robotics, hindering effective utilisation in robotics.\nTo address this gap, this paper introduces ROS-Causal, a ROS-based framework\nfor onboard data collection and causal discovery in human-robot spatial\ninteractions. An ad-hoc simulator, integrated with ROS, illustrates the\napproach's effectiveness, showcasing the robot onboard generation of causal\nmodels during data collection. ROS-Causal is available on GitHub:\nhttps://github.com/lcastri/roscausal.git.\n", "date": "2024-02-25", "categories": []}
{"id": "2403.14327", "title": "Investigating the validity of structure learning algorithms in\n  identifying risk factors for intervention in patients with diabetes", "abstract": "  Diabetes, a pervasive and enduring health challenge, imposes significant\nglobal implications on health, financial healthcare systems, and societal\nwell-being. This study undertakes a comprehensive exploration of various\nstructural learning algorithms to discern causal pathways amongst potential\nrisk factors influencing diabetes progression. The methodology involves the\napplication of these algorithms to relevant diabetes data, followed by the\nconversion of their output graphs into Causal Bayesian Networks (CBNs),\nenabling predictive analysis and the evaluation of discrepancies in the effect\nof hypothetical interventions within our context-specific case study.\n  This study highlights the substantial impact of algorithm selection on\nintervention outcomes. To consolidate insights from diverse algorithms, we\nemploy a model-averaging technique that helps us obtain a unique causal model\nfor diabetes derived from a varied set of structural learning algorithms. We\nalso investigate how each of those individual graphs, as well as the average\ngraph, compare to the structures elicited by a domain expert who categorised\ngraph edges into high confidence, moderate, and low confidence types, leading\ninto three individual graphs corresponding to the three levels of confidence.\n  The resulting causal model and data are made available online, and serve as a\nvaluable resource and a guide for informed decision-making by healthcare\npractitioners, offering a comprehensive understanding of the interactions\nbetween relevant risk factors and the effect of hypothetical interventions.\nTherefore, this research not only contributes to the academic discussion on\ndiabetes, but also provides practical guidance for healthcare professionals in\ndeveloping efficient intervention and risk management strategies.\n", "date": "2024-03-21", "categories": []}
{"id": "2311.00118", "title": "Extracting the Multiscale Causal Backbone of Brain Dynamics", "abstract": "  The bulk of the research effort on brain connectivity revolves around\nstatistical associations among brain regions, which do not directly relate to\nthe causal mechanisms governing brain dynamics. Here we propose the multiscale\ncausal backbone (MCB) of brain dynamics, shared by a set of individuals across\nmultiple temporal scales, and devise a principled methodology to extract it.\n  Our approach leverages recent advances in multiscale causal structure\nlearning and optimizes the trade-off between the model fit and its complexity.\nEmpirical assessment on synthetic data shows the superiority of our methodology\nover a baseline based on canonical functional connectivity networks. When\napplied to resting-state fMRI data, we find sparse MCBs for both the left and\nright brain hemispheres. Thanks to its multiscale nature, our approach shows\nthat at low-frequency bands, causal dynamics are driven by brain regions\nassociated with high-level cognitive functions; at higher frequencies instead,\nnodes related to sensory processing play a crucial role. Finally, our analysis\nof individual multiscale causal structures confirms the existence of a causal\nfingerprint of brain connectivity, thus supporting the existing extensive\nresearch in brain connectivity fingerprinting from a causal perspective.\n", "date": "2023-10-31", "categories": []}
{"id": "2310.17405", "title": "Causal Modeling with Stationary Diffusions", "abstract": "  We develop a novel approach towards causal inference. Rather than structural\nequations over a causal graph, we learn stochastic differential equations\n(SDEs) whose stationary densities model a system's behavior under\ninterventions. These stationary diffusion models do not require the formalism\nof causal graphs, let alone the common assumption of acyclicity. We show that\nin several cases, they generalize to unseen interventions on their variables,\noften better than classical approaches. Our inference method is based on a new\ntheoretical result that expresses a stationarity condition on the diffusion's\ngenerator in a reproducing kernel Hilbert space. The resulting kernel deviation\nfrom stationarity (KDS) is an objective function of independent interest.\n", "date": "2023-10-26", "categories": []}
{"id": "2307.09552", "title": "Self-Compatibility: Evaluating Causal Discovery without Ground Truth", "abstract": "  As causal ground truth is incredibly rare, causal discovery algorithms are\ncommonly only evaluated on simulated data. This is concerning, given that\nsimulations reflect preconceptions about generating processes regarding noise\ndistributions, model classes, and more. In this work, we propose a novel method\nfor falsifying the output of a causal discovery algorithm in the absence of\nground truth. Our key insight is that while statistical learning seeks\nstability across subsets of data points, causal learning should seek stability\nacross subsets of variables. Motivated by this insight, our method relies on a\nnotion of compatibility between causal graphs learned on different subsets of\nvariables. We prove that detecting incompatibilities can falsify wrongly\ninferred causal relations due to violation of assumptions or errors from finite\nsample effects. Although passing such compatibility tests is only a necessary\ncriterion for good performance, we argue that it provides strong evidence for\nthe causal models whenever compatibility entails strong implications for the\njoint distribution. We also demonstrate experimentally that detection of\nincompatibilities can aid in causal model selection.\n", "date": "2023-07-18", "categories": []}
{"id": "2403.05407", "title": "Algorithmic Identification of Essential Exogenous Nodes for Causal\n  Sufficiency in Brain Networks", "abstract": "  In the investigation of any causal mechanisms, such as the brain's causal\nnetworks, the assumption of causal sufficiency plays a critical role. Notably,\nneglecting this assumption can result in significant errors, a fact that is\noften disregarded in the causal analysis of brain networks. In this study, we\npropose an algorithmic identification approach for determining essential\nexogenous nodes that satisfy the critical need for causal sufficiency to adhere\nto it in such inquiries. Our approach consists of three main steps: First, by\ncapturing the essence of the Peter-Clark (PC) algorithm, we conduct\nindependence tests for pairs of regions within a network, as well as for the\nsame pairs conditioned on nodes from other networks. Next, we distinguish\ncandidate confounders by analyzing the differences between the conditional and\nunconditional results, using the Kolmogorov-Smirnov test. Subsequently, we\nutilize Non-Factorized identifiable Variational Autoencoders (NF-iVAE) along\nwith the Correlation Coefficient index (CCI) metric to identify the confounding\nvariables within these candidate nodes. Applying our method to the Human\nConnectome Projects (HCP) movie-watching task data, we demonstrate that while\ninteractions exist between dorsal and ventral regions, only dorsal regions\nserve as confounders for the visual networks, and vice versa. These findings\nalign consistently with those resulting from the neuroscientific perspective.\nFinally, we show the reliability of our results by testing 30 independent runs\nfor NF-iVAE initialization.\n", "date": "2024-03-08", "categories": []}
{"id": "2403.09300", "title": "Recursive Causal Discovery", "abstract": "  Causal discovery, i.e., learning the causal graph from data, is often the\nfirst step toward the identification and estimation of causal effects, a key\nrequirement in numerous scientific domains. Causal discovery is hampered by two\nmain challenges: limited data results in errors in statistical testing and the\ncomputational complexity of the learning task is daunting. This paper builds\nupon and extends four of our prior publications (Mokhtarian et al., 2021;\nAkbari et al., 2021; Mokhtarian et al., 2022, 2023a). These works introduced\nthe concept of removable variables, which are the only variables that can be\nremoved recursively for the purpose of causal discovery. Presence and\nidentification of removable variables allow recursive approaches for causal\ndiscovery, a promising solution that helps to address the aforementioned\nchallenges by reducing the problem size successively. This reduction not only\nminimizes conditioning sets in each conditional independence (CI) test, leading\nto fewer errors but also significantly decreases the number of required CI\ntests. The worst-case performances of these methods nearly match the lower\nbound. In this paper, we present a unified framework for the proposed\nalgorithms, refined with additional details and enhancements for a coherent\npresentation. A comprehensive literature review is also included, comparing the\ncomputational complexity of our methods with existing approaches, showcasing\ntheir state-of-the-art efficiency. Another contribution of this paper is the\nrelease of RCD, a Python package that efficiently implements these algorithms.\nThis package is designed for practitioners and researchers interested in\napplying these methods in practical scenarios. The package is available at\ngithub.com/ban-epfl/rcd, with comprehensive documentation provided at\nrcdpackage.com.\n", "date": "2024-03-14", "categories": []}
{"id": "2303.15027", "title": "A Survey on Causal Discovery Methods for I.I.D. and Time Series Data", "abstract": "  The ability to understand causality from data is one of the major milestones\nof human-level intelligence. Causal Discovery (CD) algorithms can identify the\ncause-effect relationships among the variables of a system from related\nobservational data with certain assumptions. Over the years, several methods\nhave been developed primarily based on the statistical properties of data to\nuncover the underlying causal mechanism. In this study, we present an extensive\ndiscussion on the methods designed to perform causal discovery from both\nindependent and identically distributed (I.I.D.) data and time series data. For\nthis purpose, we first introduce the common terminologies used in causal\ndiscovery literature and then provide a comprehensive discussion of the\nalgorithms designed to identify causal relations in different settings. We\nfurther discuss some of the benchmark datasets available for evaluating the\nalgorithmic performance, off-the-shelf tools or software packages to perform\ncausal discovery readily, and the common metrics used to evaluate these\nmethods. We also evaluate some widely used causal discovery algorithms on\nmultiple benchmark datasets and compare their performances. Finally, we\nconclude by discussing the research challenges and the applications of causal\ndiscovery algorithms in multiple areas of interest.\n", "date": "2023-03-27", "categories": []}
{"id": "2310.02895", "title": "CoLiDE: Concomitant Linear DAG Estimation", "abstract": "  We deal with the combinatorial problem of learning directed acyclic graph\n(DAG) structure from observational data adhering to a linear structural\nequation model (SEM). Leveraging advances in differentiable, nonconvex\ncharacterizations of acyclicity, recent efforts have advocated a continuous\nconstrained optimization paradigm to efficiently explore the space of DAGs.\nMost existing methods employ lasso-type score functions to guide this search,\nwhich (i) require expensive penalty parameter retuning when the\n$\\textit{unknown}$ SEM noise variances change across problem instances; and\n(ii) implicitly rely on limiting homoscedasticity assumptions. In this work, we\npropose a new convex score function for sparsity-aware learning of linear DAGs,\nwhich incorporates concomitant estimation of scale and thus effectively\ndecouples the sparsity parameter from the exogenous noise levels.\nRegularization via a smooth, nonconvex acyclicity penalty term yields CoLiDE\n($\\textbf{Co}$ncomitant $\\textbf{Li}$near $\\textbf{D}$AG\n$\\textbf{E}$stimation), a regression-based criterion amenable to efficient\ngradient computation and closed-form estimation of noise variances in\nheteroscedastic scenarios. Our algorithm outperforms state-of-the-art methods\nwithout incurring added complexity, especially when the DAGs are larger and the\nnoise level profile is heterogeneous. We also find CoLiDE exhibits enhanced\nstability manifested via reduced standard deviations in several domain-specific\nmetrics, underscoring the robustness of our novel linear DAG estimator.\n", "date": "2023-10-04", "categories": []}
{"id": "2306.14114", "title": "TNPAR: Topological Neural Poisson Auto-Regressive Model for Learning\n  Granger Causal Structure from Event Sequences", "abstract": "  Learning Granger causality from event sequences is a challenging but\nessential task across various applications. Most existing methods rely on the\nassumption that event sequences are independent and identically distributed\n(i.i.d.). However, this i.i.d. assumption is often violated due to the inherent\ndependencies among the event sequences. Fortunately, in practice, we find these\ndependencies can be modeled by a topological network, suggesting a potential\nsolution to the non-i.i.d. problem by introducing the prior topological network\ninto Granger causal discovery. This observation prompts us to tackle two\nensuing challenges: 1) how to model the event sequences while incorporating\nboth the prior topological network and the latent Granger causal structure, and\n2) how to learn the Granger causal structure. To this end, we devise a unified\ntopological neural Poisson auto-regressive model with two processes. In the\ngeneration process, we employ a variant of the neural Poisson process to model\nthe event sequences, considering influences from both the topological network\nand the Granger causal structure. In the inference process, we formulate an\namortized inference algorithm to infer the latent Granger causal structure. We\nencapsulate these two processes within a unified likelihood function, providing\nan end-to-end framework for this task. Experiments on simulated and real-world\ndata demonstrate the effectiveness of our approach.\n", "date": "2023-06-25", "categories": []}
{"id": "2302.05451", "title": "Brain Effective Connectome based on fMRI and DTI Data: Bayesian Causal\n  Learning and Assessment", "abstract": "  Neuroscientific studies aim to find an accurate and reliable brain Effective\nConnectome (EC). Although current EC discovery methods have contributed to our\nunderstanding of brain organization, their performances are severely\nconstrained by the short sample size and poor temporal resolution of fMRI data,\nand high dimensionality of the brain connectome. By leveraging the DTI data as\nprior knowledge, we introduce two Bayesian causal discovery frameworks -- the\nBayesian GOLEM (BGOLEM) and Bayesian FGES (BFGES) methods -- that offer\nsignificantly more accurate and reliable ECs and address the shortcomings of\nthe existing causal discovery methods in discovering ECs based on only fMRI\ndata. Through a series of simulation studies on synthetic and hybrid (DTI of\nthe Human Connectome Project (HCP) subjects and synthetic fMRI) data, we\ndemonstrate the effectiveness of the proposed methods in discovering EC. To\nnumerically assess the improvement in the accuracy of ECs with our method on\nempirical data, we first introduce the Pseudo False Discovery Rate (PFDR) as a\nnew computational accuracy metric for causal discovery in the brain. We show\nthat our Bayesian methods achieve higher accuracy than traditional methods on\nHCP data. Additionally, we measure the reliability of discovered ECs using the\nRogers-Tanimoto index for test-retest data and show that our Bayesian methods\nprovide significantly more reproducible ECs than traditional methods. Overall,\nour study's numerical and graphical results highlight the potential for these\nframeworks to advance our understanding of brain function and organization\nsignificantly.\n", "date": "2023-02-10", "categories": []}
{"id": "2312.06091", "title": "Learning Unknown Intervention Targets in Structural Causal Models from\n  Heterogeneous Data", "abstract": "  We study the problem of identifying the unknown intervention targets in\nstructural causal models where we have access to heterogeneous data collected\nfrom multiple environments. The unknown intervention targets are the set of\nendogenous variables whose corresponding exogenous noises change across the\nenvironments. We propose a two-phase approach which in the first phase recovers\nthe exogenous noises corresponding to unknown intervention targets whose\ndistributions have changed across environments. In the second phase, the\nrecovered noises are matched with the corresponding endogenous variables. For\nthe recovery phase, we provide sufficient conditions for learning these\nexogenous noises up to some component-wise invertible transformation. For the\nmatching phase, under the causal sufficiency assumption, we show that the\nproposed method uniquely identifies the intervention targets. In the presence\nof latent confounders, the intervention targets among the observed variables\ncannot be determined uniquely. We provide a candidate intervention target set\nwhich is a superset of the true intervention targets. Our approach improves\nupon the state of the art as the returned candidate set is always a subset of\nthe target set returned by previous work. Moreover, we do not require\nrestrictive assumptions such as linearity of the causal model or performing\ninvariance tests to learn whether a distribution is changing across\nenvironments which could be highly sample inefficient. Our experimental results\nshow the effectiveness of our proposed algorithm in practice.\n", "date": "2023-12-11", "categories": []}
{"id": "2403.05759", "title": "Membership Testing in Markov Equivalence Classes via Independence Query\n  Oracles", "abstract": "  Understanding causal relationships between variables is a fundamental problem\nwith broad impact in numerous scientific fields. While extensive research has\nbeen dedicated to learning causal graphs from data, its complementary concept\nof testing causal relationships has remained largely unexplored. While learning\ninvolves the task of recovering the Markov equivalence class (MEC) of the\nunderlying causal graph from observational data, the testing counterpart\naddresses the following critical question: Given a specific MEC and\nobservational data from some causal graph, can we determine if the\ndata-generating causal graph belongs to the given MEC?\n  We explore constraint-based testing methods by establishing bounds on the\nrequired number of conditional independence tests. Our bounds are in terms of\nthe size of the maximum undirected clique ($s$) of the given MEC. In the worst\ncase, we show a lower bound of $\\exp(\\Omega(s))$ independence tests. We then\ngive an algorithm that resolves the task with $\\exp(O(s))$ tests, matching our\nlower bound. Compared to the learning problem, where algorithms often use a\nnumber of independence tests that is exponential in the maximum in-degree, this\nshows that testing is relatively easier. In particular, it requires\nexponentially less independence tests in graphs featuring high in-degrees and\nsmall clique sizes. Additionally, using the DAG associahedron, we provide a\ngeometric interpretation of testing versus learning and discuss how our testing\nresult can aid learning.\n", "date": "2024-03-09", "categories": []}
{"id": "2403.06499", "title": "Detection of Unobserved Common Causes based on NML Code in Discrete,\n  Mixed, and Continuous Variables", "abstract": "  Causal discovery in the presence of unobserved common causes from\nobservational data only is a crucial but challenging problem. We categorize all\npossible causal relationships between two random variables into the following\nfour categories and aim to identify one from observed data: two cases in which\neither of the direct causality exists, a case that variables are independent,\nand a case that variables are confounded by latent confounders. Although\nexisting methods have been proposed to tackle this problem, they require\nunobserved variables to satisfy assumptions on the form of their equation\nmodels. In our previous study (Kobayashi et al., 2022), the first causal\ndiscovery method without such assumptions is proposed for discrete data and\nnamed CLOUD. Using Normalized Maximum Likelihood (NML) Code, CLOUD selects a\nmodel that yields the minimum codelength of the observed data from a set of\nmodel candidates. This paper extends CLOUD to apply for various data types\nacross discrete, mixed, and continuous. We not only performed theoretical\nanalysis to show the consistency of CLOUD in terms of the model selection, but\nalso demonstrated that CLOUD is more effective than existing methods in\ninferring causal relationships by extensive experiments on both synthetic and\nreal-world data.\n", "date": "2024-03-11", "categories": []}
{"id": "2403.04793", "title": "A Data-Driven Two-Phase Multi-Split Causal Ensemble Model for Time\n  Series", "abstract": "  Causal inference is a fundamental research topic for discovering the\ncause-effect relationships in many disciplines. However, not all algorithms are\nequally well-suited for a given dataset. For instance, some approaches may only\nbe able to identify linear relationships, while others are applicable for\nnon-linearities. Algorithms further vary in their sensitivity to noise and\ntheir ability to infer causal information from coupled vs. non-coupled time\nseries. Therefore, different algorithms often generate different causal\nrelationships for the same input. To achieve a more robust causal inference\nresult, this publication proposes a novel data-driven two-phase multi-split\ncausal ensemble model to combine the strengths of different causality base\nalgorithms. In comparison to existing approaches, the proposed ensemble method\nreduces the influence of noise through a data partitioning scheme in the first\nphase. To achieve this, the data are initially divided into several partitions\nand the base algorithms are applied to each partition. Subsequently, Gaussian\nmixture models are used to identify the causal relationships derived from the\ndifferent partitions that are likely to be valid. In the second phase, the\nidentified relationships from each base algorithm are then merged based on\nthree combination rules. The proposed ensemble approach is evaluated using\nmultiple metrics, among them a newly developed evaluation index for causal\nensemble approaches. We perform experiments using three synthetic datasets with\ndifferent volumes and complexity, which are specifically designed to test\ncausality detection methods under different circumstances while knowing the\nground truth causal relationships. In these experiments, our causality ensemble\noutperforms each of its base algorithms. In practical applications, the use of\nthe proposed method could hence lead to more robust and reliable causality\nresults.\n", "date": "2024-03-04", "categories": []}
{"id": "2212.01551", "title": "Quantify the Causes of Causal Emergence: Critical Conditions of\n  Uncertainty and Asymmetry in Causal Structure", "abstract": "  Beneficial to advanced computing devices, models with massive parameters are\nincreasingly employed to extract more information to enhance the precision in\ndescribing and predicting the patterns of objective systems. This phenomenon is\nparticularly pronounced in research domains associated with deep learning.\nHowever, investigations of causal relationships based on statistical and\ninformational theories have posed an interesting and valuable challenge to\nlarge-scale models in the recent decade. Macroscopic models with fewer\nparameters can outperform their microscopic counterparts with more parameters\nin effectively representing the system. This valuable situation is called\n\"Causal Emergence.\" This paper introduces a quantification framework, according\nto the Effective Information and Transition Probability Matrix, for assessing\nnumerical conditions of Causal Emergence as theoretical constraints of its\noccurrence. Specifically, our results quantitatively prove the cause of Causal\nEmergence. By a particular coarse-graining strategy, optimizing uncertainty and\nasymmetry within the model's causal structure is significantly more influential\nthan losing maximum information due to variations in model scales. Moreover, by\ndelving into the potential exhibited by Partial Information Decomposition and\nDeep Learning networks in the study of Causal Emergence, we discuss potential\napplication scenarios where our quantification framework could play a role in\nfuture investigations of Causal Emergence.\n", "date": "2022-12-03", "categories": []}
{"id": "2302.00064", "title": "Evaluating Temporal Observation-Based Causal Discovery Techniques\n  Applied to Road Driver Behaviour", "abstract": "  Autonomous robots are required to reason about the behaviour of dynamic\nagents in their environment. The creation of models to describe these\nrelationships is typically accomplished through the application of causal\ndiscovery techniques. However, as it stands observational causal discovery\ntechniques struggle to adequately cope with conditions such as causal sparsity\nand non-stationarity typically seen during online usage in autonomous agent\ndomains. Meanwhile, interventional techniques are not always feasible due to\ndomain restrictions. In order to better explore the issues facing observational\ntechniques and promote further discussion of these topics we carry out a\nbenchmark across 10 contemporary observational temporal causal discovery\nmethods in the domain of autonomous driving. By evaluating these methods upon\ncausal scenes drawn from real world datasets in addition to those generated\nsynthetically we highlight where improvements need to be made in order to\nfacilitate the application of causal discovery techniques to the aforementioned\nuse-cases. Finally, we discuss potential directions for future work that could\nhelp better tackle the difficulties currently experienced by state of the art\ntechniques.\n", "date": "2023-01-31", "categories": []}
{"id": "2306.03354", "title": "Simulation-Based Counterfactual Causal Discovery on Real World Driver\n  Behaviour", "abstract": "  Being able to reason about how one's behaviour can affect the behaviour of\nothers is a core skill required of intelligent driving agents. Despite this,\nthe state of the art struggles to meet the need of agents to discover causal\nlinks between themselves and others. Observational approaches struggle because\nof the non-stationarity of causal links in dynamic environments, and the\nsparsity of causal interactions while requiring the approaches to work in an\nonline fashion. Meanwhile interventional approaches are impractical as a\nvehicle cannot experiment with its actions on a public road. To counter the\nissue of non-stationarity we reformulate the problem in terms of extracted\nevents, while the previously mentioned restriction upon interventions can be\novercome with the use of counterfactual simulation. We present three variants\nof the proposed counterfactual causal discovery method and evaluate these\nagainst state of the art observational temporal causal discovery methods across\n3396 causal scenes extracted from a real world driving dataset. We find that\nthe proposed method significantly outperforms the state of the art on the\nproposed task quantitatively and can offer additional insights by comparing the\noutcome of an alternate series of decisions in a way that observational and\ninterventional approaches cannot.\n", "date": "2023-06-06", "categories": []}
{"id": "2403.03772", "title": "AcceleratedLiNGAM: Learning Causal DAGs at the speed of GPUs", "abstract": "  Existing causal discovery methods based on combinatorial optimization or\nsearch are slow, prohibiting their application on large-scale datasets. In\nresponse, more recent methods attempt to address this limitation by formulating\ncausal discovery as structure learning with continuous optimization but such\napproaches thus far provide no statistical guarantees. In this paper, we show\nthat by efficiently parallelizing existing causal discovery methods, we can in\nfact scale them to thousands of dimensions, making them practical for\nsubstantially larger-scale problems. In particular, we parallelize the LiNGAM\nmethod, which is quadratic in the number of variables, obtaining up to a\n32-fold speed-up on benchmark datasets when compared with existing sequential\nimplementations. Specifically, we focus on the causal ordering subprocedure in\nDirectLiNGAM and implement GPU kernels to accelerate it. This allows us to\napply DirectLiNGAM to causal inference on large-scale gene expression data with\ngenetic interventions yielding competitive results compared with specialized\ncontinuous optimization methods, and Var-LiNGAM for causal discovery on U.S.\nstock data.\n", "date": "2024-03-06", "categories": []}
{"id": "2211.17029", "title": "Directed Acyclic Graph Structure Learning from Dynamic Graphs", "abstract": "  Estimating the structure of directed acyclic graphs (DAGs) of features\n(variables) plays a vital role in revealing the latent data generation process\nand providing causal insights in various applications. Although there have been\nmany studies on structure learning with various types of data, the structure\nlearning on the dynamic graph has not been explored yet, and thus we study the\nlearning problem of node feature generation mechanism on such ubiquitous\ndynamic graph data. In a dynamic graph, we propose to simultaneously estimate\ncontemporaneous relationships and time-lagged interaction relationships between\nthe node features. These two kinds of relationships form a DAG, which could\neffectively characterize the feature generation process in a concise way. To\nlearn such a DAG, we cast the learning problem as a continuous score-based\noptimization problem, which consists of a differentiable score function to\nmeasure the validity of the learned DAGs and a smooth acyclicity constraint to\nensure the acyclicity of the learned DAGs. These two components are translated\ninto an unconstraint augmented Lagrangian objective which could be minimized by\nmature continuous optimization techniques. The resulting algorithm, named\nGraphNOTEARS, outperforms baselines on simulated data across a wide range of\nsettings that may encounter in real-world applications. We also apply the\nproposed approach on two dynamic graphs constructed from the real-world Yelp\ndataset, demonstrating our method could learn the connections between node\nfeatures, which conforms with the domain knowledge.\n", "date": "2022-11-30", "categories": []}
{"id": "2402.03726", "title": "Learning Granger Causality from Instance-wise Self-attentive Hawkes\n  Processes", "abstract": "  We address the problem of learning Granger causality from asynchronous,\ninterdependent, multi-type event sequences. In particular, we are interested in\ndiscovering instance-level causal structures in an unsupervised manner.\nInstance-level causality identifies causal relationships among individual\nevents, providing more fine-grained information for decision-making. Existing\nwork in the literature either requires strong assumptions, such as linearity in\nthe intensity function, or heuristically defined model parameters that do not\nnecessarily meet the requirements of Granger causality. We propose\nInstance-wise Self-Attentive Hawkes Processes (ISAHP), a novel deep learning\nframework that can directly infer the Granger causality at the event instance\nlevel. ISAHP is the first neural point process model that meets the\nrequirements of Granger causality. It leverages the self-attention mechanism of\nthe transformer to align with the principles of Granger causality. We\nempirically demonstrate that ISAHP is capable of discovering complex\ninstance-level causal structures that cannot be handled by classical models. We\nalso show that ISAHP achieves state-of-the-art performance in proxy tasks\ninvolving type-level causal discovery and instance-level event type prediction.\n", "date": "2024-02-06", "categories": []}
{"id": "2402.10240", "title": "A Dynamical View of the Question of Why", "abstract": "  We address causal reasoning in multivariate time series data generated by\nstochastic processes. Existing approaches are largely restricted to static\nsettings, ignoring the continuity and emission of variations across time. In\ncontrast, we propose a learning paradigm that directly establishes causation\nbetween events in the course of time. We present two key lemmas to compute\ncausal contributions and frame them as reinforcement learning problems. Our\napproach offers formal and computational tools for uncovering and quantifying\ncausal relationships in diffusion processes, subsuming various important\nsettings such as discrete-time Markov decision processes. Finally, in fairly\nintricate experiments and through sheer learning, our framework reveals and\nquantifies causal links, which otherwise seem inexplicable.\n", "date": "2024-02-14", "categories": []}
{"id": "2402.13241", "title": "Federated Causal Discovery from Heterogeneous Data", "abstract": "  Conventional causal discovery methods rely on centralized data, which is\ninconsistent with the decentralized nature of data in many real-world\nsituations. This discrepancy has motivated the development of federated causal\ndiscovery (FCD) approaches. However, existing FCD methods may be limited by\ntheir potentially restrictive assumptions of identifiable functional causal\nmodels or homogeneous data distributions, narrowing their applicability in\ndiverse scenarios. In this paper, we propose a novel FCD method attempting to\naccommodate arbitrary causal models and heterogeneous data. We first utilize a\nsurrogate variable corresponding to the client index to account for the data\nheterogeneity across different clients. We then develop a federated conditional\nindependence test (FCIT) for causal skeleton discovery and establish a\nfederated independent change principle (FICP) to determine causal directions.\nThese approaches involve constructing summary statistics as a proxy of the raw\ndata to protect data privacy. Owing to the nonparametric properties, FCIT and\nFICP make no assumption about particular functional forms, thereby facilitating\nthe handling of arbitrary causal models. We conduct extensive experiments on\nsynthetic and real datasets to show the efficacy of our method. The code is\navailable at https://github.com/lokali/FedCDH.git.\n", "date": "2024-02-20", "categories": []}
{"id": "2402.15625", "title": "Learning Cyclic Causal Models from Incomplete Data", "abstract": "  Causal learning is a fundamental problem in statistics and science, offering\ninsights into predicting the effects of unseen treatments on a system. Despite\nrecent advances in this topic, most existing causal discovery algorithms\noperate under two key assumptions: (i) the underlying graph is acyclic, and\n(ii) the available data is complete. These assumptions can be problematic as\nmany real-world systems contain feedback loops (e.g., biological systems), and\npractical scenarios frequently involve missing data. In this work, we propose a\nnovel framework, named MissNODAGS, for learning cyclic causal graphs from\npartially missing data. Under the additive noise model, MissNODAGS learns the\ncausal graph by alternating between imputing the missing data and maximizing\nthe expected log-likelihood of the visible part of the data in each training\nstep, following the principles of the expectation-maximization (EM) framework.\nThrough synthetic experiments and real-world single-cell perturbation data, we\ndemonstrate improved performance when compared to using state-of-the-art\nimputation techniques followed by causal learning on partially missing\ninterventional data.\n", "date": "2024-02-23", "categories": []}
{"id": "2303.05279", "title": "Can large language models build causal graphs?", "abstract": "  Building causal graphs can be a laborious process. To ensure all relevant\ncausal pathways have been captured, researchers often have to discuss with\nclinicians and experts while also reviewing extensive relevant medical\nliterature. By encoding common and medical knowledge, large language models\n(LLMs) represent an opportunity to ease this process by automatically scoring\nedges (i.e., connections between two variables) in potential graphs. LLMs\nhowever have been shown to be brittle to the choice of probing words, context,\nand prompts that the user employs. In this work, we evaluate if LLMs can be a\nuseful tool in complementing causal graph development.\n", "date": "2023-03-07", "categories": []}
{"id": "2402.14481", "title": "Towards Automated Causal Discovery: a case study on 5G telecommunication\n  data", "abstract": "  We introduce the concept of Automated Causal Discovery (AutoCD), defined as\nany system that aims to fully automate the application of causal discovery and\ncausal reasoning methods. AutoCD's goal is to deliver all causal information\nthat an expert human analyst would and answer a user's causal queries. We\ndescribe the architecture of such a platform, and illustrate its performance on\nsynthetic data sets. As a case study, we apply it on temporal telecommunication\ndata. The system is general and can be applied to a plethora of causal\ndiscovery problems.\n", "date": "2024-02-22", "categories": []}
{"id": "2305.19215", "title": "dotears: Scalable, consistent DAG estimation using observational and\n  interventional data", "abstract": "  New biological assays like Perturb-seq link highly parallel CRISPR\ninterventions to a high-dimensional transcriptomic readout, providing insight\ninto gene regulatory networks. Causal gene regulatory networks can be\nrepresented by directed acyclic graph (DAGs), but learning DAGs from\nobservational data is complicated by lack of identifiability and a\ncombinatorial solution space. Score-based structure learning improves practical\nscalability of inferring DAGs. Previous score-based methods are sensitive to\nerror variance structure; on the other hand, estimation of error variance is\ndifficult without prior knowledge of structure. Accordingly, we present\n$\\texttt{dotears}$ [doo-tairs], a continuous optimization framework which\nleverages observational and interventional data to infer a single causal\nstructure, assuming a linear Structural Equation Model (SEM).\n$\\texttt{dotears}$ exploits structural consequences of hard interventions to\ngive a marginal estimate of exogenous error structure, bypassing the circular\nestimation problem. We show that $\\texttt{dotears}$ is a provably consistent\nestimator of the true DAG under mild assumptions. $\\texttt{dotears}$\noutperforms other methods in varied simulations, and in real data infers edges\nthat validate with higher precision and recall than state-of-the-art methods\nthrough differential expression tests and high-confidence protein-protein\ninteractions.\n", "date": "2023-05-30", "categories": []}
{"id": "2211.14221", "title": "Learning Large Causal Structures from Inverse Covariance Matrix via\n  Sparse Matrix Decomposition", "abstract": "  Learning causal structures from observational data is a fundamental problem\nfacing important computational challenges when the number of variables is\nlarge. In the context of linear structural equation models (SEMs), this paper\nfocuses on learning causal structures from the inverse covariance matrix. The\nproposed method, called ICID for Independence-preserving Decomposition from\nInverse Covariance matrix, is based on continuous optimization of a matrix\ndecomposition model that preserves the nonzero patterns of the inverse\ncovariance matrix. Through theoretical and empirical evidences, we show that\nICID efficiently identifies the sought directed acyclic graph (DAG) assuming\nthe knowledge of noise variances. Moreover, ICID is shown empirically to be\nrobust under bounded misspecification of noise variances in the case where the\nnoise variances are non-equal. The proposed method enjoys a low complexity, as\nreflected by its time efficiency in the experiments, and also enables a novel\nregularization scheme that yields highly accurate solutions on the Simulated\nfMRI data (Smith et al., 2011) in comparison with state-of-the-art algorithms.\n", "date": "2022-11-25", "categories": []}
{"id": "2310.15627", "title": "Contextual Directed Acyclic Graphs", "abstract": "  Estimating the structure of directed acyclic graphs (DAGs) from observational\ndata remains a significant challenge in machine learning. Most research in this\narea concentrates on learning a single DAG for the entire population. This\npaper considers an alternative setting where the graph structure varies across\nindividuals based on available \"contextual\" features. We tackle this contextual\nDAG problem via a neural network that maps the contextual features to a DAG,\nrepresented as a weighted adjacency matrix. The neural network is equipped with\na novel projection layer that ensures the output matrices are sparse and\nsatisfy a recently developed characterization of acyclicity. We devise a\nscalable computational framework for learning contextual DAGs and provide a\nconvergence guarantee and an analytical gradient for backpropagating through\nthe projection layer. Our experiments suggest that the new approach can recover\nthe true context-specific graph where existing approaches fail.\n", "date": "2023-10-24", "categories": []}
{"id": "2310.18212", "title": "Robustness of Algorithms for Causal Structure Learning to Hyperparameter\n  Choice", "abstract": "  Hyperparameters play a critical role in machine learning. Hyperparameter\ntuning can make the difference between state-of-the-art and poor prediction\nperformance for any algorithm, but it is particularly challenging for structure\nlearning due to its unsupervised nature. As a result, hyperparameter tuning is\noften neglected in favour of using the default values provided by a particular\nimplementation of an algorithm. While there have been numerous studies on\nperformance evaluation of causal discovery algorithms, how hyperparameters\naffect individual algorithms, as well as the choice of the best algorithm for a\nspecific problem, has not been studied in depth before. This work addresses\nthis gap by investigating the influence of hyperparameters on causal structure\nlearning tasks. Specifically, we perform an empirical evaluation of\nhyperparameter selection for some seminal learning algorithms on datasets of\nvarying levels of complexity. We find that, while the choice of algorithm\nremains crucial to obtaining state-of-the-art performance, hyperparameter\nselection in ensemble settings strongly influences the choice of algorithm, in\nthat a poor choice of hyperparameters can lead to analysts using algorithms\nwhich do not give state-of-the-art performance for their data.\n", "date": "2023-10-27", "categories": []}
{"id": "2308.07480", "title": "Order-based Structure Learning with Normalizing Flows", "abstract": "  Estimating the causal structure of observational data is a challenging\ncombinatorial search problem that scales super-exponentially with graph size.\nExisting methods use continuous relaxations to make this problem\ncomputationally tractable but often restrict the data-generating process to\nadditive noise models (ANMs) through explicit or implicit assumptions. We\npresent Order-based Structure Learning with Normalizing Flows (OSLow), a\nframework that relaxes these assumptions using autoregressive normalizing\nflows. We leverage the insight that searching over topological orderings is a\nnatural way to enforce acyclicity in structure discovery and propose a novel,\ndifferentiable permutation learning method to find such orderings. Through\nextensive experiments on synthetic and real-world data, we demonstrate that\nOSLow outperforms prior baselines and improves performance on the observational\nSachs and SynTReN datasets as measured by structural hamming distance and\nstructural intervention distance, highlighting the importance of relaxing the\nANM assumption made by existing methods.\n", "date": "2023-08-14", "categories": []}
{"id": "2402.00623", "title": "Bayesian Causal Inference with Gaussian Process Networks", "abstract": "  Causal discovery and inference from observational data is an essential\nproblem in statistics posing both modeling and computational challenges. These\nare typically addressed by imposing strict assumptions on the joint\ndistribution such as linearity. We consider the problem of the Bayesian\nestimation of the effects of hypothetical interventions in the Gaussian Process\nNetwork (GPN) model, a flexible causal framework which allows describing the\ncausal relationships nonparametrically. We detail how to perform causal\ninference on GPNs by simulating the effect of an intervention across the whole\nnetwork and propagating the effect of the intervention on downstream variables.\nWe further derive a simpler computational approximation by estimating the\nintervention distribution as a function of local variables only, modeling the\nconditional distributions via additive Gaussian processes. We extend both\nframeworks beyond the case of a known causal graph, incorporating uncertainty\nabout the causal structure via Markov chain Monte Carlo methods. Simulation\nstudies show that our approach is able to identify the effects of hypothetical\ninterventions with non-Gaussian, non-linear observational data and accurately\nreflect the posterior uncertainty of the causal estimates. Finally we compare\nthe results of our GPN-based causal inference approach to existing methods on a\ndataset of $A.~thaliana$ gene expressions.\n", "date": "2024-02-01", "categories": []}
{"id": "2303.02186", "title": "Causal Deep Learning", "abstract": "  Causality has the potential to truly transform the way we solve a large\nnumber of real-world problems. Yet, so far, its potential largely remains to be\nunlocked as causality often requires crucial assumptions which cannot be tested\nin practice. To address this challenge, we propose a new way of thinking about\ncausality -- we call this causal deep learning. Our causal deep learning\nframework spans three dimensions: (1) a structural dimension, which\nincorporates partial yet testable causal knowledge rather than assuming either\ncomplete or no causal knowledge among the variables of interest; (2) a\nparametric dimension, which encompasses parametric forms that capture the type\nof relationships among the variables of interest; and (3) a temporal dimension,\nwhich captures exposure times or how the variables of interest interact\n(possibly causally) over time. Causal deep learning enables us to make progress\non a variety of real-world problems by leveraging partial causal knowledge\n(including independencies among variables) and quantitatively characterising\ncausal relationships among variables of interest (possibly over time). Our\nframework clearly identifies which assumptions are testable and which ones are\nnot, such that the resulting solutions can be judiciously adopted in practice.\nUsing our formulation we can combine or chain together causal representations\nto solve specific problems without losing track of which assumptions are\nrequired to build these solutions, pushing real-world impact in healthcare,\neconomics and business, environmental sciences and education, through causal\ndeep learning.\n", "date": "2023-03-03", "categories": []}
{"id": "2306.10816", "title": "$\\texttt{causalAssembly}$: Generating Realistic Production Data for\n  Benchmarking Causal Discovery", "abstract": "  Algorithms for causal discovery have recently undergone rapid advances and\nincreasingly draw on flexible nonparametric methods to process complex data.\nWith these advances comes a need for adequate empirical validation of the\ncausal relationships learned by different algorithms. However, for most real\ndata sources true causal relations remain unknown. This issue is further\ncompounded by privacy concerns surrounding the release of suitable high-quality\ndata. To help address these challenges, we gather a complex dataset comprising\nmeasurements from an assembly line in a manufacturing context. This line\nconsists of numerous physical processes for which we are able to provide ground\ntruth causal relationships on the basis of a detailed study of the underlying\nphysics. We use the assembly line data and associated ground truth information\nto build a system for generation of semisynthetic manufacturing data that\nsupports benchmarking of causal discovery methods. To accomplish this, we\nemploy distributional random forests in order to flexibly estimate and\nrepresent conditional distributions that may be combined into joint\ndistributions that strictly adhere to a causal model over the observed\nvariables. The estimated conditionals and tools for data generation are made\navailable in our Python library $\\texttt{causalAssembly}$. Using the library,\nwe showcase how to benchmark several well-known causal discovery algorithms.\n", "date": "2023-06-19", "categories": []}
{"id": "2310.15450", "title": "General Identifiability and Achievability for Causal Representation\n  Learning", "abstract": "  This paper focuses on causal representation learning (CRL) under a general\nnonparametric latent causal model and a general transformation model that maps\nthe latent data to the observational data. It establishes identifiability and\nachievability results using two hard uncoupled interventions per node in the\nlatent causal graph. Notably, one does not know which pair of intervention\nenvironments have the same node intervened (hence, uncoupled). For\nidentifiability, the paper establishes that perfect recovery of the latent\ncausal model and variables is guaranteed under uncoupled interventions. For\nachievability, an algorithm is designed that uses observational and\ninterventional data and recovers the latent causal model and variables with\nprovable guarantees. This algorithm leverages score variations across different\nenvironments to estimate the inverse of the transformer and, subsequently, the\nlatent variables. The analysis, additionally, recovers the identifiability\nresult for two hard coupled interventions, that is when metadata about the pair\nof environments that have the same node intervened is known. This paper also\nshows that when observational data is available, additional faithfulness\nassumptions that are adopted by the existing literature are unnecessary.\n", "date": "2023-10-24", "categories": []}
{"id": "2402.09305", "title": "Embracing the black box: Heading towards foundation models for causal\n  discovery from time series data", "abstract": "  Causal discovery from time series data encompasses many existing solutions,\nincluding those based on deep learning techniques. However, these methods\ntypically do not endorse one of the most prevalent paradigms in deep learning:\nEnd-to-end learning. To address this gap, we explore what we call Causal\nPretraining. A methodology that aims to learn a direct mapping from\nmultivariate time series to the underlying causal graphs in a supervised\nmanner. Our empirical findings suggest that causal discovery in a supervised\nmanner is possible, assuming that the training and test time series samples\nshare most of their dynamics. More importantly, we found evidence that the\nperformance of Causal Pretraining can increase with data and model size, even\nif the additional data do not share the same dynamics. Further, we provide\nexamples where causal discovery for real-world data with causally pretrained\nneural networks is possible within limits. We argue that this hints at the\npossibility of a foundation model for causal discovery.\n", "date": "2024-02-14", "categories": []}
{"id": "2301.03180", "title": "Subset verification and search algorithms for causal DAGs", "abstract": "  Learning causal relationships between variables is a fundamental task in\ncausal inference and directed acyclic graphs (DAGs) are a popular choice to\nrepresent the causal relationships. As one can recover a causal graph only up\nto its Markov equivalence class from observations, interventions are often used\nfor the recovery task. Interventions are costly in general and it is important\nto design algorithms that minimize the number of interventions performed. In\nthis work, we study the problem of identifying the smallest set of\ninterventions required to learn the causal relationships between a subset of\nedges (target edges). Under the assumptions of faithfulness, causal\nsufficiency, and ideal interventions, we study this problem in two settings:\nwhen the underlying ground truth causal graph is known (subset verification)\nand when it is unknown (subset search). For the subset verification problem, we\nprovide an efficient algorithm to compute a minimum sized interventional set;\nwe further extend these results to bounded size non-atomic interventions and\nnode-dependent interventional costs. For the subset search problem, in the\nworst case, we show that no algorithm (even with adaptivity or randomization)\ncan achieve an approximation ratio that is asymptotically better than the\nvertex cover of the target edges when compared with the subset verification\nnumber. This result is surprising as there exists a logarithmic approximation\nalgorithm for the search problem when we wish to recover the whole causal\ngraph. To obtain our results, we prove several interesting structural\nproperties of interventional causal graphs that we believe have applications\nbeyond the subset verification/search problems studied here.\n", "date": "2023-01-09", "categories": []}
{"id": "2310.13576", "title": "Tree Search in DAG Space with Model-based Reinforcement Learning for\n  Causal Discovery", "abstract": "  Identifying causal structure is central to many fields ranging from strategic\ndecision-making to biology and economics. In this work, we propose CD-UCT, a\nmodel-based reinforcement learning method for causal discovery based on tree\nsearch that builds directed acyclic graphs incrementally. We also formalize and\nprove the correctness of an efficient algorithm for excluding edges that would\nintroduce cycles, which enables deeper discrete search and sampling in DAG\nspace. The proposed method can be applied broadly to causal Bayesian networks\nwith both discrete and continuous random variables. We conduct a comprehensive\nevaluation on synthetic and real-world datasets, showing that CD-UCT\nsubstantially outperforms the state-of-the-art model-free reinforcement\nlearning technique and greedy search, constituting a promising advancement for\ncombinatorial methods.\n", "date": "2023-10-20", "categories": []}
{"id": "2402.08229", "title": "Causal Discovery under Off-Target Interventions", "abstract": "  Causal graph discovery is a significant problem with applications across\nvarious disciplines. However, with observational data alone, the underlying\ncausal graph can only be recovered up to its Markov equivalence class, and\nfurther assumptions or interventions are necessary to narrow down the true\ngraph. This work addresses the causal discovery problem under the setting of\nstochastic interventions with the natural goal of minimizing the number of\ninterventions performed. We propose the following stochastic intervention model\nwhich subsumes existing adaptive noiseless interventions in the literature\nwhile capturing scenarios such as fat-hand interventions and CRISPR gene\nknockouts: any intervention attempt results in an actual intervention on a\nrandom subset of vertices, drawn from a distribution dependent on attempted\naction. Under this model, we study the two fundamental problems in causal\ndiscovery of verification and search and provide approximation algorithms with\npolylogarithmic competitive ratios and provide some preliminary experimental\nresults.\n", "date": "2024-02-13", "categories": []}
{"id": "2211.03846", "title": "Federated Causal Discovery From Interventions", "abstract": "  Causal discovery serves a pivotal role in mitigating model uncertainty\nthrough recovering the underlying causal mechanisms among variables. In many\npractical domains, such as healthcare, access to the data gathered by\nindividual entities is limited, primarily for privacy and regulatory\nconstraints. However, the majority of existing causal discovery methods require\nthe data to be available in a centralized location. In response, researchers\nhave introduced federated causal discovery. While previous federated methods\nconsider distributed observational data, the integration of interventional data\nremains largely unexplored. We propose FedCDI, a federated framework for\ninferring causal structures from distributed data containing interventional\nsamples. In line with the federated learning framework, FedCDI improves privacy\nby exchanging belief updates rather than raw samples. Additionally, it\nintroduces a novel intervention-aware method for aggregating individual\nupdates. We analyze scenarios with shared or disjoint intervened covariates,\nand mitigate the adverse effects of interventional data heterogeneity. The\nperformance and scalability of FedCDI is rigorously tested across a variety of\nsynthetic and real-world graphs.\n", "date": "2022-11-07", "categories": []}
{"id": "2312.05974", "title": "Learning the Causal Structure of Networked Dynamical Systems under\n  Latent Nodes and Structured Noise", "abstract": "  This paper considers learning the hidden causal network of a linear networked\ndynamical system (NDS) from the time series data at some of its nodes --\npartial observability. The dynamics of the NDS are driven by colored noise that\ngenerates spurious associations across pairs of nodes, rendering the problem\nmuch harder. To address the challenge of noise correlation and partial\nobservability, we assign to each pair of nodes a feature vector computed from\nthe time series data of observed nodes. The feature embedding is engineered to\nyield structural consistency: there exists an affine hyperplane that\nconsistently partitions the set of features, separating the feature vectors\ncorresponding to connected pairs of nodes from those corresponding to\ndisconnected pairs. The causal inference problem is thus addressed via\nclustering the designed features. We demonstrate with simple baseline\nsupervised methods the competitive performance of the proposed causal inference\nmechanism under broad connectivity regimes and noise correlation levels,\nincluding a real world network. Further, we devise novel technical guarantees\nof structural consistency for linear NDS under the considered regime.\n", "date": "2023-12-10", "categories": []}
{"id": "2402.05940", "title": "Causal Relationship Network of Risk Factors Impacting Workday Loss in\n  Underground Coal Mines", "abstract": "  This study aims to establish the causal relationship network between various\nfactors leading to workday loss in underground coal mines using a novel causal\nartificial intelligence (AI) method. The analysis utilizes data obtained from\nthe National Institute for Occupational Safety and Health (NIOSH). A total of\n101,010 injury records from 3,982 unique underground coal mines spanning the\nyears from 1990 to 2020 were extracted from the NIOSH database. Causal\nrelationships were analyzed and visualized using a novel causal AI method\ncalled Grouped Greedy Equivalence Search (GGES). The impact of each variable on\nworkday loss was assessed through intervention do-calculus adjustment (IDA)\nscores. Model training and validation were performed using the 10-fold\ncross-validation technique. Performance metrics, including adjacency precision\n(AP), adjacency recall (AR), arrowhead precision (AHP), and arrowhead recall\n(AHR), were utilized to evaluate the models. Findings revealed that after 2006,\nkey direct causes of workday loss among mining employees included total mining\nexperience, mean office employees, mean underground employees, county, and\ntotal mining experience (years). Total mining experience emerged as the most\ninfluential factor, whereas mean employees per mine exhibited the least\ninfluence. The analyses emphasized the significant role of total mining\nexperience in determining workday loss. The models achieved optimal\nperformance, with AP, AR, AHP, and AHR values measuring 0.694, 0.653, 0.386,\nand 0.345, respectively. This study demonstrates the feasibility of utilizing\nthe new GGES method to clarify the causal factors behind the workday loss by\nanalyzing employment demographics and injury records and establish their causal\nrelationship network.\n", "date": "2024-01-24", "categories": []}
{"id": "2402.04777", "title": "A fast score-based search algorithm for maximal ancestral graphs using\n  entropy", "abstract": "  \\emph{Maximal ancestral graph} (MAGs) is a class of graphical model that\nextend the famous \\emph{directed acyclic graph} in the presence of latent\nconfounders. Most score-based approaches to learn the unknown MAG from\nempirical data rely on BIC score which suffers from instability and heavy\ncomputations. We propose to use the framework of imsets\n\\citep{studeny2006probabilistic} to score MAGs using empirical entropy\nestimation and the newly proposed \\emph{refined Markov property}\n\\citep{hu2023towards}. Our graphical search procedure is similar to\n\\citet{claassen2022greedy} but improved from our theoretical results. We show\nthat our search algorithm is polynomial in number of nodes by restricting\ndegree, maximal head size and number of discriminating paths. In simulated\nexperiment, our algorithm shows superior performance compared to other state of\nart MAG learning algorithms.\n", "date": "2024-02-07", "categories": []}
{"id": "2402.02357", "title": "Multi-modal Causal Structure Learning and Root Cause Analysis", "abstract": "  Effective root cause analysis (RCA) is vital for swiftly restoring services,\nminimizing losses, and ensuring the smooth operation and management of complex\nsystems. Previous data-driven RCA methods, particularly those employing causal\ndiscovery techniques, have primarily focused on constructing dependency or\ncausal graphs for backtracking the root causes. However, these methods often\nfall short as they rely solely on data from a single modality, thereby\nresulting in suboptimal solutions. In this work, we propose Mulan, a unified\nmulti-modal causal structure learning method for root cause localization. We\nleverage a log-tailored language model to facilitate log representation\nlearning, converting log sequences into time-series data. To explore intricate\nrelationships across different modalities, we propose a contrastive\nlearning-based approach to extract modality-invariant and modality-specific\nrepresentations within a shared latent space. Additionally, we introduce a\nnovel key performance indicator-aware attention mechanism for assessing\nmodality reliability and co-learning a final causal graph. Finally, we employ\nrandom walk with restart to simulate system fault propagation and identify\npotential root causes. Extensive experiments on three real-world datasets\nvalidate the effectiveness of our proposed framework.\n", "date": "2024-02-04", "categories": []}
{"id": "2311.12267", "title": "Learning Causal Representations from General Environments:\n  Identifiability and Intrinsic Ambiguity", "abstract": "  We study causal representation learning, the task of recovering high-level\nlatent variables and their causal relationships in the form of a causal graph\nfrom low-level observed data (such as text and images), assuming access to\nobservations generated from multiple environments. Prior results on the\nidentifiability of causal representations typically assume access to\nsingle-node interventions which is rather unrealistic in practice, since the\nlatent variables are unknown in the first place. In this work, we provide the\nfirst identifiability results based on data that stem from general\nenvironments. We show that for linear causal models, while the causal graph can\nbe fully recovered, the latent variables are only identified up to the\nsurrounded-node ambiguity (SNA) \\citep{varici2023score}. We provide a\ncounterpart of our guarantee, showing that SNA is basically unavoidable in our\nsetting. We also propose an algorithm, \\texttt{LiNGCReL} which provably\nrecovers the ground-truth model up to SNA, and we demonstrate its effectiveness\nvia numerical experiments. Finally, we consider general non-parametric causal\nmodels and show that the same identification barrier holds when assuming access\nto groups of soft single-node interventions.\n", "date": "2023-11-21", "categories": []}
{"id": "2401.02930", "title": "Dagma-DCE: Interpretable, Non-Parametric Differentiable Causal Discovery", "abstract": "  We introduce Dagma-DCE, an interpretable and model-agnostic scheme for\ndifferentiable causal discovery. Current non- or over-parametric methods in\ndifferentiable causal discovery use opaque proxies of ``independence'' to\njustify the inclusion or exclusion of a causal relationship. We show\ntheoretically and empirically that these proxies may be arbitrarily different\nthan the actual causal strength. Juxtaposed to existing differentiable causal\ndiscovery algorithms, \\textsc{Dagma-DCE} uses an interpretable measure of\ncausal strength to define weighted adjacency matrices. In a number of simulated\ndatasets, we show our method achieves state-of-the-art level performance. We\nadditionally show that \\textsc{Dagma-DCE} allows for principled thresholding\nand sparsity penalties by domain-experts. The code for our method is available\nopen-source at https://github.com/DanWaxman/DAGMA-DCE, and can easily be\nadapted to arbitrary differentiable models.\n", "date": "2024-01-05", "categories": []}
{"id": "2402.01140", "title": "Root Cause Analysis In Microservice Using Neural Granger Causal\n  Discovery", "abstract": "  In recent years, microservices have gained widespread adoption in IT\noperations due to their scalability, maintenance, and flexibility. However, it\nbecomes challenging for site reliability engineers (SREs) to pinpoint the root\ncause due to the complex relationships in microservices when facing system\nmalfunctions. Previous research employed structured learning methods (e.g.,\nPC-algorithm) to establish causal relationships and derive root causes from\ncausal graphs. Nevertheless, they ignored the temporal order of time series\ndata and failed to leverage the rich information inherent in the temporal\nrelationships. For instance, in cases where there is a sudden spike in CPU\nutilization, it can lead to an increase in latency for other microservices.\nHowever, in this scenario, the anomaly in CPU utilization occurs before the\nlatency increase, rather than simultaneously. As a result, the PC-algorithm\nfails to capture such characteristics. To address these challenges, we propose\nRUN, a novel approach for root cause analysis using neural Granger causal\ndiscovery with contrastive learning. RUN enhances the backbone encoder by\nintegrating contextual information from time series, and leverages a time\nseries forecasting model to conduct neural Granger causal discovery. In\naddition, RUN incorporates Pagerank with a personalization vector to\nefficiently recommend the top-k root causes. Extensive experiments conducted on\nthe synthetic and real-world microservice-based datasets demonstrate that RUN\nnoticeably outperforms the state-of-the-art root cause analysis methods.\nMoreover, we provide an analysis scenario for the sock-shop case to showcase\nthe practicality and efficacy of RUN in microservice-based applications. Our\ncode is publicly available at https://github.com/zmlin1998/RUN.\n", "date": "2024-02-02", "categories": []}
{"id": "2401.18017", "title": "Causal Discovery by Kernel Deviance Measures with Heterogeneous\n  Transforms", "abstract": "  The discovery of causal relationships in a set of random variables is a\nfundamental objective of science and has also recently been argued as being an\nessential component towards real machine intelligence. One class of causal\ndiscovery techniques are founded based on the argument that there are inherent\nstructural asymmetries between the causal and anti-causal direction which could\nbe leveraged in determining the direction of causation. To go about capturing\nthese discrepancies between cause and effect remains to be a challenge and many\ncurrent state-of-the-art algorithms propose to compare the norms of the kernel\nmean embeddings of the conditional distributions. In this work, we argue that\nsuch approaches based on RKHS embeddings are insufficient in capturing\nprincipal markers of cause-effect asymmetry involving higher-order structural\nvariabilities of the conditional distributions. We propose Kernel Intrinsic\nInvariance Measure with Heterogeneous Transform (KIIM-HT) which introduces a\nnovel score measure based on heterogeneous transformation of RKHS embeddings to\nextract relevant higher-order moments of the conditional densities for causal\ndiscovery. Inference is made via comparing the score of each hypothetical\ncause-effect direction. Tests and comparisons on a synthetic dataset, a\ntwo-dimensional synthetic dataset and the real-world benchmark dataset\nT\\\"ubingen Cause-Effect Pairs verify our approach. In addition, we conduct a\nsensitivity analysis to the regularization parameter to faithfully compare\nprevious work to our method and an experiment with trials on varied\nhyperparameter values to showcase the robustness of our algorithm.\n", "date": "2024-01-31", "categories": []}
{"id": "2401.16974", "title": "CORE: Towards Scalable and Efficient Causal Discovery with Reinforcement\n  Learning", "abstract": "  Causal discovery is the challenging task of inferring causal structure from\ndata. Motivated by Pearl's Causal Hierarchy (PCH), which tells us that passive\nobservations alone are not enough to distinguish correlation from causation,\nthere has been a recent push to incorporate interventions into machine learning\nresearch. Reinforcement learning provides a convenient framework for such an\nactive approach to learning. This paper presents CORE, a deep reinforcement\nlearning-based approach for causal discovery and intervention planning. CORE\nlearns to sequentially reconstruct causal graphs from data while learning to\nperform informative interventions. Our results demonstrate that CORE\ngeneralizes to unseen graphs and efficiently uncovers causal structures.\nFurthermore, CORE scales to larger graphs with up to 10 variables and\noutperforms existing approaches in structure estimation accuracy and sample\nefficiency. All relevant code and supplementary material can be found at\nhttps://github.com/sa-and/CORE\n", "date": "2024-01-30", "categories": []}
{"id": "2401.10495", "title": "Causal Layering via Conditional Entropy", "abstract": "  Causal discovery aims to recover information about an unobserved causal graph\nfrom the observable data it generates. Layerings are orderings of the variables\nwhich place causes before effects. In this paper, we provide ways to recover\nlayerings of a graph by accessing the data via a conditional entropy oracle,\nwhen distributions are discrete. Our algorithms work by repeatedly removing\nsources or sinks from the graph. Under appropriate assumptions and\nconditioning, we can separate the sources or sinks from the remainder of the\nnodes by comparing their conditional entropy to the unconditional entropy of\ntheir noise. Our algorithms are provably correct and run in worst-case\nquadratic time. The main assumptions are faithfulness and injective noise, and\neither known noise entropies or weakly monotonically increasing noise entropies\nalong directed paths. In addition, we require one of either a very mild\nextension of faithfulness, or strictly monotonically increasing noise\nentropies, or expanding noise injectivity to include an additional single\nargument in the structural functions.\n", "date": "2024-01-19", "categories": []}
{"id": "2401.07231", "title": "Use of Prior Knowledge to Discover Causal Additive Models with\n  Unobserved Variables and its Application to Time Series Data", "abstract": "  This paper proposes two methods for causal additive models with unobserved\nvariables (CAM-UV). CAM-UV assumes that the causal functions take the form of\ngeneralized additive models and that latent confounders are present. First, we\npropose a method that leverages prior knowledge for efficient causal discovery.\nThen, we propose an extension of this method for inferring causality in time\nseries data. The original CAM-UV algorithm differs from other existing causal\nfunction models in that it does not seek the causal order between observed\nvariables, but rather aims to identify the causes for each observed variable.\nTherefore, the first proposed method in this paper utilizes prior knowledge,\nsuch as understanding that certain variables cannot be causes of specific\nothers. Moreover, by incorporating the prior knowledge that causes precedes\ntheir effects in time, we extend the first algorithm to the second method for\ncausal discovery in time series data. We validate the first proposed method by\nusing simulated data to demonstrate that the accuracy of causal discovery\nincreases as more prior knowledge is accumulated. Additionally, we test the\nsecond proposed method by comparing it with existing time series causal\ndiscovery methods, using both simulated data and real-world data.\n", "date": "2024-01-14", "categories": []}
{"id": "2306.17361", "title": "iSCAN: Identifying Causal Mechanism Shifts among Nonlinear Additive\n  Noise Models", "abstract": "  Structural causal models (SCMs) are widely used in various disciplines to\nrepresent causal relationships among variables in complex systems.\nUnfortunately, the underlying causal structure is often unknown, and estimating\nit from data remains a challenging task. In many situations, however, the end\ngoal is to localize the changes (shifts) in the causal mechanisms between\nrelated datasets instead of learning the full causal structure of the\nindividual datasets. Some applications include root cause analysis, analyzing\ngene regulatory network structure changes between healthy and cancerous\nindividuals, or explaining distribution shifts. This paper focuses on\nidentifying the causal mechanism shifts in two or more related datasets over\nthe same set of variables -- without estimating the entire DAG structure of\neach SCM. Prior work under this setting assumed linear models with Gaussian\nnoises; instead, in this work we assume that each SCM belongs to the more\ngeneral class of nonlinear additive noise models (ANMs). A key technical\ncontribution of this work is to show that the Jacobian of the score function\nfor the mixture distribution allows for the identification of shifts under\ngeneral non-parametric functional mechanisms. Once the shifted variables are\nidentified, we leverage recent work to estimate the structural differences, if\nany, for the shifted variables. Experiments on synthetic and real-world data\nare provided to showcase the applicability of this approach. Code implementing\nthe proposed method is open-source and publicly available at\nhttps://github.com/kevinsbello/iSCAN.\n", "date": "2023-06-30", "categories": []}
{"id": "2401.08221", "title": "Towards Causal Relationship in Indefinite Data: Baseline Model and New\n  Datasets", "abstract": "  Integrating deep learning and causal discovery has encouraged us to spot that\nlearning causal structures and representations in dialogue and video is full of\nchallenges. We defined These data forms as \"Indefinite Data\", characterized by\nmulti-structure data and multi-value representations. Unlike existing adaptable\ndata forms, Indefinite Data still faces gaps in datasets and methods. To\naddress the dataset gap, we release two high-quality datasets - Causalogue and\nCausaction, containing text dialogue samples and video action samples with\ncausal annotations respectively. Moreover, the method gap arises from the\ncoexistence of multi-structure data and multi-value representations, breaking\nthe assumptions of all current methods and rendering them infeasible on\nIndefinite Data. To this end, we propose a probabilistic framework as a\nbaseline, incorporating three designed highlights for this gap: 1) establishing\nCausation Condition of representations using the independence of noise terms\nunder non-fixed causal structures, 2) treating causal strength as a latent\nvariable and measuring the reconstruction loss in the correlation space, and 3)\nestimating the effects of latent confounders. These highpoints make the\nprobabilistic model capable of overcoming challenges brought by the coexistence\nof multi-structure data and multi-value representations and pave the way for\nthe extension of latent confounders. Comprehensive experiments have evaluated\nbaseline results of causal structures, causal representations, and confounding\ndisentanglement.\n", "date": "2024-01-16", "categories": []}
{"id": "2401.08386", "title": "Deep Learning-based Group Causal Inference in Multivariate Time-series", "abstract": "  Causal inference in a nonlinear system of multivariate timeseries is\ninstrumental in disentangling the intricate web of relationships among\nvariables, enabling us to make more accurate predictions and gain deeper\ninsights into real-world complex systems. Causality methods typically identify\nthe causal structure of a multivariate system by considering the cause-effect\nrelationship of each pair of variables while ignoring the collective effect of\na group of variables or interactions involving more than two-time series\nvariables. In this work, we test model invariance by group-level interventions\non the trained deep networks to infer causal direction in groups of variables,\nsuch as climate and ecosystem, brain networks, etc. Extensive testing with\nsynthetic and real-world time series data shows a significant improvement of\nour method over other applied group causality methods and provides us insights\ninto real-world time series. The code for our method can be found\nat:https://github.com/wasimahmadpk/gCause.\n", "date": "2024-01-16", "categories": []}
{"id": "2401.06523", "title": "Boosting Causal Additive Models", "abstract": "  We present a boosting-based method to learn additive Structural Equation\nModels (SEMs) from observational data, with a focus on the theoretical aspects\nof determining the causal order among variables. We introduce a family of score\nfunctions based on arbitrary regression techniques, for which we establish\nnecessary conditions to consistently favor the true causal ordering. Our\nanalysis reveals that boosting with early stopping meets these criteria and\nthus offers a consistent score function for causal orderings. To address the\nchallenges posed by high-dimensional data sets, we adapt our approach through a\ncomponent-wise gradient descent in the space of additive SEMs. Our simulation\nstudy underlines our theoretical results for lower dimensions and demonstrates\nthat our high-dimensional adaptation is competitive with state-of-the-art\nmethods. In addition, it exhibits robustness with respect to the choice of the\nhyperparameters making the procedure easy to tune.\n", "date": "2024-01-12", "categories": []}
{"id": "2308.04365", "title": "SLEM: Machine Learning for Path Modeling and Causal Inference with Super\n  Learner Equation Modeling", "abstract": "  Causal inference is a crucial goal of science, enabling researchers to arrive\nat meaningful conclusions regarding the predictions of hypothetical\ninterventions using observational data. Path models, Structural Equation Models\n(SEMs), and, more generally, Directed Acyclic Graphs (DAGs), provide a means to\nunambiguously specify assumptions regarding the causal structure underlying a\nphenomenon. Unlike DAGs, which make very few assumptions about the functional\nand parametric form, SEM assumes linearity. This can result in functional\nmisspecification which prevents researchers from undertaking reliable effect\nsize estimation. In contrast, we propose Super Learner Equation Modeling, a\npath modeling technique integrating machine learning Super Learner ensembles.\nWe empirically demonstrate its ability to provide consistent and unbiased\nestimates of causal effects, its competitive performance for linear models when\ncompared with SEM, and highlight its superiority over SEM when dealing with\nnon-linear relationships. We provide open-source code, and a tutorial notebook\nwith example usage, accentuating the easy-to-use nature of the method.\n", "date": "2023-08-08", "categories": []}
{"id": "2308.07520", "title": "Nonlinearity, Feedback and Uniform Consistency in Causal Structural\n  Learning", "abstract": "  The goal of Causal Discovery is to find automated search methods for learning\ncausal structures from observational data. In some cases all variables of the\ninterested causal mechanism are measured, and the task is to predict the\neffects one measured variable has on another. In contrast, sometimes the\nvariables of primary interest are not directly observable but instead inferred\nfrom their manifestations in the data. These are referred to as latent\nvariables. One commonly known example is the psychological construct of\nintelligence, which cannot directly measured so researchers try to assess\nthrough various indicators such as IQ tests. In this case, casual discovery\nalgorithms can uncover underlying patterns and structures to reveal the causal\nconnections between the latent variables and between the latent and observed\nvariables. This thesis focuses on two questions in causal discovery: providing\nan alternative definition of k-Triangle Faithfulness that (i) is weaker than\nstrong faithfulness when applied to the Gaussian family of distributions, (ii)\ncan be applied to non-Gaussian families of distributions, and (iii) under the\nassumption that the modified version of Strong Faithfulness holds, can be used\nto show the uniform consistency of a modified causal discovery algorithm;\nrelaxing the sufficiency assumption to learn causal structures with latent\nvariables. Given the importance of inferring cause-and-effect relationships for\nunderstanding and forecasting complex systems, the work in this thesis of\nrelaxing various simplification assumptions is expected to extend the causal\ndiscovery method to be applicable in a wider range with diversified causal\nmechanism and statistical phenomena.\n", "date": "2023-08-15", "categories": []}
{"id": "2302.00293", "title": "A Survey of Methods, Challenges and Perspectives in Causality", "abstract": "  Deep Learning models have shown success in a large variety of tasks by\nextracting correlation patterns from high-dimensional data but still struggle\nwhen generalizing out of their initial distribution. As causal engines aim to\nlearn mechanisms independent from a data distribution, combining Deep Learning\nwith Causality can have a great impact on the two fields. In this paper, we\nfurther motivate this assumption. We perform an extensive overview of the\ntheories and methods for Causality from different perspectives, with an\nemphasis on Deep Learning and the challenges met by the two domains. We show\nearly attempts to bring the fields together and the possible perspectives for\nthe future. We finish by providing a large variety of applications for\ntechniques from Causality.\n", "date": "2023-02-01", "categories": []}
{"id": "2312.16211", "title": "An Explainable AI Approach to Large Language Model Assisted Causal Model\n  Auditing and Development", "abstract": "  Causal networks are widely used in many fields, including epidemiology,\nsocial science, medicine, and engineering, to model the complex relationships\nbetween variables. While it can be convenient to algorithmically infer these\nmodels directly from observational data, the resulting networks are often\nplagued with erroneous edges. Auditing and correcting these networks may\nrequire domain expertise frequently unavailable to the analyst. We propose the\nuse of large language models such as ChatGPT as an auditor for causal networks.\nOur method presents ChatGPT with a causal network, one edge at a time, to\nproduce insights about edge directionality, possible confounders, and mediating\nvariables. We ask ChatGPT to reflect on various aspects of each causal link and\nwe then produce visualizations that summarize these viewpoints for the human\nanalyst to direct the edge, gather more data, or test further hypotheses. We\nenvision a system where large language models, automated causal inference, and\nthe human analyst and domain expert work hand in hand as a team to derive\nholistic and comprehensive causal models for any given case scenario. This\npaper presents first results obtained with an emerging prototype.\n", "date": "2023-12-23", "categories": []}
{"id": "2312.16707", "title": "Modeling Systemic Risk: A Time-Varying Nonparametric Causal Inference\n  Framework", "abstract": "  We propose a nonparametric and time-varying directed information graph\n(TV-DIG) framework to estimate the evolving causal structure in time series\nnetworks, thereby addressing the limitations of traditional econometric models\nin capturing high-dimensional, nonlinear, and time-varying interconnections\namong series. This framework employs an information-theoretic measure rooted in\na generalized version of Granger-causality, which is applicable to both linear\nand nonlinear dynamics. Our framework offers advancements in measuring systemic\nrisk and establishes meaningful connections with established econometric\nmodels, including vector autoregression and switching models. We evaluate the\nefficacy of our proposed model through simulation experiments and empirical\nanalysis, reporting promising results in recovering simulated time-varying\nnetworks with nonlinear and multivariate structures. We apply this framework to\nidentify and monitor the evolution of interconnectedness and systemic risk\namong major assets and industrial sectors within the financial network. We\nfocus on cryptocurrencies' potential systemic risks to financial stability,\nincluding spillover effects on other sectors during crises like the COVID-19\npandemic and the Federal Reserve's 2020 emergency response. Our findings\nreveals significant, previously underrecognized pre-2020 influences of\ncryptocurrencies on certain financial sectors, highlighting their potential\nsystemic risks and offering a systematic approach in tracking evolving\ncross-sector interactions within financial networks.\n", "date": "2023-12-27", "categories": []}
{"id": "2305.05276", "title": "Causal Discovery from Subsampled Time Series with Proxy Variables", "abstract": "  Inferring causal structures from time series data is the central interest of\nmany scientific inquiries. A major barrier to such inference is the problem of\nsubsampling, i.e., the frequency of measurement is much lower than that of\ncausal influence. To overcome this problem, numerous methods have been\nproposed, yet either was limited to the linear case or failed to achieve\nidentifiability. In this paper, we propose a constraint-based algorithm that\ncan identify the entire causal structure from subsampled time series, without\nany parametric constraint. Our observation is that the challenge of subsampling\narises mainly from hidden variables at the unobserved time steps. Meanwhile,\nevery hidden variable has an observed proxy, which is essentially itself at\nsome observable time in the future, benefiting from the temporal structure.\nBased on these, we can leverage the proxies to remove the bias induced by the\nhidden variables and hence achieve identifiability. Following this intuition,\nwe propose a proxy-based causal discovery algorithm. Our algorithm is\nnonparametric and can achieve full causal identification. Theoretical\nadvantages are reflected in synthetic and real-world experiments.\n", "date": "2023-05-09", "categories": []}
{"id": "2312.15919", "title": "Review on Causality Detection Based on Empirical Dynamic Modeling", "abstract": "  In contemporary scientific research, understanding the distinction between\ncorrelation and causation is crucial. While correlation is a widely used\nanalytical standard, it does not inherently imply causation. This paper\naddresses the potential for misinterpretation in relying solely on correlation,\nespecially in the context of nonlinear dynamics. Despite the rapid development\nof various correlation research methodologies, including machine learning, the\nexploration into mining causal correlations between variables remains ongoing.\nEmpirical Dynamic Modeling (EDM) emerges as a data-driven framework for\nmodeling dynamic systems, distinguishing itself by eschewing traditional\nformulaic methods in data analysis. Instead, it reconstructs dynamic system\nbehavior directly from time series data. The fundamental premise of EDM is that\ndynamic systems can be conceptualized as processes where a set of states,\ngoverned by specific rules, evolve over time in a high-dimensional space. By\nreconstructing these evolving states, dynamic systems can be effectively\nmodeled. Using EDM, this paper explores the detection of causal relationships\nbetween variables within dynamic systems through their time series data. It\nposits that if variable X causes variable Y, then the information about X is\ninherent in Y and can be extracted from Y's data. This study begins by\nexamining the dialectical relationship between correlation and causation,\nemphasizing that correlation does not equate to causation, and the absence of\ncorrelation does not necessarily indicate a lack of causation.\n", "date": "2023-12-26", "categories": []}
{"id": "2312.14670", "title": "Zero-shot Causal Graph Extrapolation from Text via LLMs", "abstract": "  We evaluate the ability of large language models (LLMs) to infer causal\nrelations from natural language. Compared to traditional natural language\nprocessing and deep learning techniques, LLMs show competitive performance in a\nbenchmark of pairwise relations without needing (explicit) training samples.\nThis motivates us to extend our approach to extrapolating causal graphs through\niterated pairwise queries. We perform a preliminary analysis on a benchmark of\nbiomedical abstracts with ground-truth causal graphs validated by experts. The\nresults are promising and support the adoption of LLMs for such a crucial step\nin causal inference, especially in medical domains, where the amount of\nscientific text to analyse might be huge, and the causal statements are often\nimplicit.\n", "date": "2023-12-22", "categories": []}
{"id": "2312.12678", "title": "Causal Discovery for fMRI data: Challenges, Solutions, and a Case Study", "abstract": "  Designing studies that apply causal discovery requires navigating many\nresearcher degrees of freedom. This complexity is exacerbated when the study\ninvolves fMRI data. In this paper we (i) describe nine challenges that occur\nwhen applying causal discovery to fMRI data, (ii) discuss the space of\ndecisions that need to be made, (iii) review how a recent case study made those\ndecisions, (iv) and identify existing gaps that could potentially be solved by\nthe development of new methods. Overall, causal discovery is a promising\napproach for analyzing fMRI data, and multiple successful applications have\nindicated that it is superior to traditional fMRI functional connectivity\nmethods, but current causal discovery methods for fMRI leave room for\nimprovement.\n", "date": "2023-12-20", "categories": []}
{"id": "2312.11934", "title": "Identification of Causal Structure with Latent Variables Based on Higher\n  Order Cumulants", "abstract": "  Causal discovery with latent variables is a crucial but challenging task.\nDespite the emergence of numerous methods aimed at addressing this challenge,\nthey are not fully identified to the structure that two observed variables are\ninfluenced by one latent variable and there might be a directed edge in\nbetween. Interestingly, we notice that this structure can be identified through\nthe utilization of higher-order cumulants. By leveraging the higher-order\ncumulants of non-Gaussian data, we provide an analytical solution for\nestimating the causal coefficients or their ratios. With the estimated (ratios\nof) causal coefficients, we propose a novel approach to identify the existence\nof a causal edge between two observed variables subject to latent variable\ninfluence. In case when such a causal edge exits, we introduce an asymmetry\ncriterion to determine the causal direction. The experimental results\ndemonstrate the effectiveness of our proposed method.\n", "date": "2023-12-19", "categories": []}
{"id": "2312.12206", "title": "Identification of Causal Structure in the Presence of Missing Data with\n  Additive Noise Model", "abstract": "  Missing data are an unavoidable complication frequently encountered in many\ncausal discovery tasks. When a missing process depends on the missing values\nthemselves (known as self-masking missingness), the recovery of the joint\ndistribution becomes unattainable, and detecting the presence of such\nself-masking missingness remains a perplexing challenge. Consequently, due to\nthe inability to reconstruct the original distribution and to discern the\nunderlying missingness mechanism, simply applying existing causal discovery\nmethods would lead to wrong conclusions. In this work, we found that the recent\nadvances additive noise model has the potential for learning causal structure\nunder the existence of the self-masking missingness. With this observation, we\naim to investigate the identification problem of learning causal structure from\nmissing data under an additive noise model with different missingness\nmechanisms, where the `no self-masking missingness' assumption can be\neliminated appropriately. Specifically, we first elegantly extend the scope of\nidentifiability of causal skeleton to the case with weak self-masking\nmissingness (i.e., no other variable could be the cause of self-masking\nindicators except itself). We further provide the sufficient and necessary\nidentification conditions of the causal direction under additive noise model\nand show that the causal structure can be identified up to an IN-equivalent\npattern. We finally propose a practical algorithm based on the above\ntheoretical results on learning the causal skeleton and causal direction.\nExtensive experiments on synthetic and real data demonstrate the efficiency and\neffectiveness of the proposed algorithms.\n", "date": "2023-12-19", "categories": []}
{"id": "2301.12212", "title": "Efficient Enumeration of Markov Equivalent DAGs", "abstract": "  Enumerating the directed acyclic graphs (DAGs) of a Markov equivalence class\n(MEC) is an important primitive in causal analysis. The central resource from\nthe perspective of computational complexity is the delay, that is, the time an\nalgorithm that lists all members of the class requires between two consecutive\noutputs. Commonly used algorithms for this task utilize the rules proposed by\nMeek (1995) or the transformational characterization by Chickering (1995), both\nresulting in superlinear delay. In this paper, we present the first linear-time\ndelay algorithm. On the theoretical side, we show that our algorithm can be\ngeneralized to enumerate DAGs represented by models that incorporate background\nknowledge, such as MPDAGs; on the practical side, we provide an efficient\nimplementation and evaluate it in a series of experiments. Complementary to the\nlinear-time delay algorithm, we also provide intriguing insights into Markov\nequivalence itself: All members of an MEC can be enumerated such that two\nsuccessive DAGs have structural Hamming distance at most three.\n", "date": "2023-01-28", "categories": []}
{"id": "2312.10102", "title": "Robust Estimation of Causal Heteroscedastic Noise Models", "abstract": "  Distinguishing the cause and effect from bivariate observational data is the\nfoundational problem that finds applications in many scientific disciplines.\nOne solution to this problem is assuming that cause and effect are generated\nfrom a structural causal model, enabling identification of the causal direction\nafter estimating the model in each direction. The heteroscedastic noise model\nis a type of structural causal model where the cause can contribute to both the\nmean and variance of the noise. Current methods for estimating heteroscedastic\nnoise models choose the Gaussian likelihood as the optimization objective which\ncan be suboptimal and unstable when the data has a non-Gaussian distribution.\nTo address this limitation, we propose a novel approach to estimating this\nmodel with Student's $t$-distribution, which is known for its robustness in\naccounting for sampling variability with smaller sample sizes and extreme\nvalues without significantly altering the overall distribution shape. This\nadaptability is beneficial for capturing the parameters of the noise\ndistribution in heteroscedastic noise models. Our empirical evaluations\ndemonstrate that our estimators are more robust and achieve better overall\nperformance across synthetic and real benchmarks.\n", "date": "2023-12-15", "categories": []}
{"id": "2312.11001", "title": "A Versatile Causal Discovery Framework to Allow Causally-Related Hidden\n  Variables", "abstract": "  Most existing causal discovery methods rely on the assumption of no latent\nconfounders, limiting their applicability in solving real-life problems. In\nthis paper, we introduce a novel, versatile framework for causal discovery that\naccommodates the presence of causally-related hidden variables almost\neverywhere in the causal network (for instance, they can be effects of observed\nvariables), based on rank information of covariance matrix over observed\nvariables. We start by investigating the efficacy of rank in comparison to\nconditional independence and, theoretically, establish necessary and sufficient\nconditions for the identifiability of certain latent structural patterns.\nFurthermore, we develop a Rank-based Latent Causal Discovery algorithm, RLCD,\nthat can efficiently locate hidden variables, determine their cardinalities,\nand discover the entire causal structure over both measured and hidden ones. We\nalso show that, under certain graphical conditions, RLCD correctly identifies\nthe Markov Equivalence Class of the whole latent causal graph asymptotically.\nExperimental results on both synthetic and real-world personality data sets\ndemonstrate the efficacy of the proposed approach in finite-sample cases.\n", "date": "2023-12-18", "categories": []}
{"id": "2312.05549", "title": "Multi-granularity Causal Structure Learning", "abstract": "  Unveil, model, and comprehend the causal mechanisms underpinning natural\nphenomena stand as fundamental endeavors across myriad scientific disciplines.\nMeanwhile, new knowledge emerges when discovering causal relationships from\ndata. Existing causal learning algorithms predominantly focus on the isolated\neffects of variables, overlook the intricate interplay of multiple variables\nand their collective behavioral patterns. Furthermore, the ubiquity of\nhigh-dimensional data exacts a substantial temporal cost for causal algorithms.\nIn this paper, we develop a novel method called MgCSL (Multi-granularity Causal\nStructure Learning), which first leverages sparse auto-encoder to explore\ncoarse-graining strategies and causal abstractions from micro-variables to\nmacro-ones. MgCSL then takes multi-granularity variables as inputs to train\nmultilayer perceptrons and to delve the causality between variables. To enhance\nthe efficacy on high-dimensional data, MgCSL introduces a simplified acyclicity\nconstraint to adeptly search the directed acyclic graph among variables.\nExperimental results show that MgCSL outperforms competitive baselines, and\nfinds out explainable causal connections on fMRI datasets.\n", "date": "2023-12-09", "categories": []}
{"id": "2306.02822", "title": "Discovering Dynamic Causal Space for DAG Structure Learning", "abstract": "  Discovering causal structure from purely observational data (i.e., causal\ndiscovery), aiming to identify causal relationships among variables, is a\nfundamental task in machine learning. The recent invention of differentiable\nscore-based DAG learners is a crucial enabler, which reframes the combinatorial\noptimization problem into a differentiable optimization with a DAG constraint\nover directed graph space. Despite their great success, these cutting-edge DAG\nlearners incorporate DAG-ness independent score functions to evaluate the\ndirected graph candidates, lacking in considering graph structure. As a result,\nmeasuring the data fitness alone regardless of DAG-ness inevitably leads to\ndiscovering suboptimal DAGs and model vulnerabilities. Towards this end, we\npropose a dynamic causal space for DAG structure learning, coined CASPER, that\nintegrates the graph structure into the score function as a new measure in the\ncausal space to faithfully reflect the causal distance between estimated and\nground truth DAG. CASPER revises the learning process as well as enhances the\nDAG structure learning via adaptive attention to DAG-ness. Grounded by\nempirical visualization, CASPER, as a space, satisfies a series of desired\nproperties, such as structure awareness and noise robustness. Extensive\nexperiments on both synthetic and real-world datasets clearly validate the\nsuperiority of our CASPER over the state-of-the-art causal discovery methods in\nterms of accuracy and robustness.\n", "date": "2023-06-05", "categories": []}
{"id": "2312.05540", "title": "Federated Causality Learning with Explainable Adaptive Optimization", "abstract": "  Discovering the causality from observational data is a crucial task in\nvarious scientific domains. With increasing awareness of privacy, data are not\nallowed to be exposed, and it is very hard to learn causal graphs from\ndispersed data, since these data may have different distributions. In this\npaper, we propose a federated causal discovery strategy (FedCausal) to learn\nthe unified global causal graph from decentralized heterogeneous data. We\ndesign a global optimization formula to naturally aggregate the causal graphs\nfrom client data and constrain the acyclicity of the global graph without\nexposing local data. Unlike other federated causal learning algorithms,\nFedCausal unifies the local and global optimizations into a complete directed\nacyclic graph (DAG) learning process with a flexible optimization objective. We\nprove that this optimization objective has a high interpretability and can\nadaptively handle homogeneous and heterogeneous data. Experimental results on\nsynthetic and real datasets show that FedCausal can effectively deal with\nnon-independently and identically distributed (non-iid) data and has a superior\nperformance.\n", "date": "2023-12-09", "categories": []}
{"id": "2306.05415", "title": "Causal normalizing flows: from theory to practice", "abstract": "  In this work, we deepen on the use of normalizing flows for causal reasoning.\nSpecifically, we first leverage recent results on non-linear ICA to show that\ncausal models are identifiable from observational data given a causal ordering,\nand thus can be recovered using autoregressive normalizing flows (NFs). Second,\nwe analyze different design and learning choices for causal normalizing flows\nto capture the underlying causal data-generating process. Third, we describe\nhow to implement the do-operator in causal NFs, and thus, how to answer\ninterventional and counterfactual questions. Finally, in our experiments, we\nvalidate our design and training choices through a comprehensive ablation\nstudy; compare causal NFs to other approaches for approximating causal models;\nand empirically demonstrate that causal NFs can be used to address real-world\nproblems, where the presence of mixed discrete-continuous data and partial\nknowledge on the causal graph is the norm. The code for this work can be found\nat https://github.com/psanch21/causal-flows.\n", "date": "2023-06-08", "categories": []}
{"id": "2307.13917", "title": "BayesDAG: Gradient-Based Posterior Inference for Causal Discovery", "abstract": "  Bayesian causal discovery aims to infer the posterior distribution over\ncausal models from observed data, quantifying epistemic uncertainty and\nbenefiting downstream tasks. However, computational challenges arise due to\njoint inference over combinatorial space of Directed Acyclic Graphs (DAGs) and\nnonlinear functions. Despite recent progress towards efficient posterior\ninference over DAGs, existing methods are either limited to variational\ninference on node permutation matrices for linear causal models, leading to\ncompromised inference accuracy, or continuous relaxation of adjacency matrices\nconstrained by a DAG regularizer, which cannot ensure resulting graphs are\nDAGs. In this work, we introduce a scalable Bayesian causal discovery framework\nbased on a combination of stochastic gradient Markov Chain Monte Carlo\n(SG-MCMC) and Variational Inference (VI) that overcomes these limitations. Our\napproach directly samples DAGs from the posterior without requiring any DAG\nregularization, simultaneously draws function parameter samples and is\napplicable to both linear and nonlinear causal models. To enable our approach,\nwe derive a novel equivalence to the permutation-based DAG learning, which\nopens up possibilities of using any relaxed gradient estimator defined over\npermutations. To our knowledge, this is the first framework applying\ngradient-based MCMC sampling for causal discovery. Empirical evaluation on\nsynthetic and real-world datasets demonstrate our approach's effectiveness\ncompared to state-of-the-art baselines.\n", "date": "2023-07-26", "categories": []}
{"id": "2208.09590", "title": "Data-Driven Causal Effect Estimation Based on Graphical Causal\n  Modelling: A Survey", "abstract": "  In many fields of scientific research and real-world applications, unbiased\nestimation of causal effects from non-experimental data is crucial for\nunderstanding the mechanism underlying the data and for decision-making on\neffective responses or interventions. A great deal of research has been\nconducted to address this challenging problem from different angles. For\nestimating causal effect in observational data, assumptions such as Markov\ncondition, faithfulness and causal sufficiency are always made. Under the\nassumptions, full knowledge such as, a set of covariates or an underlying\ncausal graph, is typically required. A practical challenge is that in many\napplications, no such full knowledge or only some partial knowledge is\navailable. In recent years, research has emerged to use search strategies based\non graphical causal modelling to discover useful knowledge from data for causal\neffect estimation, with some mild assumptions, and has shown promise in\ntackling the practical challenge. In this survey, we review these data-driven\nmethods on causal effect estimation for a single treatment with a single\noutcome of interest and focus on the challenges faced by data-driven causal\neffect estimation. We concisely summarise the basic concepts and theories that\nare essential for data-driven causal effect estimation using graphical causal\nmodelling but are scattered around the literature. We identify and discuss the\nchallenges faced by data-driven causal effect estimation and characterise the\nexisting methods by their assumptions and the approaches to tackling the\nchallenges. We analyse the strengths and limitations of the different types of\nmethods and present an empirical evaluation to support the discussions. We hope\nthis review will motivate more researchers to design better data-driven methods\nbased on graphical causal modelling for the challenging problem of causal\neffect estimation.\n", "date": "2022-08-20", "categories": []}
{"id": "2306.09433", "title": "Towards Practical Federated Causal Structure Learning", "abstract": "  Understanding causal relations is vital in scientific discovery. The process\nof causal structure learning involves identifying causal graphs from\nobservational data to understand such relations. Usually, a central server\nperforms this task, but sharing data with the server poses privacy risks.\nFederated learning can solve this problem, but existing solutions for federated\ncausal structure learning make unrealistic assumptions about data and lack\nconvergence guarantees. FedC2SL is a federated constraint-based causal\nstructure learning scheme that learns causal graphs using a federated\nconditional independence test, which examines conditional independence between\ntwo variables under a condition set without collecting raw data from clients.\nFedC2SL requires weaker and more realistic assumptions about data and offers\nstronger resistance to data variability among clients. FedPC and FedFCI are the\ntwo variants of FedC2SL for causal structure learning in causal sufficiency and\ncausal insufficiency, respectively. The study evaluates FedC2SL using both\nsynthetic datasets and real-world data against existing solutions and finds it\ndemonstrates encouraging performance and strong resilience to data\nheterogeneity among clients.\n", "date": "2023-06-15", "categories": []}
{"id": "2312.00509", "title": "Bayesian causal discovery from unknown general interventions", "abstract": "  We consider the problem of learning causal Directed Acyclic Graphs (DAGs)\nusing combinations of observational and interventional experimental data.\nCurrent methods tailored to this setting assume that interventions either\ndestroy parent-child relations of the intervened (target) nodes or only alter\nsuch relations without modifying the parent sets, even when the intervention\ntargets are unknown. We relax this assumption by proposing a Bayesian method\nfor causal discovery from general interventions, which allow for modifications\nof the parent sets of the unknown targets. Even in this framework, DAGs and\ngeneral interventions may be identifiable only up to some equivalence classes.\nWe provide graphical characterizations of such interventional Markov\nequivalence and devise compatible priors for Bayesian inference that guarantee\nscore equivalence of indistinguishable structures. We then develop a Markov\nChain Monte Carlo (MCMC) scheme to approximate the posterior distribution over\nDAGs, intervention targets and induced parent sets. Finally, we evaluate the\nproposed methodology on both simulated and real protein expression data.\n", "date": "2023-12-01", "categories": []}
{"id": "2311.14994", "title": "Exploring Causal Learning through Graph Neural Networks: An In-depth\n  Review", "abstract": "  In machine learning, exploring data correlations to predict outcomes is a\nfundamental task. Recognizing causal relationships embedded within data is\npivotal for a comprehensive understanding of system dynamics, the significance\nof which is paramount in data-driven decision-making processes. Beyond\ntraditional methods, there has been a surge in the use of graph neural networks\n(GNNs) for causal learning, given their capabilities as universal data\napproximators. Thus, a thorough review of the advancements in causal learning\nusing GNNs is both relevant and timely. To structure this review, we introduce\na novel taxonomy that encompasses various state-of-the-art GNN methods employed\nin studying causality. GNNs are further categorized based on their applications\nin the causality domain. We further provide an exhaustive compilation of\ndatasets integral to causal learning with GNNs to serve as a resource for\npractical study. This review also touches upon the application of causal\nlearning across diverse sectors. We conclude the review with insights into\npotential challenges and promising avenues for future exploration in this\nrapidly evolving field of machine learning.\n", "date": "2023-11-25", "categories": []}
{"id": "2208.14989", "title": "Learning Multiscale Non-stationary Causal Structures", "abstract": "  This paper addresses a gap in the current state of the art by providing a\nsolution for modeling causal relationships that evolve over time and occur at\ndifferent time scales. Specifically, we introduce the multiscale non-stationary\ndirected acyclic graph (MN-DAG), a framework for modeling multivariate time\nseries data. Our contribution is twofold. Firstly, we expose a probabilistic\ngenerative model by leveraging results from spectral and causality theories.\nOur model allows sampling an MN-DAG according to user-specified priors on the\ntime-dependence and multiscale properties of the causal graph. Secondly, we\ndevise a Bayesian method named Multiscale Non-stationary Causal Structure\nLearner (MN-CASTLE) that uses stochastic variational inference to estimate\nMN-DAGs. The method also exploits information from the local partial\ncorrelation between time series over different time resolutions. The data\ngenerated from an MN-DAG reproduces well-known features of time series in\ndifferent domains, such as volatility clustering and serial correlation.\nAdditionally, we show the superior performance of MN-CASTLE on synthetic data\nwith different multiscale and non-stationary properties compared to baseline\nmodels. Finally, we apply MN-CASTLE to identify the drivers of the natural gas\nprices in the US market. Causal relationships have strengthened during the\nCOVID-19 outbreak and the Russian invasion of Ukraine, a fact that baseline\nmethods fail to capture. MN-CASTLE identifies the causal impact of critical\neconomic drivers on natural gas prices, such as seasonal factors, economic\nuncertainty, oil prices, and gas storage deviations.\n", "date": "2022-08-31", "categories": []}
{"id": "2311.11212", "title": "Can We Utilize Pre-trained Language Models within Causal Discovery\n  Algorithms?", "abstract": "  Scaling laws have allowed Pre-trained Language Models (PLMs) into the field\nof causal reasoning. Causal reasoning of PLM relies solely on text-based\ndescriptions, in contrast to causal discovery which aims to determine the\ncausal relationships between variables utilizing data. Recently, there has been\ncurrent research regarding a method that mimics causal discovery by aggregating\nthe outcomes of repetitive causal reasoning, achieved through specifically\ndesigned prompts. It highlights the usefulness of PLMs in discovering cause and\neffect, which is often limited by a lack of data, especially when dealing with\nmultiple variables. Conversely, the characteristics of PLMs which are that PLMs\ndo not analyze data and they are highly dependent on prompt design leads to a\ncrucial limitation for directly using PLMs in causal discovery. Accordingly,\nPLM-based causal reasoning deeply depends on the prompt design and carries out\nthe risk of overconfidence and false predictions in determining causal\nrelationships. In this paper, we empirically demonstrate the aforementioned\nlimitations of PLM-based causal reasoning through experiments on\nphysics-inspired synthetic data. Then, we propose a new framework that\nintegrates prior knowledge obtained from PLM with a causal discovery algorithm.\nThis is accomplished by initializing an adjacency matrix for causal discovery\nand incorporating regularization using prior knowledge. Our proposed framework\nnot only demonstrates improved performance through the integration of PLM and\ncausal discovery but also suggests how to leverage PLM-extracted prior\nknowledge with existing causal discovery algorithms.\n", "date": "2023-11-19", "categories": []}
{"id": "2311.11689", "title": "Causal Structure Learning Supervised by Large Language Model", "abstract": "  Causal discovery from observational data is pivotal for deciphering complex\nrelationships. Causal Structure Learning (CSL), which focuses on deriving\ncausal Directed Acyclic Graphs (DAGs) from data, faces challenges due to vast\nDAG spaces and data sparsity. The integration of Large Language Models (LLMs),\nrecognized for their causal reasoning capabilities, offers a promising\ndirection to enhance CSL by infusing it with knowledge-based causal inferences.\nHowever, existing approaches utilizing LLMs for CSL have encountered issues,\nincluding unreliable constraints from imperfect LLM inferences and the\ncomputational intensity of full pairwise variable analyses. In response, we\nintroduce the Iterative LLM Supervised CSL (ILS-CSL) framework. ILS-CSL\ninnovatively integrates LLM-based causal inference with CSL in an iterative\nprocess, refining the causal DAG using feedback from LLMs. This method not only\nutilizes LLM resources more efficiently but also generates more robust and\nhigh-quality structural constraints compared to previous methodologies. Our\ncomprehensive evaluation across eight real-world datasets demonstrates\nILS-CSL's superior performance, setting a new standard in CSL efficacy and\nshowcasing its potential to significantly advance the field of causal\ndiscovery. The codes are available at\n\\url{https://github.com/tyMadara/ILS-CSL}.\n", "date": "2023-11-20", "categories": []}
{"id": "2311.07191", "title": "Applying Large Language Models for Causal Structure Learning in Non\n  Small Cell Lung Cancer", "abstract": "  Causal discovery is becoming a key part in medical AI research. These methods\ncan enhance healthcare by identifying causal links between biomarkers,\ndemographics, treatments and outcomes. They can aid medical professionals in\nchoosing more impactful treatments and strategies. In parallel, Large Language\nModels (LLMs) have shown great potential in identifying patterns and generating\ninsights from text data. In this paper we investigate applying LLMs to the\nproblem of determining the directionality of edges in causal discovery.\nSpecifically, we test our approach on a deidentified set of Non Small Cell Lung\nCancer(NSCLC) patients that have both electronic health record and genomic\npanel data. Graphs are validated using Bayesian Dirichlet estimators using\ntabular data. Our result shows that LLMs can accurately predict the\ndirectionality of edges in causal graphs, outperforming existing\nstate-of-the-art methods. These findings suggests that LLMs can play a\nsignificant role in advancing causal discovery and help us better understand\ncomplex systems.\n", "date": "2023-11-13", "categories": []}
{"id": "2307.06250", "title": "Identifiability Guarantees for Causal Disentanglement from Soft\n  Interventions", "abstract": "  Causal disentanglement aims to uncover a representation of data using latent\nvariables that are interrelated through a causal model. Such a representation\nis identifiable if the latent model that explains the data is unique. In this\npaper, we focus on the scenario where unpaired observational and interventional\ndata are available, with each intervention changing the mechanism of a latent\nvariable. When the causal variables are fully observed, statistically\nconsistent algorithms have been developed to identify the causal model under\nfaithfulness assumptions. We here show that identifiability can still be\nachieved with unobserved causal variables, given a generalized notion of\nfaithfulness. Our results guarantee that we can recover the latent causal model\nup to an equivalence class and predict the effect of unseen combinations of\ninterventions, in the limit of infinite data. We implement our causal\ndisentanglement framework by developing an autoencoding variational Bayes\nalgorithm and apply it to the problem of predicting combinatorial perturbation\neffects in genomics.\n", "date": "2023-07-12", "categories": []}
{"id": "2309.04069", "title": "Inferring physical laws by artificial intelligence based causal models", "abstract": "  The advances in Artificial Intelligence (AI) and Machine Learning (ML) have\nopened up many avenues for scientific research, and are adding new dimensions\nto the process of knowledge creation. However, even the most powerful and\nversatile of ML applications till date are primarily in the domain of analysis\nof associations and boil down to complex data fitting. Judea Pearl has pointed\nout that Artificial General Intelligence must involve interventions involving\nthe acts of doing and imagining. Any machine assisted scientific discovery thus\nmust include casual analysis and interventions. In this context, we propose a\ncausal learning model of physical principles, which not only recognizes\ncorrelations but also brings out casual relationships. We use the principles of\ncausal inference and interventions to study the cause-and-effect relationships\nin the context of some well-known physical phenomena. We show that this\ntechnique can not only figure out associations among data, but is also able to\ncorrectly ascertain the cause-and-effect relations amongst the variables,\nthereby strengthening (or weakening) our confidence in the proposed model of\nthe underlying physical process.\n", "date": "2023-09-08", "categories": []}
{"id": "2311.05421", "title": "Diffusion Based Causal Representation Learning", "abstract": "  Causal reasoning can be considered a cornerstone of intelligent systems.\nHaving access to an underlying causal graph comes with the promise of\ncause-effect estimation and the identification of efficient and safe\ninterventions. However, learning causal representations remains a major\nchallenge, due to the complexity of many real-world systems. Previous works on\ncausal representation learning have mostly focused on Variational Auto-Encoders\n(VAE). These methods only provide representations from a point estimate, and\nthey are unsuitable to handle high dimensions. To overcome these problems, we\nproposed a new Diffusion-based Causal Representation Learning (DCRL) algorithm.\nThis algorithm uses diffusion-based representations for causal discovery. DCRL\noffers access to infinite dimensional latent codes, which encode different\nlevels of information in the latent code. In a first proof of principle, we\ninvestigate the use of DCRL for causal representation learning. We further\ndemonstrate experimentally that this approach performs comparably well in\nidentifying the causal structure and causal variables.\n", "date": "2023-11-09", "categories": []}
{"id": "2310.18471", "title": "Causal disentanglement of multimodal data", "abstract": "  Causal representation learning algorithms discover lower-dimensional\nrepresentations of data that admit a decipherable interpretation of cause and\neffect; as achieving such interpretable representations is challenging, many\ncausal learning algorithms utilize elements indicating prior information, such\nas (linear) structural causal models, interventional data, or weak supervision.\nUnfortunately, in exploratory causal representation learning, such elements and\nprior information may not be available or warranted. Alternatively, scientific\ndatasets often have multiple modalities or physics-based constraints, and the\nuse of such scientific, multimodal data has been shown to improve\ndisentanglement in fully unsupervised settings. Consequently, we introduce a\ncausal representation learning algorithm (causalPIMA) that can use multimodal\ndata and known physics to discover important features with causal\nrelationships. Our innovative algorithm utilizes a new differentiable\nparametrization to learn a directed acyclic graph (DAG) together with a latent\nspace of a variational autoencoder in an end-to-end differentiable framework\nvia a single, tractable evidence lower bound loss function. We place a Gaussian\nmixture prior on the latent space and identify each of the mixtures with an\noutcome of the DAG nodes; this novel identification enables feature discovery\nwith causal relationships. Tested against a synthetic and a scientific dataset,\nour results demonstrate the capability of learning an interpretable causal\nstructure while simultaneously discovering key features in a fully unsupervised\nsetting.\n", "date": "2023-10-27", "categories": []}
{"id": "2311.03989", "title": "Learned Causal Method Prediction", "abstract": "  For a given causal question, it is important to efficiently decide which\ncausal inference method to use for a given dataset. This is challenging because\ncausal methods typically rely on complex and difficult-to-verify assumptions,\nand cross-validation is not applicable since ground truth causal quantities are\nunobserved. In this work, we propose CAusal Method Predictor (CAMP), a\nframework for predicting the best method for a given dataset. To this end, we\ngenerate datasets from a diverse set of synthetic causal models, score the\ncandidate methods, and train a model to directly predict the highest-scoring\nmethod for that dataset. Next, by formulating a self-supervised pre-training\nobjective centered on dataset assumptions relevant for causal inference, we\nsignificantly reduce the need for costly labeled data and enhance training\nefficiency. Our strategy learns to map implicit dataset properties to the best\nmethod in a data-driven manner. In our experiments, we focus on method\nprediction for causal discovery. CAMP outperforms selecting any individual\ncandidate method and demonstrates promising generalization to unseen\nsemi-synthetic and real-world benchmarks.\n", "date": "2023-11-07", "categories": []}
{"id": "2311.04636", "title": "Learning Linear Gaussian Polytree Models with Interventions", "abstract": "  We present a consistent and highly scalable local approach to learn the\ncausal structure of a linear Gaussian polytree using data from interventional\nexperiments with known intervention targets. Our methods first learn the\nskeleton of the polytree and then orient its edges. The output is a CPDAG\nrepresenting the interventional equivalence class of the polytree of the true\nunderlying distribution. The skeleton and orientation recovery procedures we\nuse rely on second order statistics and low-dimensional marginal distributions.\nWe assess the performance of our methods under different scenarios in synthetic\ndata sets and apply our algorithm to learn a polytree in a gene expression\ninterventional data set. Our simulation studies demonstrate that our approach\nis fast, has good accuracy in terms of structural Hamming distance, and handles\nproblems with thousands of nodes.\n", "date": "2023-11-08", "categories": []}
{"id": "2310.11132", "title": "Non-parametric Conditional Independence Testing for Mixed\n  Continuous-Categorical Variables: A Novel Method and Numerical Evaluation", "abstract": "  Conditional independence testing (CIT) is a common task in machine learning,\ne.g., for variable selection, and a main component of constraint-based causal\ndiscovery. While most current CIT approaches assume that all variables are\nnumerical or all variables are categorical, many real-world applications\ninvolve mixed-type datasets that include numerical and categorical variables.\nNon-parametric CIT can be conducted using conditional mutual information (CMI)\nestimators combined with a local permutation scheme. Recently, two novel CMI\nestimators for mixed-type datasets based on k-nearest-neighbors (k-NN) have\nbeen proposed. As with any k-NN method, these estimators rely on the definition\nof a distance metric. One approach computes distances by a one-hot encoding of\nthe categorical variables, essentially treating categorical variables as\ndiscrete-numerical, while the other expresses CMI by entropy terms where the\ncategorical variables appear as conditions only. In this work, we study these\nestimators and propose a variation of the former approach that does not treat\ncategorical variables as numeric. Our numerical experiments show that our\nvariant detects dependencies more robustly across different data distributions\nand preprocessing types.\n", "date": "2023-10-17", "categories": []}
{"id": "2305.10050", "title": "The Impact of Missing Data on Causal Discovery: A Multicentric Clinical\n  Study", "abstract": "  Causal inference for testing clinical hypotheses from observational data\npresents many difficulties because the underlying data-generating model and the\nassociated causal graph are not usually available. Furthermore, observational\ndata may contain missing values, which impact the recovery of the causal graph\nby causal discovery algorithms: a crucial issue often ignored in clinical\nstudies. In this work, we use data from a multi-centric study on endometrial\ncancer to analyze the impact of different missingness mechanisms on the\nrecovered causal graph. This is achieved by extending state-of-the-art causal\ndiscovery algorithms to exploit expert knowledge without sacrificing\ntheoretical soundness. We validate the recovered graph with expert physicians,\nshowing that our approach finds clinically-relevant solutions. Finally, we\ndiscuss the goodness of fit of our graph and its consistency from a clinical\ndecision-making perspective using graphical separation to validate causal\npathways.\n", "date": "2023-05-17", "categories": []}
{"id": "2306.02899", "title": "Learning nonparametric latent causal graphs with unknown interventions", "abstract": "  We establish conditions under which latent causal graphs are\nnonparametrically identifiable and can be reconstructed from unknown\ninterventions in the latent space. Our primary focus is the identification of\nthe latent structure in measurement models without parametric assumptions such\nas linearity or Gaussianity. Moreover, we do not assume the number of hidden\nvariables is known, and we show that at most one unknown intervention per\nhidden variable is needed. This extends a recent line of work on learning\ncausal representations from observations and interventions. The proofs are\nconstructive and introduce two new graphical concepts -- imaginary subsets and\nisolated edges -- that may be useful in their own right. As a matter of\nindependent interest, the proofs also involve a novel characterization of the\nlimits of edge orientations within the equivalence class of DAGs induced by\nunknown interventions. These are the first results to characterize the\nconditions under which causal representations are identifiable without making\nany parametric assumptions in a general setting with unknown interventions and\nwithout faithfulness.\n", "date": "2023-06-05", "categories": []}
{"id": "2301.12389", "title": "On Learning Necessary and Sufficient Causal Graphs", "abstract": "  The causal revolution has stimulated interest in understanding complex\nrelationships in various fields. Most of the existing methods aim to discover\ncausal relationships among all variables within a complex large-scale graph.\nHowever, in practice, only a small subset of variables in the graph are\nrelevant to the outcomes of interest. Consequently, causal estimation with the\nfull causal graph -- particularly given limited data -- could lead to numerous\nfalsely discovered, spurious variables that exhibit high correlation with, but\nexert no causal impact on, the target outcome. In this paper, we propose\nlearning a class of necessary and sufficient causal graphs (NSCG) that\nexclusively comprises causally relevant variables for an outcome of interest,\nwhich we term causal features. The key idea is to employ probabilities of\ncausation to systematically evaluate the importance of features in the causal\ngraph, allowing us to identify a subgraph relevant to the outcome of interest.\nTo learn NSCG from data, we develop a necessary and sufficient causal\nstructural learning (NSCSL) algorithm, by establishing theoretical properties\nand relationships between probabilities of causation and natural causal effects\nof features. Across empirical studies of simulated and real data, we\ndemonstrate that NSCSL outperforms existing algorithms and can reveal crucial\nyeast genes for target heritable traits of interest.\n", "date": "2023-01-29", "categories": []}
{"id": "2303.18211", "title": "A Scale-Invariant Sorting Criterion to Find a Causal Order in Additive\n  Noise Models", "abstract": "  Additive Noise Models (ANMs) are a common model class for causal discovery\nfrom observational data and are often used to generate synthetic data for\ncausal discovery benchmarking. Specifying an ANM requires choosing all\nparameters, including those not fixed by explicit assumptions. Reisach et al.\n(2021) show that sorting variables by increasing variance often yields an\nordering close to a causal order and introduce var-sortability to quantify this\nalignment. Since increasing variances may be unrealistic and are\nscale-dependent, ANM data are often standardized in benchmarks.\n  We show that synthetic ANM data are characterized by another pattern that is\nscale-invariant: the explainable fraction of a variable's variance, as captured\nby the coefficient of determination $R^2$, tends to increase along the causal\norder. The result is high $R^2$-sortability, meaning that sorting the variables\nby increasing $R^2$ yields an ordering close to a causal order. We propose an\nefficient baseline algorithm termed $R^2$-SortnRegress that exploits high\n$R^2$-sortability and that can match and exceed the performance of established\ncausal discovery algorithms. We show analytically that sufficiently high edge\nweights lead to a relative decrease of the noise contributions along causal\nchains, resulting in increasingly deterministic relationships and high $R^2$.\nWe characterize $R^2$-sortability for different simulation parameters and find\nhigh values in common settings. Our findings reveal high $R^2$-sortability as\nan assumption about the data generating process relevant to causal discovery\nand implicit in many ANM sampling schemes. It should be made explicit, as its\nprevalence in real-world data is unknown. For causal discovery benchmarking, we\nimplement $R^2$-sortability, the $R^2$-SortnRegress algorithm, and ANM\nsimulation procedures in our library CausalDisco at\nhttps://causaldisco.github.io/CausalDisco/.\n", "date": "2023-03-31", "categories": []}
{"id": "2311.00599", "title": "Structure Learning with Adaptive Random Neighborhood Informed MCMC", "abstract": "  In this paper, we introduce a novel MCMC sampler, PARNI-DAG, for a\nfully-Bayesian approach to the problem of structure learning under\nobservational data. Under the assumption of causal sufficiency, the algorithm\nallows for approximate sampling directly from the posterior distribution on\nDirected Acyclic Graphs (DAGs). PARNI-DAG performs efficient sampling of DAGs\nvia locally informed, adaptive random neighborhood proposal that results in\nbetter mixing properties. In addition, to ensure better scalability with the\nnumber of nodes, we couple PARNI-DAG with a pre-tuning procedure of the\nsampler's parameters that exploits a skeleton graph derived through some\nconstraint-based or scoring-based algorithms. Thanks to these novel features,\nPARNI-DAG quickly converges to high-probability regions and is less likely to\nget stuck in local modes in the presence of high correlation between nodes in\nhigh-dimensional settings. After introducing the technical novelties in\nPARNI-DAG, we empirically demonstrate its mixing efficiency and accuracy in\nlearning DAG structures on a variety of experiments.\n", "date": "2023-11-01", "categories": []}
{"id": "2311.00674", "title": "Recovering Linear Causal Models with Latent Variables via Cholesky\n  Factorization of Covariance Matrix", "abstract": "  Discovering the causal relationship via recovering the directed acyclic graph\n(DAG) structure from the observed data is a well-known challenging\ncombinatorial problem. When there are latent variables, the problem becomes\neven more difficult. In this paper, we first propose a DAG structure recovering\nalgorithm, which is based on the Cholesky factorization of the covariance\nmatrix of the observed data. The algorithm is fast and easy to implement and\nhas theoretical grantees for exact recovery. On synthetic and real-world\ndatasets, the algorithm is significantly faster than previous methods and\nachieves the state-of-the-art performance. Furthermore, under the equal error\nvariances assumption, we incorporate an optimization procedure into the\nCholesky factorization based algorithm to handle the DAG recovering problem\nwith latent variables. Numerical simulations show that the modified \"Cholesky +\noptimization\" algorithm is able to recover the ground truth graph in most cases\nand outperforms existing algorithms.\n", "date": "2023-11-01", "categories": []}
{"id": "2306.07916", "title": "Identification of Nonlinear Latent Hierarchical Models", "abstract": "  Identifying latent variables and causal structures from observational data is\nessential to many real-world applications involving biological data, medical\ndata, and unstructured data such as images and languages. However, this task\ncan be highly challenging, especially when observed variables are generated by\ncausally related latent variables and the relationships are nonlinear. In this\nwork, we investigate the identification problem for nonlinear latent\nhierarchical causal models in which observed variables are generated by a set\nof causally related latent variables, and some latent variables may not have\nobserved children.\n  We show that the identifiability of causal structures and latent variables\n(up to invertible transformations) can be achieved under mild assumptions: on\ncausal structures, we allow for multiple paths between any pair of variables in\nthe graph, which relaxes latent tree assumptions in prior work; on structural\nfunctions, we permit general nonlinearity and multi-dimensional continuous\nvariables, alleviating existing work's parametric assumptions. Specifically, we\nfirst develop an identification criterion in the form of novel identifiability\nguarantees for an elementary latent variable model. Leveraging this criterion,\nwe show that both causal structures and latent variables of the hierarchical\nmodel can be identified asymptotically by explicitly constructing an estimation\nprocedure. To the best of our knowledge, our work is the first to establish\nidentifiability guarantees for both causal structures and latent variables in\nnonlinear latent hierarchical models.\n", "date": "2023-06-13", "categories": []}
{"id": "2310.20075", "title": "Meek Separators and Their Applications in Targeted Causal Discovery", "abstract": "  Learning causal structures from interventional data is a fundamental problem\nwith broad applications across various fields. While many previous works have\nfocused on recovering the entire causal graph, in practice, there are scenarios\nwhere learning only part of the causal graph suffices. This is called\n$targeted$ causal discovery. In our work, we focus on two such well-motivated\nproblems: subset search and causal matching. We aim to minimize the number of\ninterventions in both cases.\n  Towards this, we introduce the $Meek~separator$, which is a subset of\nvertices that, when intervened, decomposes the remaining unoriented edges into\nsmaller connected components. We then present an efficient algorithm to find\nMeek separators that are of small sizes. Such a procedure is helpful in\ndesigning various divide-and-conquer-based approaches. In particular, we\npropose two randomized algorithms that achieve logarithmic approximation for\nsubset search and causal matching, respectively. Our results provide the first\nknown average-case provable guarantees for both problems. We believe that this\nopens up possibilities to design near-optimal methods for many other targeted\ncausal structure learning problems arising from various applications.\n", "date": "2023-10-30", "categories": []}
{"id": "2310.20307", "title": "Causal Interpretation of Self-Attention in Pre-Trained Transformers", "abstract": "  We propose a causal interpretation of self-attention in the Transformer\nneural network architecture. We interpret self-attention as a mechanism that\nestimates a structural equation model for a given input sequence of symbols\n(tokens). The structural equation model can be interpreted, in turn, as a\ncausal structure over the input symbols under the specific context of the input\nsequence. Importantly, this interpretation remains valid in the presence of\nlatent confounders. Following this interpretation, we estimate conditional\nindependence relations between input symbols by calculating partial\ncorrelations between their corresponding representations in the deepest\nattention layer. This enables learning the causal structure over an input\nsequence using existing constraint-based algorithms. In this sense, existing\npre-trained Transformers can be utilized for zero-shot causal-discovery. We\ndemonstrate this method by providing causal explanations for the outcomes of\nTransformers in two tasks: sentiment classification (NLP) and recommendation.\n", "date": "2023-10-31", "categories": []}
{"id": "2301.09028", "title": "Characterization and Learning of Causal Graphs with Small Conditioning\n  Sets", "abstract": "  Constraint-based causal discovery algorithms learn part of the causal graph\nstructure by systematically testing conditional independences observed in the\ndata. These algorithms, such as the PC algorithm and its variants, rely on\ngraphical characterizations of the so-called equivalence class of causal graphs\nproposed by Pearl. However, constraint-based causal discovery algorithms\nstruggle when data is limited since conditional independence tests quickly lose\ntheir statistical power, especially when the conditioning set is large. To\naddress this, we propose using conditional independence tests where the size of\nthe conditioning set is upper bounded by some integer $k$ for robust causal\ndiscovery. The existing graphical characterizations of the equivalence classes\nof causal graphs are not applicable when we cannot leverage all the conditional\nindependence statements. We first define the notion of $k$-Markov equivalence:\nTwo causal graphs are $k$-Markov equivalent if they entail the same conditional\nindependence constraints where the conditioning set size is upper bounded by\n$k$. We propose a novel representation that allows us to graphically\ncharacterize $k$-Markov equivalence between two causal graphs. We propose a\nsound constraint-based algorithm called the $k$-PC algorithm for learning this\nequivalence class. Finally, we conduct synthetic, and semi-synthetic\nexperiments to demonstrate that the $k$-PC algorithm enables more robust causal\ndiscovery in the small sample regime compared to the baseline algorithms.\n", "date": "2023-01-22", "categories": []}
{"id": "2305.19366", "title": "Joint Bayesian Inference of Graphical Structure and Parameters with a\n  Single Generative Flow Network", "abstract": "  Generative Flow Networks (GFlowNets), a class of generative models over\ndiscrete and structured sample spaces, have been previously applied to the\nproblem of inferring the marginal posterior distribution over the directed\nacyclic graph (DAG) of a Bayesian Network, given a dataset of observations.\nBased on recent advances extending this framework to non-discrete sample\nspaces, we propose in this paper to approximate the joint posterior over not\nonly the structure of a Bayesian Network, but also the parameters of its\nconditional probability distributions. We use a single GFlowNet whose sampling\npolicy follows a two-phase process: the DAG is first generated sequentially one\nedge at a time, and then the corresponding parameters are picked once the full\nstructure is known. Since the parameters are included in the posterior\ndistribution, this leaves more flexibility for the local probability models of\nthe Bayesian Network, making our approach applicable even to non-linear models\nparametrized by neural networks. We show that our method, called JSP-GFN,\noffers an accurate approximation of the joint posterior, while comparing\nfavorably against existing methods on both simulated and real data.\n", "date": "2023-05-30", "categories": []}
{"id": "2306.00542", "title": "Nonparametric Identifiability of Causal Representations from Unknown\n  Interventions", "abstract": "  We study causal representation learning, the task of inferring latent causal\nvariables and their causal relations from high-dimensional mixtures of the\nvariables. Prior work relies on weak supervision, in the form of counterfactual\npre- and post-intervention views or temporal structure; places restrictive\nassumptions, such as linearity, on the mixing function or latent causal model;\nor requires partial knowledge of the generative process, such as the causal\ngraph or intervention targets. We instead consider the general setting in which\nboth the causal model and the mixing function are nonparametric. The learning\nsignal takes the form of multiple datasets, or environments, arising from\nunknown interventions in the underlying causal model. Our goal is to identify\nboth the ground truth latents and their causal graph up to a set of ambiguities\nwhich we show to be irresolvable from interventional data. We study the\nfundamental setting of two causal variables and prove that the observational\ndistribution and one perfect intervention per node suffice for identifiability,\nsubject to a genericity condition. This condition rules out spurious solutions\nthat involve fine-tuning of the intervened and observational distributions,\nmirroring similar conditions for nonlinear cause-effect inference. For an\narbitrary number of variables, we show that at least one pair of distinct\nperfect interventional domains per node guarantees identifiability. Further, we\ndemonstrate that the strengths of causal influences among the latent variables\nare preserved by all equivalent solutions, rendering the inferred\nrepresentation appropriate for drawing causal conclusions from new data. Our\nstudy provides the first identifiability results for the general nonparametric\nsetting with unknown interventions, and elucidates what is possible and\nimpossible for causal representation learning without more direct supervision.\n", "date": "2023-06-01", "categories": []}
{"id": "2310.18654", "title": "Causal discovery in a complex industrial system: A time series benchmark", "abstract": "  Causal discovery outputs a causal structure, represented by a graph, from\nobserved data. For time series data, there is a variety of methods, however, it\nis difficult to evaluate these on real data as realistic use cases very rarely\ncome with a known causal graph to which output can be compared. In this paper,\nwe present a dataset from an industrial subsystem at the European Spallation\nSource along with its causal graph which has been constructed from expert\nknowledge. This provides a testbed for causal discovery from time series\nobservations of complex systems, and we believe this can help inform the\ndevelopment of causal discovery methodology.\n", "date": "2023-10-28", "categories": []}
{"id": "2208.04627", "title": "Causal Effect Identification in Uncertain Causal Networks", "abstract": "  Causal identification is at the core of the causal inference literature,\nwhere complete algorithms have been proposed to identify causal queries of\ninterest. The validity of these algorithms hinges on the restrictive assumption\nof having access to a correctly specified causal structure. In this work, we\nstudy the setting where a probabilistic model of the causal structure is\navailable. Specifically, the edges in a causal graph exist with uncertainties\nwhich may, for example, represent degree of belief from domain experts.\nAlternatively, the uncertainty about an edge may reflect the confidence of a\nparticular statistical test. The question that naturally arises in this setting\nis: Given such a probabilistic graph and a specific causal effect of interest,\nwhat is the subgraph which has the highest plausibility and for which the\ncausal effect is identifiable? We show that answering this question reduces to\nsolving an NP-complete combinatorial optimization problem which we call the\nedge ID problem. We propose efficient algorithms to approximate this problem\nand evaluate them against both real-world networks and randomly generated\ngraphs.\n", "date": "2022-08-09", "categories": []}
{"id": "2302.00993", "title": "Unpaired Multi-Domain Causal Representation Learning", "abstract": "  The goal of causal representation learning is to find a representation of\ndata that consists of causally related latent variables. We consider a setup\nwhere one has access to data from multiple domains that potentially share a\ncausal representation. Crucially, observations in different domains are assumed\nto be unpaired, that is, we only observe the marginal distribution in each\ndomain but not their joint distribution. In this paper, we give sufficient\nconditions for identifiability of the joint distribution and the shared causal\ngraph in a linear setup. Identifiability holds if we can uniquely recover the\njoint distribution and the shared causal representation from the marginal\ndistributions in each domain. We transform our identifiability results into a\npractical method to recover the shared latent causal graph.\n", "date": "2023-02-02", "categories": []}
{"id": "2310.17679", "title": "Fast Scalable and Accurate Discovery of DAGs Using the Best Order Score\n  Search and Grow-Shrink Trees", "abstract": "  Learning graphical conditional independence structures is an important\nmachine learning problem and a cornerstone of causal discovery. However, the\naccuracy and execution time of learning algorithms generally struggle to scale\nto problems with hundreds of highly connected variables -- for instance,\nrecovering brain networks from fMRI data. We introduce the best order score\nsearch (BOSS) and grow-shrink trees (GSTs) for learning directed acyclic graphs\n(DAGs) in this paradigm. BOSS greedily searches over permutations of variables,\nusing GSTs to construct and score DAGs from permutations. GSTs efficiently\ncache scores to eliminate redundant calculations. BOSS achieves\nstate-of-the-art performance in accuracy and execution time, comparing\nfavorably to a variety of combinatorial and gradient-based learning algorithms\nunder a broad range of conditions. To demonstrate its practicality, we apply\nBOSS to two sets of resting-state fMRI data: simulated data with\npseudo-empirical noise distributions derived from randomized empirical fMRI\ncortical signals and clinical data from 3T fMRI scans processed into cortical\nparcels. BOSS is available for use within the TETRAD project which includes\nPython and R wrappers.\n", "date": "2023-10-26", "categories": []}
{"id": "2310.18123", "title": "Sample Complexity Bounds for Score-Matching: Causal Discovery and\n  Generative Modeling", "abstract": "  This paper provides statistical sample complexity bounds for score-matching\nand its applications in causal discovery. We demonstrate that accurate\nestimation of the score function is achievable by training a standard deep ReLU\nneural network using stochastic gradient descent. We establish bounds on the\nerror rate of recovering causal relationships using the score-matching-based\ncausal discovery method of Rolland et al. [2022], assuming a sufficiently good\nestimation of the score function. Finally, we analyze the upper bound of\nscore-matching estimation within the score-based generative modeling, which has\nbeen applied for causal discovery but is also of independent interest within\nthe domain of generative models.\n", "date": "2023-10-27", "categories": []}
{"id": "2301.12930", "title": "Cause-Effect Inference in Location-Scale Noise Models: Maximum\n  Likelihood vs. Independence Testing", "abstract": "  A fundamental problem of causal discovery is cause-effect inference, learning\nthe correct causal direction between two random variables. Significant progress\nhas been made through modelling the effect as a function of its cause and a\nnoise term, which allows us to leverage assumptions about the generating\nfunction class. The recently introduced heteroscedastic location-scale noise\nfunctional models (LSNMs) combine expressive power with identifiability\nguarantees. LSNM model selection based on maximizing likelihood achieves\nstate-of-the-art accuracy, when the noise distributions are correctly\nspecified. However, through an extensive empirical evaluation, we demonstrate\nthat the accuracy deteriorates sharply when the form of the noise distribution\nis misspecified by the user. Our analysis shows that the failure occurs mainly\nwhen the conditional variance in the anti-causal direction is smaller than that\nin the causal direction. As an alternative, we find that causal model selection\nthrough residual independence testing is much more robust to noise\nmisspecification and misleading conditional variance.\n", "date": "2023-01-26", "categories": []}
{"id": "2310.14925", "title": "Efficient Causal Discovery for Robotics Applications", "abstract": "  Using robots for automating tasks in environments shared with humans, such as\nwarehouses, shopping centres, or hospitals, requires these robots to comprehend\nthe fundamental physical interactions among nearby agents and objects.\nSpecifically, creating models to represent cause-and-effect relationships among\nthese elements can aid in predicting unforeseen human behaviours and anticipate\nthe outcome of particular robot actions. To be suitable for robots, causal\nanalysis must be both fast and accurate, meeting real-time demands and the\nlimited computational resources typical in most robotics applications. In this\npaper, we present a practical demonstration of our approach for fast and\naccurate causal analysis, known as Filtered PCMCI (F-PCMCI), along with a\nreal-world robotics application. The provided application illustrates how our\nF-PCMCI can accurately and promptly reconstruct the causal model of a\nhuman-robot interaction scenario, which can then be leveraged to enhance the\nquality of the interaction.\n", "date": "2023-10-23", "categories": []}
{"id": "2310.14246", "title": "Shortcuts for causal discovery of nonlinear models by score matching", "abstract": "  The use of simulated data in the field of causal discovery is ubiquitous due\nto the scarcity of annotated real data. Recently, Reisach et al., 2021\nhighlighted the emergence of patterns in simulated linear data, which displays\nincreasing marginal variance in the casual direction. As an ablation in their\nexperiments, Montagna et al., 2023 found that similar patterns may emerge in\nnonlinear models for the variance of the score vector $\\nabla \\log\np_{\\mathbf{X}}$, and introduced the ScoreSort algorithm. In this work, we\nformally define and characterize this score-sortability pattern of nonlinear\nadditive noise models. We find that it defines a class of identifiable\n(bivariate) causal models overlapping with nonlinear additive noise models. We\ntheoretically demonstrate the advantages of ScoreSort in terms of statistical\nefficiency compared to prior state-of-the-art score matching-based methods and\nempirically show the score-sortability of the most common synthetic benchmarks\nin the literature. Our findings remark (1) the lack of diversity in the data as\nan important limitation in the evaluation of nonlinear causal discovery\napproaches, (2) the importance of thoroughly testing different settings within\na problem class, and (3) the importance of analyzing statistical properties in\ncausal discovery, where research is often limited to defining identifiability\nconditions of the model.\n", "date": "2023-10-22", "categories": []}
{"id": "2310.13553", "title": "On sample complexity of conditional independence testing with Von Mises\n  estimator with application to causal discovery", "abstract": "  Motivated by conditional independence testing, an essential step in\nconstraint-based causal discovery algorithms, we study the nonparametric Von\nMises estimator for the entropy of multivariate distributions built on a kernel\ndensity estimator. We establish an exponential concentration inequality for\nthis estimator. We design a test for conditional independence (CI) based on our\nestimator, called VM-CI, which achieves optimal parametric rates under\nsmoothness assumptions. Leveraging the exponential concentration, we prove a\ntight upper bound for the overall error of VM-CI. This, in turn, allows us to\ncharacterize the sample complexity of any constraint-based causal discovery\nalgorithm that uses VM-CI for CI tests. To the best of our knowledge, this is\nthe first sample complexity guarantee for causal discovery for continuous\nvariables. Furthermore, we empirically show that VM-CI outperforms other\npopular CI tests in terms of either time or sample complexity (or both), which\ntranslates to a better performance in structure learning as well.\n", "date": "2023-10-20", "categories": []}
{"id": "2302.03246", "title": "CDANs: Temporal Causal Discovery from Autocorrelated and Non-Stationary\n  Time Series Data", "abstract": "  Time series data are found in many areas of healthcare such as medical time\nseries, electronic health records (EHR), measurements of vitals, and wearable\ndevices. Causal discovery, which involves estimating causal relationships from\nobservational data, holds the potential to play a significant role in\nextracting actionable insights about human health. In this study, we present a\nnovel constraint-based causal discovery approach for autocorrelated and\nnon-stationary time series data (CDANs). Our proposed method addresses several\nlimitations of existing causal discovery methods for autocorrelated and\nnon-stationary time series data, such as high dimensionality, the inability to\nidentify lagged causal relationships, and overlooking changing modules. Our\napproach identifies lagged and instantaneous/contemporaneous causal\nrelationships along with changing modules that vary over time. The method\noptimizes the conditioning sets in a constraint-based search by considering\nlagged parents instead of conditioning on the entire past that addresses high\ndimensionality. The changing modules are detected by considering both\ncontemporaneous and lagged parents. The approach first detects the lagged\nadjacencies, then identifies the changing modules and contemporaneous\nadjacencies, and finally determines the causal direction. We extensively\nevaluated our proposed method on synthetic and real-world clinical datasets,\nand compared its performance with several baseline approaches. The experimental\nresults demonstrate the effectiveness of the proposed method in detecting\ncausal relationships and changing modules for autocorrelated and non-stationary\ntime series data.\n", "date": "2023-02-07", "categories": []}
{"id": "2310.11154", "title": "Causal discovery using dynamically requested knowledge", "abstract": "  Causal Bayesian Networks (CBNs) are an important tool for reasoning under\nuncertainty in complex real-world systems. Determining the graphical structure\nof a CBN remains a key challenge and is undertaken either by eliciting it from\nhumans, using machine learning to learn it from data, or using a combination of\nthese two approaches. In the latter case, human knowledge is generally provided\nto the algorithm before it starts, but here we investigate a novel approach\nwhere the structure learning algorithm itself dynamically identifies and\nrequests knowledge for relationships that the algorithm identifies as uncertain\nduring structure learning. We integrate this approach into the Tabu structure\nlearning algorithm and show that it offers considerable gains in structural\naccuracy, which are generally larger than those offered by existing approaches\nfor integrating knowledge. We suggest that a variant which requests only arc\norientation information may be particularly useful where the practitioner has\nlittle preexisting knowledge of the causal relationships. As well as offering\nimproved accuracy, the approach can use human expertise more effectively and\ncontributes to making the structure learning process more transparent.\n", "date": "2023-10-17", "categories": []}
{"id": "2310.10239", "title": "Structural transfer learning of non-Gaussian DAG", "abstract": "  Directed acyclic graph (DAG) has been widely employed to represent\ndirectional relationships among a set of collected nodes. Yet, the available\ndata in one single study is often limited for accurate DAG reconstruction,\nwhereas heterogeneous data may be collected from multiple relevant studies. It\nremains an open question how to pool the heterogeneous data together for better\nDAG structure reconstruction in the target study. In this paper, we first\nintroduce a novel set of structural similarity measures for DAG and then\npresent a transfer DAG learning framework by effectively leveraging information\nfrom auxiliary DAGs of different levels of similarities. Our theoretical\nanalysis shows substantial improvement in terms of DAG reconstruction in the\ntarget study, even when no auxiliary DAG is overall similar to the target DAG,\nwhich is in sharp contrast to most existing transfer learning methods. The\nadvantage of the proposed transfer DAG learning is also supported by extensive\nnumerical experiments on both synthetic data and multi-site brain functional\nconnectivity network data.\n", "date": "2023-10-16", "categories": []}
{"id": "2209.05598", "title": "Learning domain-specific causal discovery from time series", "abstract": "  Causal discovery (CD) from time-varying data is important in neuroscience,\nmedicine, and machine learning. Techniques for CD encompass randomized\nexperiments, which are generally unbiased but expensive, and algorithms such as\nGranger causality, conditional-independence-based, structural-equation-based,\nand score-based methods that are only accurate under strong assumptions made by\nhuman designers. However, as demonstrated in other areas of machine learning,\nhuman expertise is often not entirely accurate and tends to be outperformed in\ndomains with abundant data. In this study, we examine whether we can enhance\ndomain-specific causal discovery for time series using a data-driven approach.\nOur findings indicate that this procedure significantly outperforms\nhuman-designed, domain-agnostic causal discovery methods, such as Mutual\nInformation, VAR-LiNGAM, and Granger Causality on the MOS 6502 microprocessor,\nthe NetSim fMRI dataset, and the Dream3 gene dataset. We argue that, when\nfeasible, the causality field should consider a supervised approach in which\ndomain-specific CD procedures are learned from extensive datasets with known\ncausal relationships, rather than being designed by human specialists. Our\nfindings promise a new approach toward improving CD in neural and medical data\nand for the broader machine learning community.\n", "date": "2022-09-12", "categories": []}
{"id": "2310.05526", "title": "Projecting infinite time series graphs to finite marginal graphs using\n  number theory", "abstract": "  In recent years, a growing number of method and application works have\nadapted and applied the causal-graphical-model framework to time series data.\nMany of these works employ time-resolved causal graphs that extend infinitely\ninto the past and future and whose edges are repetitive in time, thereby\nreflecting the assumption of stationary causal relationships. However, most\nresults and algorithms from the causal-graphical-model framework are not\ndesigned for infinite graphs. In this work, we develop a method for projecting\ninfinite time series graphs with repetitive edges to marginal graphical models\non a finite time window. These finite marginal graphs provide the answers to\n$m$-separation queries with respect to the infinite graph, a task that was\npreviously unresolved. Moreover, we argue that these marginal graphs are useful\nfor causal discovery and causal effect estimation in time series, effectively\nenabling to apply results developed for finite graphs to the infinite graphs.\nThe projection procedure relies on finding common ancestors in the\nto-be-projected graph and is, by itself, not new. However, the projection\nprocedure has not yet been algorithmically implemented for time series graphs\nsince in these infinite graphs there can be infinite sets of paths that might\ngive rise to common ancestors. We solve the search over these possibly infinite\nsets of paths by an intriguing combination of path-finding techniques for\nfinite directed graphs and solution theory for linear Diophantine equations. By\nproviding an algorithm that carries out the projection, our paper makes an\nimportant step towards a theoretically-grounded and method-agnostic\ngeneralization of a range of causal inference methods and results to time\nseries.\n", "date": "2023-10-09", "categories": []}
{"id": "2310.03579", "title": "Causal Inference in Gene Regulatory Networks with GFlowNet: Towards\n  Scalability in Large Systems", "abstract": "  Understanding causal relationships within Gene Regulatory Networks (GRNs) is\nessential for unraveling the gene interactions in cellular processes. However,\ncausal discovery in GRNs is a challenging problem for multiple reasons\nincluding the existence of cyclic feedback loops and uncertainty that yields\ndiverse possible causal structures. Previous works in this area either ignore\ncyclic dynamics (assume acyclic structure) or struggle with scalability. We\nintroduce Swift-DynGFN as a novel framework that enhances causal structure\nlearning in GRNs while addressing scalability concerns. Specifically,\nSwift-DynGFN exploits gene-wise independence to boost parallelization and to\nlower computational cost. Experiments on real single-cell RNA velocity and\nsynthetic GRN datasets showcase the advancement in learning causal structure in\nGRNs and scalability in larger systems.\n", "date": "2023-10-05", "categories": []}
{"id": "2303.05628", "title": "On the Unlikelihood of D-Separation", "abstract": "  Causal discovery aims to recover a causal graph from data generated by it;\nconstraint based methods do so by searching for a d-separating conditioning set\nof nodes in the graph via an oracle. In this paper, we provide analytic\nevidence that on large graphs, d-separation is a rare phenomenon, even when\nguaranteed to exist, unless the graph is extremely sparse. We then provide an\nanalytic average case analysis of the PC Algorithm for causal discovery, as\nwell as a variant of the SGS Algorithm we call UniformSGS. We consider a set\n$V=\\{v_1,\\ldots,v_n\\}$ of nodes, and generate a random DAG $G=(V,E)$ where\n$(v_a, v_b) \\in E$ with i.i.d. probability $p_1$ if $a<b$ and $0$ if $a > b$.\nWe provide upper bounds on the probability that a subset of $V-\\{x,y\\}$\nd-separates $x$ and $y$, conditional on $x$ and $y$ being d-separable; our\nupper bounds decay exponentially fast to $0$ as $|V| \\rightarrow \\infty$. For\nthe PC Algorithm, while it is known that its worst-case guarantees fail on\nnon-sparse graphs, we show that the same is true for the average case, and that\nthe sparsity requirement is quite demanding: for good performance, the density\nmust go to $0$ as $|V| \\rightarrow \\infty$ even in the average case. For\nUniformSGS, while it is known that the running time is exponential for existing\nedges, we show that in the average case, that is the expected running time for\nmost non-existing edges as well.\n", "date": "2023-03-10", "categories": []}
{"id": "2310.01753", "title": "CausalTime: Realistically Generated Time-series for Benchmarking of\n  Causal Discovery", "abstract": "  Time-series causal discovery (TSCD) is a fundamental problem of machine\nlearning. However, existing synthetic datasets cannot properly evaluate or\npredict the algorithms' performance on real data. This study introduces the\nCausalTime pipeline to generate time-series that highly resemble the real data\nand with ground truth causal graphs for quantitative performance evaluation.\nThe pipeline starts from real observations in a specific scenario and produces\na matching benchmark dataset. Firstly, we harness deep neural networks along\nwith normalizing flow to accurately capture realistic dynamics. Secondly, we\nextract hypothesized causal graphs by performing importance analysis on the\nneural network or leveraging prior knowledge. Thirdly, we derive the ground\ntruth causal graphs by splitting the causal model into causal term, residual\nterm, and noise term. Lastly, using the fitted network and the derived causal\ngraph, we generate corresponding versatile time-series proper for algorithm\nassessment. In the experiments, we validate the fidelity of the generated data\nthrough qualitative and quantitative experiments, followed by a benchmarking of\nexisting TSCD algorithms using these generated datasets. CausalTime offers a\nfeasible solution to evaluating TSCD algorithms in real applications and can be\ngeneralized to a wide range of fields. For easy use of the proposed approach,\nwe also provide a user-friendly website, hosted on www.causaltime.cc.\n", "date": "2023-10-03", "categories": []}
{"id": "2308.10047", "title": "Towards Probabilistic Causal Discovery, Inference & Explanations for\n  Autonomous Drones in Mine Surveying Tasks", "abstract": "  Causal modelling offers great potential to provide autonomous agents the\nability to understand the data-generation process that governs their\ninteractions with the world. Such models capture formal knowledge as well as\nprobabilistic representations of noise and uncertainty typically encountered by\nautonomous robots in real-world environments. Thus, causality can aid\nautonomous agents in making decisions and explaining outcomes, but deploying\ncausality in such a manner introduces new challenges. Here we identify\nchallenges relating to causality in the context of a drone system operating in\na salt mine. Such environments are challenging for autonomous agents because of\nthe presence of confounders, non-stationarity, and a difficulty in building\ncomplete causal models ahead of time. To address these issues, we propose a\nprobabilistic causal framework consisting of: causally-informed POMDP planning,\nonline SCM adaptation, and post-hoc counterfactual explanations. Further, we\noutline planned experimentation to evaluate the framework integrated with a\ndrone system in simulated mine environments and on a real-world mine dataset.\n", "date": "2023-08-19", "categories": []}
{"id": "2301.10859", "title": "Salesforce CausalAI Library: A Fast and Scalable Framework for Causal\n  Analysis of Time Series and Tabular Data", "abstract": "  We introduce the Salesforce CausalAI Library, an open-source library for\ncausal analysis using observational data. It supports causal discovery and\ncausal inference for tabular and time series data, of discrete, continuous and\nheterogeneous types. This library includes algorithms that handle linear and\nnon-linear causal relationships between variables, and uses multi-processing\nfor speed-up. We also include a data generator capable of generating synthetic\ndata with specified structural equation model for the aforementioned data\nformats and types, that helps users control the ground-truth causal process\nwhile investigating various algorithms. Finally, we provide a user interface\n(UI) that allows users to perform causal analysis on data without coding. The\ngoal of this library is to provide a fast and flexible solution for a variety\nof problems in the domain of causality. This technical report describes the\nSalesforce CausalAI API along with its capabilities, the implementations of the\nsupported algorithms, and experiments demonstrating their performance and\nspeed. Our library is available at\n\\url{https://github.com/salesforce/causalai}.\n", "date": "2023-01-25", "categories": []}
{"id": "2309.13066", "title": "Causal Discovery and Counterfactual Explanations for Personalized\n  Student Learning", "abstract": "  The paper focuses on identifying the causes of student performance to provide\npersonalized recommendations for improving pass rates. We introduce the need to\nmove beyond predictive models and instead identify causal relationships. We\npropose using causal discovery techniques to achieve this. The study's main\ncontributions include using causal discovery to identify causal predictors of\nstudent performance and applying counterfactual analysis to provide\npersonalized recommendations. The paper describes the application of causal\ndiscovery methods, specifically the PC algorithm, to real-life student\nperformance data. It addresses challenges such as sample size limitations and\nemphasizes the role of domain knowledge in causal discovery. The results reveal\nthe identified causal relationships, such as the influence of earlier test\ngrades and mathematical ability on final student performance. Limitations of\nthis study include the reliance on domain expertise for accurate causal\ndiscovery, and the necessity of larger sample sizes for reliable results. The\npotential for incorrect causal structure estimations is acknowledged. A major\nchallenge remains, which is the real-time implementation and validation of\ncounterfactual recommendations. In conclusion, the paper demonstrates the value\nof causal discovery for understanding student performance and providing\npersonalized recommendations. It highlights the challenges, benefits, and\nlimitations of using causal inference in an educational context, setting the\nstage for future studies to further explore and refine these methods.\n", "date": "2023-09-18", "categories": []}
{"id": "2309.09416", "title": "Causal Discovery and Prediction: Methods and Algorithms", "abstract": "  We are not only observers but also actors of reality. Our capability to\nintervene and alter the course of some events in the space and time surrounding\nus is an essential component of how we build our model of the world. In this\ndoctoral thesis we introduce a generic a-priori assessment of each possible\nintervention, in order to select the most cost-effective interventions only,\nand avoid unnecessary systematic experimentation on the real world. Based on\nthis a-priori assessment, we propose an active learning algorithm that\nidentifies the causal relations in any given causal model, using a least cost\nsequence of interventions. There are several novel aspects introduced by our\nalgorithm. It is, in most case scenarios, able to discard many causal model\ncandidates using relatively inexpensive interventions that only test one value\nof the intervened variables. Also, the number of interventions performed by the\nalgorithm can be bounded by the number of causal model candidates. Hence, fewer\ninitial candidates (or equivalently, more prior knowledge) lead to fewer\ninterventions for causal discovery.\n  Causality is intimately related to time, as causes appear to precede their\neffects. Cyclical causal processes are a very interesting case of causality in\nrelation to time. In this doctoral thesis we introduce a formal analysis of\ntime cyclical causal settings by defining a causal analog to the purely\nobservational Dynamic Bayesian Networks, and provide a sound and complete\nalgorithm for the identification of causal effects in the cyclic setting. We\nintroduce the existence of two types of hidden confounder variables in this\nframework, which affect in substantially different ways the identification\nprocedures, a distinction with no analog in either Dynamic Bayesian Networks or\nstandard causal graphs.\n", "date": "2023-09-18", "categories": []}
{"id": "2309.08406", "title": "Constraint-Free Structure Learning with Smooth Acyclic Orientations", "abstract": "  The structure learning problem consists of fitting data generated by a\nDirected Acyclic Graph (DAG) to correctly reconstruct its arcs. In this\ncontext, differentiable approaches constrain or regularize the optimization\nproblem using a continuous relaxation of the acyclicity property. The\ncomputational cost of evaluating graph acyclicity is cubic on the number of\nnodes and significantly affects scalability. In this paper we introduce COSMO,\na constraint-free continuous optimization scheme for acyclic structure\nlearning. At the core of our method, we define a differentiable approximation\nof an orientation matrix parameterized by a single priority vector. Differently\nfrom previous work, our parameterization fits a smooth orientation matrix and\nthe resulting acyclic adjacency matrix without evaluating acyclicity at any\nstep. Despite the absence of explicit constraints, we prove that COSMO always\nconverges to an acyclic solution. In addition to being asymptotically faster,\nour empirical analysis highlights how COSMO performance on graph reconstruction\ncompares favorably with competing structure learning methods.\n", "date": "2023-09-15", "categories": []}
{"id": "2308.05969", "title": "Learning nonparametric DAGs with incremental information via high-order\n  HSIC", "abstract": "  Score-based methods for learning Bayesain networks(BN) aim to maximizing the\nglobal score functions. However, if local variables have direct and indirect\ndependence simultaneously, the global optimization on score functions misses\nedges between variables with indirect dependent relationship, of which scores\nare smaller than those with direct dependent relationship. In this paper, we\npresent an identifiability condition based on a determined subset of parents to\nidentify the underlying DAG. By the identifiability condition, we develop a\ntwo-phase algorithm namely optimal-tuning (OT) algorithm to locally amend the\nglobal optimization. In the optimal phase, an optimization problem based on\nfirst-order Hilbert-Schmidt independence criterion (HSIC) gives an estimated\nskeleton as the initial determined parents subset. In the tuning phase, the\nskeleton is locally tuned by deletion, addition and DAG-formalization\nstrategies using the theoretically proved incremental properties of high-order\nHSIC. Numerical experiments for different synthetic datasets and real-world\ndatasets show that the OT algorithm outperforms existing methods. Especially in\nSigmoid Mix model with the size of the graph being ${\\rm\\bf d=40}$, the\nstructure intervention distance (SID) of the OT algorithm is 329.7 smaller than\nthe one obtained by CAM, which indicates that the graph estimated by the OT\nalgorithm misses fewer edges compared with CAM.Source code of the OT algorithm\nis available at https://github.com/YafeiannWang/optimal-tune-algorithm.\n", "date": "2023-08-11", "categories": []}
{"id": "2309.06739", "title": "MCNS: Mining Causal Natural Structures Inside Time Series via A Novel\n  Internal Causality Scheme", "abstract": "  Causal inference permits us to discover covert relationships of various\nvariables in time series. However, in most existing works, the variables\nmentioned above are the dimensions. The causality between dimensions could be\ncursory, which hinders the comprehension of the internal relationship and the\nbenefit of the causal graph to the neural networks (NNs). In this paper, we\nfind that causality exists not only outside but also inside the time series\nbecause it reflects a succession of events in the real world. It inspires us to\nseek the relationship between internal subsequences. However, the challenges\nare the hardship of discovering causality from subsequences and utilizing the\ncausal natural structures to improve NNs. To address these challenges, we\npropose a novel framework called Mining Causal Natural Structure (MCNS), which\nis automatic and domain-agnostic and helps to find the causal natural\nstructures inside time series via the internal causality scheme. We evaluate\nthe MCNS framework and impregnation NN with MCNS on time series classification\ntasks. Experimental results illustrate that our impregnation, by refining\nattention, shape selection classification, and pruning datasets, drives NN,\neven the data itself preferable accuracy and interpretability. Besides, MCNS\nprovides an in-depth, solid summary of the time series and datasets.\n", "date": "2023-09-13", "categories": []}
{"id": "2309.05107", "title": "Nonlinear Granger Causality using Kernel Ridge Regression", "abstract": "  I introduce a novel algorithm and accompanying Python library, named\nmlcausality, designed for the identification of nonlinear Granger causal\nrelationships. This novel algorithm uses a flexible plug-in architecture that\nenables researchers to employ any nonlinear regressor as the base prediction\nmodel. Subsequently, I conduct a comprehensive performance analysis of\nmlcausality when the prediction regressor is the kernel ridge regressor with\nthe radial basis function kernel. The results demonstrate that mlcausality\nemploying kernel ridge regression achieves competitive AUC scores across a\ndiverse set of simulated data. Furthermore, mlcausality with kernel ridge\nregression yields more finely calibrated $p$-values in comparison to rival\nalgorithms. This enhancement enables mlcausality to attain superior accuracy\nscores when using intuitive $p$-value-based thresholding criteria. Finally,\nmlcausality with the kernel ridge regression exhibits significantly reduced\ncomputation times compared to existing nonlinear Granger causality algorithms.\nIn fact, in numerous instances, this innovative approach achieves superior\nsolutions within computational timeframes that are an order of magnitude\nshorter than those required by competing algorithms.\n", "date": "2023-09-10", "categories": []}
{"id": "2309.05264", "title": "Enabling Runtime Verification of Causal Discovery Algorithms with\n  Automated Conditional Independence Reasoning (Extended Version)", "abstract": "  Causal discovery is a powerful technique for identifying causal relationships\namong variables in data. It has been widely used in various applications in\nsoftware engineering. Causal discovery extensively involves conditional\nindependence (CI) tests. Hence, its output quality highly depends on the\nperformance of CI tests, which can often be unreliable in practice. Moreover,\nprivacy concerns arise when excessive CI tests are performed.\n  Despite the distinct nature between unreliable and excessive CI tests, this\npaper identifies a unified and principled approach to addressing both of them.\nGenerally, CI statements, the outputs of CI tests, adhere to Pearl's axioms,\nwhich are a set of well-established integrity constraints on conditional\nindependence. Hence, we can either detect erroneous CI statements if they\nviolate Pearl's axioms or prune excessive CI statements if they are logically\nentailed by Pearl's axioms. Holistically, both problems boil down to reasoning\nabout the consistency of CI statements under Pearl's axioms (referred to as CIR\nproblem).\n  We propose a runtime verification tool called CICheck, designed to harden\ncausal discovery algorithms from reliability and privacy perspectives. CICheck\nemploys a sound and decidable encoding scheme that translates CIR into SMT\nproblems. To solve the CIR problem efficiently, CICheck introduces a four-stage\ndecision procedure with three lightweight optimizations that actively prove or\nrefute consistency, and only resort to costly SMT-based reasoning when\nnecessary. Based on the decision procedure to CIR, CICheck includes two\nvariants: ED-CICheck and ED-CICheck, which detect erroneous CI tests (to\nenhance reliability) and prune excessive CI tests (to enhance privacy),\nrespectively. [abridged due to length limit]\n", "date": "2023-09-11", "categories": []}
{"id": "2302.12341", "title": "Rank-Based Causal Discovery for Post-Nonlinear Models", "abstract": "  Learning causal relationships from empirical observations is a central task\nin scientific research. A common method is to employ structural causal models\nthat postulate noisy functional relations among a set of interacting variables.\nTo ensure unique identifiability of causal directions, researchers consider\nrestricted subclasses of structural causal models. Post-nonlinear (PNL) causal\nmodels constitute one of the most flexible options for such restricted\nsubclasses, containing in particular the popular additive noise models as a\nfurther subclass. However, learning PNL models is not well studied beyond the\nbivariate case. The existing methods learn non-linear functional relations by\nminimizing residual dependencies and subsequently test independence from\nresiduals to determine causal orientations. However, these methods can be prone\nto overfitting and, thus, difficult to tune appropriately in practice. As an\nalternative, we propose a new approach for PNL causal discovery that uses\nrank-based methods to estimate the functional parameters. This new approach\nexploits natural invariances of PNL models and disentangles the estimation of\nthe non-linear functions from the independence tests used to find causal\norientations. We prove consistency of our method and validate our results in\nnumerical experiments.\n", "date": "2023-02-23", "categories": []}
{"id": "2309.02571", "title": "Causal Structure Recovery of Linear Dynamical Systems: An FFT based\n  Approach", "abstract": "  Learning causal effects from data is a fundamental and well-studied problem\nacross science, especially when the cause-effect relationship is static in\nnature. However, causal effect is less explored when there are dynamical\ndependencies, i.e., when dependencies exist between entities across time.\nIdentifying dynamic causal effects from time-series observations is\ncomputationally expensive when compared to the static scenario. We demonstrate\nthat the computational complexity of recovering the causation structure for the\nvector auto-regressive (VAR) model is $O(Tn^3N^2)$, where $n$ is the number of\nnodes, $T$ is the number of samples, and $N$ is the largest time-lag in the\ndependency between entities. We report a method, with a reduced complexity of\n$O(Tn^3 \\log N)$, to recover the causation structure to obtain frequency-domain\n(FD) representations of time-series. Since FFT accumulates all the time\ndependencies on every frequency, causal inference can be performed efficiently\nby considering the state variables as random variables at any given frequency.\nWe additionally show that, for systems with interactions that are LTI,\ndo-calculus machinery can be realized in the FD resulting in versions of the\nclassical single-door (with cycles), front and backdoor criteria. We\ndemonstrate, for a large class of problems, graph reconstruction using\nmultivariate Wiener projections results in a significant computational\nadvantage with $O(n)$ complexity over reconstruction algorithms such as the PC\nalgorithm which has $O(n^q)$ complexity, where $q$ is the maximum neighborhood\nsize. This advantage accrues due to some remarkable properties of the phase\nresponse of the frequency-dependent Wiener coefficients which is not present in\nany time-domain approach.\n", "date": "2023-09-05", "categories": []}
{"id": "2211.06919", "title": "Towards Privacy-Aware Causal Structure Learning in Federated Setting", "abstract": "  Causal structure learning has been extensively studied and widely used in\nmachine learning and various applications. To achieve an ideal performance,\nexisting causal structure learning algorithms often need to centralize a large\namount of data from multiple data sources. However, in the privacy-preserving\nsetting, it is impossible to centralize data from all sources and put them\ntogether as a single dataset. To preserve data privacy, federated learning as a\nnew learning paradigm has attracted much attention in machine learning in\nrecent years. In this paper, we study a privacy-aware causal structure learning\nproblem in the federated setting and propose a novel Federated PC (FedPC)\nalgorithm with two new strategies for preserving data privacy without\ncentralizing data. Specifically, we first propose a novel layer-wise\naggregation strategy for a seamless adaptation of the PC algorithm into the\nfederated learning paradigm for federated skeleton learning, then we design an\neffective strategy for learning consistent separation sets for federated edge\norientation. The extensive experiments validate that FedPC is effective for\ncausal structure learning in a federated learning setting.\n", "date": "2022-11-13", "categories": []}
{"id": "2305.03859", "title": "Open problems in causal structure learning: A case study of COVID-19 in\n  the UK", "abstract": "  Causal machine learning (ML) algorithms recover graphical structures that\ntell us something about cause-and-effect relationships. The causal\nrepresentation praovided by these algorithms enables transparency and\nexplainability, which is necessary for decision making in critical real-world\nproblems. Yet, causal ML has had limited impact in practice compared to\nassociational ML. This paper investigates the challenges of causal ML with\napplication to COVID-19 UK pandemic data. We collate data from various public\nsources and investigate what the various structure learning algorithms learn\nfrom these data. We explore the impact of different data formats on algorithms\nspanning different classes of learning, and assess the results produced by each\nalgorithm, and groups of algorithms, in terms of graphical structure, model\ndimensionality, sensitivity analysis, confounding variables, predictive and\ninterventional inference. We use these results to highlight open problems in\ncausal structure learning and directions for future research. To facilitate\nfuture work, we make all graphs, models, data sets, and source code publicly\navailable online.\n", "date": "2023-05-05", "categories": []}
{"id": "2309.01392", "title": "Differentiable Bayesian Structure Learning with Acyclicity Assurance", "abstract": "  Score-based approaches in the structure learning task are thriving because of\ntheir scalability. Continuous relaxation has been the key reason for this\nadvancement. Despite achieving promising outcomes, most of these methods are\nstill struggling to ensure that the graphs generated from the latent space are\nacyclic by minimizing a defined score. There has also been another trend of\npermutation-based approaches, which concern the search for the topological\nordering of the variables in the directed acyclic graph in order to limit the\nsearch space of the graph. In this study, we propose an alternative approach\nfor strictly constraining the acyclicty of the graphs with an integration of\nthe knowledge from the topological orderings. Our approach can reduce inference\ncomplexity while ensuring the structures of the generated graphs to be acyclic.\nOur empirical experiments with simulated and real-world data show that our\napproach can outperform related Bayesian score-based approaches.\n", "date": "2023-09-04", "categories": []}
{"id": "2309.03092", "title": "Establishing Markov Equivalence in Cyclic Directed Graphs", "abstract": "  We present a new, efficient procedure to establish Markov equivalence between\ndirected graphs that may or may not contain cycles under the\n\\textit{d}-separation criterion. It is based on the Cyclic Equivalence Theorem\n(CET) in the seminal works on cyclic models by Thomas Richardson in the mid\n'90s, but now rephrased from an ancestral perspective. The resulting\ncharacterization leads to a procedure for establishing Markov equivalence\nbetween graphs that no longer requires tests for d-separation, leading to a\nsignificantly reduced algorithmic complexity. The conceptually simplified\ncharacterization may help to reinvigorate theoretical research towards sound\nand complete cyclic discovery in the presence of latent confounders. This\nversion includes a correction to rule (iv) in Theorem 1, and the subsequent\nadjustment in part 2 of Algorithm 2.\n", "date": "2023-09-01", "categories": []}
{"id": "2308.08556", "title": "Causally Linking Health Application Data and Personal Information\n  Management Tools", "abstract": "  The proliferation of consumer health devices such as smart watches, sleep\nmonitors, smart scales, etc, in many countries, has not only led to growing\ninterest in health monitoring, but also to the development of a countless\nnumber of ``smart'' applications to support the exploration of such data by\nmembers of the general public, sometimes with integration into professional\nhealth services. While a variety of health data streams has been made available\nby such devices to users, these streams are often presented as separate\ntime-series visualizations, in which the potential relationships between health\nvariables are not explicitly made visible. Furthermore, despite the fact that\nother aspects of life, such as work and social connectivity, have become\nincreasingly digitised, health and well-being applications make little use of\nthe potentially useful contextual information provided by widely used personal\ninformation management tools, such as shared calendar and email systems. This\npaper presents a framework for the integration of these diverse data sources,\nanalytic and visualization tools, with inference methods and graphical user\ninterfaces to help users by highlighting causal connections among such\ntime-series.\n", "date": "2023-08-11", "categories": []}
{"id": "2305.05890", "title": "CUTS+: High-dimensional Causal Discovery from Irregular Time-series", "abstract": "  Causal discovery in time-series is a fundamental problem in the machine\nlearning community, enabling causal reasoning and decision-making in complex\nscenarios. Recently, researchers successfully discover causality by combining\nneural networks with Granger causality, but their performances degrade largely\nwhen encountering high-dimensional data because of the highly redundant network\ndesign and huge causal graphs. Moreover, the missing entries in the\nobservations further hamper the causal structural learning. To overcome these\nlimitations, We propose CUTS+, which is built on the Granger-causality-based\ncausal discovery method CUTS and raises the scalability by introducing a\ntechnique called Coarse-to-fine-discovery (C2FD) and leveraging a\nmessage-passing-based graph neural network (MPGNN). Compared to previous\nmethods on simulated, quasi-real, and real datasets, we show that CUTS+ largely\nimproves the causal discovery performance on high-dimensional data with\ndifferent types of irregular sampling.\n", "date": "2023-05-10", "categories": []}
{"id": "2308.08148", "title": "Hierarchical Topological Ordering with Conditional Independence Test for\n  Limited Time Series", "abstract": "  Learning directed acyclic graphs (DAGs) to identify causal relations\nunderlying observational data is crucial but also poses significant challenges.\nRecently, topology-based methods have emerged as a two-step approach to\ndiscovering DAGs by first learning the topological ordering of variables and\nthen eliminating redundant edges, while ensuring that the graph remains\nacyclic. However, one limitation is that these methods would generate numerous\nspurious edges that require subsequent pruning. To overcome this limitation, in\nthis paper, we propose an improvement to topology-based methods by introducing\nlimited time series data, consisting of only two cross-sectional records that\nneed not be adjacent in time and are subject to flexible timing. By\nincorporating conditional instrumental variables as exogenous interventions, we\naim to identify descendant nodes for each variable. Following this line, we\npropose a hierarchical topological ordering algorithm with conditional\nindependence test (HT-CIT), which enables the efficient learning of sparse DAGs\nwith a smaller search space compared to other popular approaches. The HT-CIT\nalgorithm greatly reduces the number of edges that need to be pruned. Empirical\nresults from synthetic and real-world datasets demonstrate the superiority of\nthe proposed HT-CIT algorithm.\n", "date": "2023-08-16", "categories": []}
{"id": "2308.07346", "title": "Py-Tetrad and RPy-Tetrad: A New Python Interface with R Support for\n  Tetrad Causal Search", "abstract": "  We give novel Python and R interfaces for the (Java) Tetrad project for\ncausal modeling, search, and estimation. The Tetrad project is a mainstay in\nthe literature, having been under consistent development for over 30 years.\nSome of its algorithms are now classics, like PC and FCI; others are recent\ndevelopments. It is increasingly the case, however, that researchers need to\naccess the underlying Java code from Python or R. Existing methods for doing\nthis are inadequate. We provide new, up-to-date methods using the JPype\nPython-Java interface and the Reticulate Python-R interface, directly solving\nthese issues. With the addition of some simple tools and the provision of\nworking examples for both Python and R, using JPype and Reticulate to interface\nPython and R with Tetrad is straightforward and intuitive.\n", "date": "2023-08-13", "categories": []}
{"id": "2305.02640", "title": "Towards Causal Representation Learning and Deconfounding from Indefinite\n  Data", "abstract": "  Owing to the cross-pollination between causal discovery and deep learning,\nnon-statistical data (e.g., images, text, etc.) encounters significant\nconflicts in terms of properties and methods with traditional causal data. To\nunify these data types of varying forms, we redefine causal data from two novel\nperspectives and then propose three data paradigms. Among them, the indefinite\ndata (like dialogues or video sources) induce low sample utilization and\nincapability of the distribution assumption, both leading to the fact that\nlearning causal representation from indefinite data is, as of yet, largely\nunexplored. We design the causal strength variational model to settle down\nthese two problems. Specifically, we leverage the causal strength instead of\nindependent noise as the latent variable to construct evidence lower bound. By\nthis design ethos, The causal strengths of different structures are regarded as\na distribution and can be expressed as a 2D matrix. Moreover, considering the\nlatent confounders, we disentangle the causal graph G into two relation\nsubgraphs O and C. O contains pure relations between observed variables, while\nC represents the relations from latent variables to observed variables. We\nimplement the above designs as a dynamic variational inference model, tailored\nto learn causal representation from indefinite data under latent confounding.\nFinally, we conduct comprehensive experiments on synthetic and real-world data\nto demonstrate the effectiveness of our method.\n", "date": "2023-05-04", "categories": []}
{"id": "2302.10331", "title": "Causal Razors", "abstract": "  When performing causal discovery, assumptions have to be made on how the true\ncausal mechanism corresponds to the underlying joint probability distribution.\nThese assumptions are labeled as causal razors in this work. We review numerous\ncausal razors that appeared in the literature, and offer a comprehensive\nlogical comparison of them. In particular, we scrutinize an unpopular causal\nrazor, namely parameter minimality, in multinomial causal models and its\nlogical relations with other well-studied causal razors. Our logical result\nposes a dilemma in selecting a reasonable scoring criterion for score-based\ncasual search algorithms.\n", "date": "2023-02-20", "categories": []}
{"id": "2303.10112", "title": "Causal Discovery from Temporal Data: An Overview and New Perspectives", "abstract": "  Temporal data, representing chronological observations of complex systems,\nhas always been a typical data structure that can be widely generated by many\ndomains, such as industry, medicine and finance. Analyzing this type of data is\nextremely valuable for various applications. Thus, different temporal data\nanalysis tasks, eg, classification, clustering and prediction, have been\nproposed in the past decades. Among them, causal discovery, learning the causal\nrelations from temporal data, is considered an interesting yet critical task\nand has attracted much research attention. Existing causal discovery works can\nbe divided into two highly correlated categories according to whether the\ntemporal data is calibrated, ie, multivariate time series causal discovery, and\nevent sequence causal discovery. However, most previous surveys are only\nfocused on the time series causal discovery and ignore the second category. In\nthis paper, we specify the correlation between the two categories and provide a\nsystematical overview of existing solutions. Furthermore, we provide public\ndatasets, evaluation metrics and new perspectives for temporal data causal\ndiscovery.\n", "date": "2023-03-17", "categories": []}
{"id": "2307.04988", "title": "Benchmarking Bayesian Causal Discovery Methods for Downstream Treatment\n  Effect Estimation", "abstract": "  The practical utility of causality in decision-making is widespread and\nbrought about by the intertwining of causal discovery and causal inference.\nNevertheless, a notable gap exists in the evaluation of causal discovery\nmethods, where insufficient emphasis is placed on downstream inference. To\naddress this gap, we evaluate seven established baseline causal discovery\nmethods including a newly proposed method based on GFlowNets, on the downstream\ntask of treatment effect estimation. Through the implementation of a\ndistribution-level evaluation, we offer valuable and unique insights into the\nefficacy of these causal discovery methods for treatment effect estimation,\nconsidering both synthetic and real-world scenarios, as well as low-data\nscenarios. The results of our study demonstrate that some of the algorithms\nstudied are able to effectively capture a wide range of useful and diverse ATE\nmodes, while some tend to learn many low-probability modes which impacts the\n(unrelaxed) recall and precision.\n", "date": "2023-07-11", "categories": []}
{"id": "2307.15678", "title": "Case Studies of Causal Discovery from IT Monitoring Time Series", "abstract": "  Information technology (IT) systems are vital for modern businesses, handling\ndata storage, communication, and process automation. Monitoring these systems\nis crucial for their proper functioning and efficiency, as it allows collecting\nextensive observational time series data for analysis. The interest in causal\ndiscovery is growing in IT monitoring systems as knowing causal relations\nbetween different components of the IT system helps in reducing downtime,\nenhancing system performance and identifying root causes of anomalies and\nincidents. It also allows proactive prediction of future issues through\nhistorical data analysis. Despite its potential benefits, applying causal\ndiscovery algorithms on IT monitoring data poses challenges, due to the\ncomplexity of the data. For instance, IT monitoring data often contains\nmisaligned time series, sleeping time series, timestamp errors and missing\nvalues. This paper presents case studies on applying causal discovery\nalgorithms to different IT monitoring datasets, highlighting benefits and\nongoing challenges.\n", "date": "2023-07-28", "categories": []}
{"id": "2307.13757", "title": "UPREVE: An End-to-End Causal Discovery Benchmarking System", "abstract": "  Discovering causal relationships in complex socio-behavioral systems is\nchallenging but essential for informed decision-making. We present Upload,\nPREprocess, Visualize, and Evaluate (UPREVE), a user-friendly web-based\ngraphical user interface (GUI) designed to simplify the process of causal\ndiscovery. UPREVE allows users to run multiple algorithms simultaneously,\nvisualize causal relationships, and evaluate the accuracy of learned causal\ngraphs. With its accessible interface and customizable features, UPREVE\nempowers researchers and practitioners in social computing and\nbehavioral-cultural modeling (among others) to explore and understand causal\nrelationships effectively. Our proposed solution aims to make causal discovery\nmore accessible and user-friendly, enabling users to gain valuable insights for\nbetter decision-making.\n", "date": "2023-07-25", "categories": []}
{"id": "2305.16165", "title": "A Conceptual Model for End-to-End Causal Discovery in Knowledge Tracing", "abstract": "  In this paper, we take a preliminary step towards solving the problem of\ncausal discovery in knowledge tracing, i.e., finding the underlying causal\nrelationship among different skills from real-world student response data. This\nproblem is important since it can potentially help us understand the causal\nrelationship between different skills without extensive A/B testing, which can\npotentially help educators to design better curricula according to skill\nprerequisite information. Specifically, we propose a conceptual solution, a\nnovel causal gated recurrent unit (GRU) module in a modified deep knowledge\ntracing model, which uses i) a learnable permutation matrix for causal ordering\namong skills and ii) an optionally learnable lower-triangular matrix for causal\nstructure among skills. We also detail how to learn the model parameters in an\nend-to-end, differentiable way. Our solution placed among the top entries in\nTask 3 of the NeurIPS 2022 Challenge on Causal Insights for Learning Paths in\nEducation. We detail preliminary experiments as evaluated on the challenge's\npublic leaderboard since the ground truth causal structure has not been\npublicly released, making detailed local evaluation impossible.\n", "date": "2023-05-11", "categories": []}
{"id": "2307.09770", "title": "Perturbing a Neural Network to Infer Effective Connectivity: Evidence\n  from Synthetic EEG Data", "abstract": "  Identifying causal relationships among distinct brain areas, known as\neffective connectivity, holds key insights into the brain's information\nprocessing and cognitive functions. Electroencephalogram (EEG) signals exhibit\nintricate dynamics and inter-areal interactions within the brain. However,\nmethods for characterizing nonlinear causal interactions among multiple brain\nregions remain relatively underdeveloped. In this study, we proposed a\ndata-driven framework to infer effective connectivity by perturbing the trained\nneural networks. Specifically, we trained neural networks (i.e., CNN, vanilla\nRNN, GRU, LSTM, and Transformer) to predict future EEG signals according to\nhistorical data and perturbed the networks' input to obtain effective\nconnectivity (EC) between the perturbed EEG channel and the rest of the\nchannels. The EC reflects the causal impact of perturbing one node on others.\nThe performance was tested on the synthetic EEG generated by a\nbiological-plausible Jansen-Rit model. CNN and Transformer obtained the best\nperformance on both 3-channel and 90-channel synthetic EEG data, outperforming\nthe classical Granger causality method. Our work demonstrated the potential of\nperturbing an artificial neural network, learned to predict future system\ndynamics, to uncover the underlying causal structure.\n", "date": "2023-07-19", "categories": []}
{"id": "2211.16596", "title": "Towards Dynamic Causal Discovery with Rare Events: A Nonparametric\n  Conditional Independence Test", "abstract": "  Causal phenomena associated with rare events occur across a wide range of\nengineering problems, such as risk-sensitive safety analysis, accident analysis\nand prevention, and extreme value theory. However, current methods for causal\ndiscovery are often unable to uncover causal links, between random variables in\na dynamic setting, that manifest only when the variables first experience\nlow-probability realizations. To address this issue, we introduce a novel\nstatistical independence test on data collected from time-invariant dynamical\nsystems in which rare but consequential events occur. In particular, we exploit\nthe time-invariance of the underlying data to construct a superimposed dataset\nof the system state before rare events happen at different timesteps. We then\ndesign a conditional independence test on the reorganized data. We provide\nnon-asymptotic sample complexity bounds for the consistency of our method, and\nvalidate its performance across various simulated and real-world datasets,\nincluding incident data collected from the Caltrans Performance Measurement\nSystem (PeMS). Code containing the datasets and experiments is publicly\navailable.\n", "date": "2022-11-29", "categories": []}
{"id": "2307.07973", "title": "Heteroscedastic Causal Structure Learning", "abstract": "  Heretofore, learning the directed acyclic graphs (DAGs) that encode the\ncause-effect relationships embedded in observational data is a computationally\nchallenging problem. A recent trend of studies has shown that it is possible to\nrecover the DAGs with polynomial time complexity under the equal variances\nassumption. However, this prohibits the heteroscedasticity of the noise, which\nallows for more flexible modeling capabilities, but at the same time is\nsubstantially more challenging to handle. In this study, we tackle the\nheteroscedastic causal structure learning problem under Gaussian noises. By\nexploiting the normality of the causal mechanisms, we can recover a valid\ncausal ordering, which can uniquely identify the causal DAG using a series of\nconditional independence tests. The result is HOST (Heteroscedastic causal\nSTructure learning), a simple yet effective causal structure learning algorithm\nthat scales polynomially in both sample size and dimensionality. In addition,\nvia extensive empirical evaluations on a wide range of both controlled and real\ndatasets, we show that the proposed HOST method is competitive with\nstate-of-the-art approaches in both the causal order learning and structure\nlearning problems.\n", "date": "2023-07-16", "categories": []}
{"id": "2307.04353", "title": "On Sufficient Graphical Models", "abstract": "  We introduce a sufficient graphical model by applying the recently developed\nnonlinear sufficient dimension reduction techniques to the evaluation of\nconditional independence. The graphical model is nonparametric in nature, as it\ndoes not make distributional assumptions such as the Gaussian or copula\nGaussian assumptions. However, unlike a fully nonparametric graphical model,\nwhich relies on the high-dimensional kernel to characterize conditional\nindependence, our graphical model is based on conditional independence given a\nset of sufficient predictors with a substantially reduced dimension. In this\nway we avoid the curse of dimensionality that comes with a high-dimensional\nkernel. We develop the population-level properties, convergence rate, and\nvariable selection consistency of our estimate. By simulation comparisons and\nan analysis of the DREAM 4 Challenge data set, we demonstrate that our method\noutperforms the existing methods when the Gaussian or copula Gaussian\nassumptions are violated, and its performance remains excellent in the\nhigh-dimensional setting.\n", "date": "2023-07-10", "categories": []}
{"id": "2307.02390", "title": "Causal Discovery with Language Models as Imperfect Experts", "abstract": "  Understanding the causal relationships that underlie a system is a\nfundamental prerequisite to accurate decision-making. In this work, we explore\nhow expert knowledge can be used to improve the data-driven identification of\ncausal graphs, beyond Markov equivalence classes. In doing so, we consider a\nsetting where we can query an expert about the orientation of causal\nrelationships between variables, but where the expert may provide erroneous\ninformation. We propose strategies for amending such expert knowledge based on\nconsistency properties, e.g., acyclicity and conditional independencies in the\nequivalence class. We then report a case study, on real data, where a large\nlanguage model is used as an imperfect expert.\n", "date": "2023-07-05", "categories": []}
{"id": "2210.17283", "title": "CausalBench: A Large-scale Benchmark for Network Inference from\n  Single-cell Perturbation Data", "abstract": "  Causal inference is a vital aspect of multiple scientific disciplines and is\nroutinely applied to high-impact applications such as medicine. However,\nevaluating the performance of causal inference methods in real-world\nenvironments is challenging due to the need for observations under both\ninterventional and control conditions. Traditional evaluations conducted on\nsynthetic datasets do not reflect the performance in real-world systems. To\naddress this, we introduce CausalBench, a benchmark suite for evaluating\nnetwork inference methods on real-world interventional data from large-scale\nsingle-cell perturbation experiments. CausalBench incorporates\nbiologically-motivated performance metrics, including new distribution-based\ninterventional metrics. A systematic evaluation of state-of-the-art causal\ninference methods using our CausalBench suite highlights how poor scalability\nof current methods limits performance. Moreover, methods that use\ninterventional information do not outperform those that only use observational\ndata, contrary to what is observed on synthetic benchmarks. Thus, CausalBench\nopens new avenues in causal network inference research and provides a\nprincipled and reliable way to track progress in leveraging real-world\ninterventional data.\n", "date": "2022-10-31", "categories": []}
{"id": "2307.00227", "title": "Causal Structure Learning by Using Intersection of Markov Blankets", "abstract": "  In this paper, we introduce a novel causal structure learning algorithm\ncalled Endogenous and Exogenous Markov Blankets Intersection (EEMBI), which\ncombines the properties of Bayesian networks and Structural Causal Models\n(SCM). Furthermore, we propose an extended version of EEMBI, namely EEMBI-PC,\nwhich integrates the last step of the PC algorithm into EEMBI.\n", "date": "2023-07-01", "categories": []}
{"id": "2304.05294", "title": "Selecting Robust Features for Machine Learning Applications using\n  Multidata Causal Discovery", "abstract": "  Robust feature selection is vital for creating reliable and interpretable\nMachine Learning (ML) models. When designing statistical prediction models in\ncases where domain knowledge is limited and underlying interactions are\nunknown, choosing the optimal set of features is often difficult. To mitigate\nthis issue, we introduce a Multidata (M) causal feature selection approach that\nsimultaneously processes an ensemble of time series datasets and produces a\nsingle set of causal drivers. This approach uses the causal discovery\nalgorithms PC1 or PCMCI that are implemented in the Tigramite Python package.\nThese algorithms utilize conditional independence tests to infer parts of the\ncausal graph. Our causal feature selection approach filters out\ncausally-spurious links before passing the remaining causal features as inputs\nto ML models (Multiple linear regression, Random Forest) that predict the\ntargets. We apply our framework to the statistical intensity prediction of\nWestern Pacific Tropical Cyclones (TC), for which it is often difficult to\naccurately choose drivers and their dimensionality reduction (time lags,\nvertical levels, and area-averaging). Using more stringent significance\nthresholds in the conditional independence tests helps eliminate spurious\ncausal relationships, thus helping the ML model generalize better to unseen TC\ncases. M-PC1 with a reduced number of features outperforms M-PCMCI, non-causal\nML, and other feature selection methods (lagged correlation, random), even\nslightly outperforming feature selection based on eXplainable Artificial\nIntelligence. The optimal causal drivers obtained from our causal feature\nselection help improve our understanding of underlying relationships and\nsuggest new potential drivers of TC intensification.\n", "date": "2023-04-11", "categories": []}
{"id": "2306.17378", "title": "Global Optimality in Bivariate Gradient-based DAG Learning", "abstract": "  Recently, a new class of non-convex optimization problems motivated by the\nstatistical problem of learning an acyclic directed graphical model from data\nhas attracted significant interest. While existing work uses standard\nfirst-order optimization schemes to solve this problem, proving the global\noptimality of such approaches has proven elusive. The difficulty lies in the\nfact that unlike other non-convex problems in the literature, this problem is\nnot \"benign\", and possesses multiple spurious solutions that standard\napproaches can easily get trapped in. In this paper, we prove that a simple\npath-following optimization scheme globally converges to the global minimum of\nthe population loss in the bivariate setting.\n", "date": "2023-06-30", "categories": []}
{"id": "2208.04405", "title": "Recovering the Graph Underlying Networked Dynamical Systems under\n  Partial Observability: A Deep Learning Approach", "abstract": "  We study the problem of graph structure identification, i.e., of recovering\nthe graph of dependencies among time series. We model these time series data as\ncomponents of the state of linear stochastic networked dynamical systems. We\nassume partial observability, where the state evolution of only a subset of\nnodes comprising the network is observed. We devise a new feature vector\ncomputed from the observed time series and prove that these features are\nlinearly separable, i.e., there exists a hyperplane that separates the cluster\nof features associated with connected pairs of nodes from those associated with\ndisconnected pairs. This renders the features amenable to train a variety of\nclassifiers to perform causal inference. In particular, we use these features\nto train Convolutional Neural Networks (CNNs). The resulting causal inference\nmechanism outperforms state-of-the-art counterparts w.r.t. sample-complexity.\nThe trained CNNs generalize well over structurally distinct networks (dense or\nsparse) and noise-level profiles. Remarkably, they also generalize well to\nreal-world networks while trained over a synthetic network (realization of a\nrandom graph). Finally, the proposed method consistently reconstructs the graph\nin a pairwise manner, that is, by deciding if an edge or arrow is present or\nabsent in each pair of nodes, from the corresponding time series of each pair.\nThis fits the framework of large-scale systems, where observation or processing\nof all nodes in the network is prohibitive.\n", "date": "2022-08-08", "categories": []}
{"id": "2210.06201", "title": "Diffusion Models for Causal Discovery via Topological Ordering", "abstract": "  Discovering causal relations from observational data becomes possible with\nadditional assumptions such as considering the functional relations to be\nconstrained as nonlinear with additive noise (ANM). Even with strong\nassumptions, causal discovery involves an expensive search problem over the\nspace of directed acyclic graphs (DAGs). \\emph{Topological ordering} approaches\nreduce the optimisation space of causal discovery by searching over a\npermutation rather than graph space. For ANMs, the \\emph{Hessian} of the data\nlog-likelihood can be used for finding leaf nodes in a causal graph, allowing\nits topological ordering. However, existing computational methods for obtaining\nthe Hessian still do not scale as the number of variables and the number of\nsamples increase. Therefore, inspired by recent innovations in diffusion\nprobabilistic models (DPMs), we propose \\emph{DiffAN}\\footnote{Implementation\nis available at \\url{https://github.com/vios-s/DiffAN} .}, a topological\nordering algorithm that leverages DPMs for learning a Hessian function. We\nintroduce theory for updating the learned Hessian without re-training the\nneural network, and we show that computing with a subset of samples gives an\naccurate approximation of the ordering, which allows scaling to datasets with\nmore samples and variables. We show empirically that our method scales\nexceptionally well to datasets with up to $500$ nodes and up to $10^5$ samples\nwhile still performing on par over small datasets with state-of-the-art causal\ndiscovery methods. Implementation is available at\nhttps://github.com/vios-s/DiffAN .\n", "date": "2022-10-12", "categories": []}
{"id": "2306.13932", "title": "Tuning structure learning algorithms with out-of-sample and resampling\n  strategies", "abstract": "  One of the challenges practitioners face when applying structure learning\nalgorithms to their data involves determining a set of hyperparameters;\notherwise, a set of hyperparameter defaults is assumed. The optimal\nhyperparameter configuration often depends on multiple factors, including the\nsize and density of the usually unknown underlying true graph, the sample size\nof the input data, and the structure learning algorithm. We propose a novel\nhyperparameter tuning method, called the Out-of-sample Tuning for Structure\nLearning (OTSL), that employs out-of-sample and resampling strategies to\nestimate the optimal hyperparameter configuration for structure learning, given\nthe input data set and structure learning algorithm. Synthetic experiments show\nthat employing OTSL as a means to tune the hyperparameters of hybrid and\nscore-based structure learning algorithms leads to improvements in graphical\naccuracy compared to the state-of-the-art. We also illustrate the applicability\nof this approach to real datasets from different disciplines.\n", "date": "2023-06-24", "categories": []}
{"id": "2301.11214", "title": "Returning The Favour: When Regression Benefits From Probabilistic Causal\n  Knowledge", "abstract": "  A directed acyclic graph (DAG) provides valuable prior knowledge that is\noften discarded in regression tasks in machine learning. We show that the\nindependences arising from the presence of collider structures in DAGs provide\nmeaningful inductive biases, which constrain the regression hypothesis space\nand improve predictive performance. We introduce collider regression, a\nframework to incorporate probabilistic causal knowledge from a collider in a\nregression problem. When the hypothesis space is a reproducing kernel Hilbert\nspace, we prove a strictly positive generalisation benefit under mild\nassumptions and provide closed-form estimators of the empirical risk minimiser.\nExperiments on synthetic and climate model data demonstrate performance gains\nof the proposed methodology.\n", "date": "2023-01-26", "categories": []}
{"id": "2306.09643", "title": "BISCUIT: Causal Representation Learning from Binary Interactions", "abstract": "  Identifying the causal variables of an environment and how to intervene on\nthem is of core value in applications such as robotics and embodied AI. While\nan agent can commonly interact with the environment and may implicitly perturb\nthe behavior of some of these causal variables, often the targets it affects\nremain unknown. In this paper, we show that causal variables can still be\nidentified for many common setups, e.g., additive Gaussian noise models, if the\nagent's interactions with a causal variable can be described by an unknown\nbinary variable. This happens when each causal variable has two different\nmechanisms, e.g., an observational and an interventional one. Using this\nidentifiability result, we propose BISCUIT, a method for simultaneously\nlearning causal variables and their corresponding binary interaction variables.\nOn three robotic-inspired datasets, BISCUIT accurately identifies causal\nvariables and can even be scaled to complex, realistic environments for\nembodied AI.\n", "date": "2023-06-16", "categories": []}
{"id": "2306.09302", "title": "Knowledge Guided Representation Learning and Causal Structure Learning\n  in Soil Science", "abstract": "  An improved understanding of soil can enable more sustainable land-use\npractices. Nevertheless, soil is called a complex, living medium due to the\ncomplex interaction of different soil processes that limit our understanding of\nsoil. Process-based models and analyzing observed data provide two avenues for\nimproving our understanding of soil processes. Collecting observed data is\ncost-prohibitive but reflects real-world behavior, while process-based models\ncan be used to generate ample synthetic data which may not be representative of\nreality. We propose a framework, knowledge-guided representation learning, and\ncausal structure learning (KGRCL), to accelerate scientific discoveries in soil\nscience. The framework improves representation learning for simulated soil\nprocesses via conditional distribution matching with observed soil processes.\nSimultaneously, the framework leverages both observed and simulated data to\nlearn a causal structure among the soil processes. The learned causal graph is\nmore representative of ground truth than other graphs generated from other\ncausal discovery methods. Furthermore, the learned causal graph is leveraged in\na supervised learning setup to predict the impact of fertilizer use and\nchanging weather on soil carbon. We present the results in five different\nlocations to show the improvement in the prediction performance in\nout-of-sample and few-shots setting.\n", "date": "2023-06-15", "categories": []}
{"id": "2206.06744", "title": "Counting Markov Equivalent Directed Acyclic Graphs Consistent with\n  Background Knowledge", "abstract": "  A polynomial-time exact algorithm for counting the number of directed acyclic\ngraphs in a Markov equivalence class was recently given by Wien\\\"obst, Bannach,\nand Li\\'skiewicz (AAAI 2021). In this paper, we consider the more general\nproblem of counting the number of directed acyclic graphs in a Markov\nequivalence class when the directions of some of the edges are also fixed (this\nsetting arises, for example, when interventional data is partially available).\nThis problem has been shown in earlier work to be complexity-theoretically\nhard. In contrast, we show that the problem is nevertheless tractable in an\ninteresting class of instances, by establishing that it is ``fixed-parameter\ntractable''. In particular, our counting algorithm runs in time that is bounded\nby a polynomial in the size of the graph, where the degree of the polynomial\ndoes \\emph{not} depend upon the number of additional edges provided as input.\n", "date": "2022-06-14", "categories": []}
{"id": "2206.06354", "title": "Differentiable and Transportable Structure Learning", "abstract": "  Directed acyclic graphs (DAGs) encode a lot of information about a particular\ndistribution in their structure. However, compute required to infer these\nstructures is typically super-exponential in the number of variables, as\ninference requires a sweep of a combinatorially large space of potential\nstructures. That is, until recent advances made it possible to search this\nspace using a differentiable metric, drastically reducing search time. While\nthis technique -- named NOTEARS -- is widely considered a seminal work in\nDAG-discovery, it concedes an important property in favour of\ndifferentiability: transportability. To be transportable, the structures\ndiscovered on one dataset must apply to another dataset from the same domain.\nWe introduce D-Struct which recovers transportability in the discovered\nstructures through a novel architecture and loss function while remaining fully\ndifferentiable. Because D-Struct remains differentiable, our method can be\neasily adopted in existing differentiable architectures, as was previously done\nwith NOTEARS. In our experiments, we empirically validate D-Struct with respect\nto edge accuracy and structural Hamming distance in a variety of settings.\n", "date": "2022-06-13", "categories": []}
{"id": "2211.16467", "title": "Linear Causal Disentanglement via Interventions", "abstract": "  Causal disentanglement seeks a representation of data involving latent\nvariables that relate to one another via a causal model. A representation is\nidentifiable if both the latent model and the transformation from latent to\nobserved variables are unique. In this paper, we study observed variables that\nare a linear transformation of a linear latent causal model. Data from\ninterventions are necessary for identifiability: if one latent variable is\nmissing an intervention, we show that there exist distinct models that cannot\nbe distinguished. Conversely, we show that a single intervention on each latent\nvariable is sufficient for identifiability. Our proof uses a generalization of\nthe RQ decomposition of a matrix that replaces the usual orthogonal and upper\ntriangular conditions with analogues depending on a partial order on the rows\nof the matrix, with partial order determined by a latent causal model. We\ncorroborate our theoretical results with a method for causal disentanglement\nthat accurately recovers a latent causal model.\n", "date": "2022-11-29", "categories": []}
{"id": "2306.05781", "title": "Adaptivity Complexity for Causal Graph Discovery", "abstract": "  Causal discovery from interventional data is an important problem, where the\ntask is to design an interventional strategy that learns the hidden ground\ntruth causal graph $G(V,E)$ on $|V| = n$ nodes while minimizing the number of\nperformed interventions. Most prior interventional strategies broadly fall into\ntwo categories: non-adaptive and adaptive. Non-adaptive strategies decide on a\nsingle fixed set of interventions to be performed while adaptive strategies can\ndecide on which nodes to intervene on sequentially based on past interventions.\nWhile adaptive algorithms may use exponentially fewer interventions than their\nnon-adaptive counterparts, there are practical concerns that constrain the\namount of adaptivity allowed. Motivated by this trade-off, we study the problem\nof $r$-adaptivity, where the algorithm designer recovers the causal graph under\na total of $r$ sequential rounds whilst trying to minimize the total number of\ninterventions. For this problem, we provide a $r$-adaptive algorithm that\nachieves $O(\\min\\{r,\\log n\\} \\cdot n^{1/\\min\\{r,\\log n\\}})$ approximation with\nrespect to the verification number, a well-known lower bound for adaptive\nalgorithms. Furthermore, for every $r$, we show that our approximation is\ntight. Our definition of $r$-adaptivity interpolates nicely between the\nnon-adaptive ($r=1$) and fully adaptive ($r=n$) settings where our\napproximation simplifies to $O(n)$ and $O(\\log n)$ respectively, matching the\nbest-known approximation guarantees for both extremes. Our results also extend\nnaturally to the bounded size interventions.\n", "date": "2023-06-09", "categories": []}
{"id": "2306.04792", "title": "On the Use of Generative Models in Observational Causal Analysis", "abstract": "  The use of a hypothetical generative model was been suggested for causal\nanalysis of observational data. The very assumption of a particular model is a\ncommitment to a certain set of variables and therefore to a certain set of\npossible causes. Estimating the joint probability distribution of can be useful\nfor predicting values of variables in view of the observed values of others,\nbut it is not sufficient for inferring causal relationships. The model\ndescribes a single observable distribution and cannot a chain of effects of\nintervention that deviate from the observed distribution.\n", "date": "2023-06-07", "categories": []}
{"id": "2306.02831", "title": "MM-DAG: Multi-task DAG Learning for Multi-modal Data -- with Application\n  for Traffic Congestion Analysis", "abstract": "  This paper proposes to learn Multi-task, Multi-modal Direct Acyclic Graphs\n(MM-DAGs), which are commonly observed in complex systems, e.g., traffic,\nmanufacturing, and weather systems, whose variables are multi-modal with\nscalars, vectors, and functions. This paper takes the traffic congestion\nanalysis as a concrete case, where a traffic intersection is usually regarded\nas a DAG. In a road network of multiple intersections, different intersections\ncan only have some overlapping and distinct variables observed. For example, a\nsignalized intersection has traffic light-related variables, whereas\nunsignalized ones do not. This encourages the multi-task design: with each DAG\nas a task, the MM-DAG tries to learn the multiple DAGs jointly so that their\nconsensus and consistency are maximized. To this end, we innovatively propose a\nmulti-modal regression for linear causal relationship description of different\nvariables. Then we develop a novel Causality Difference (CD) measure and its\ndifferentiable approximator. Compared with existing SOTA measures, CD can\npenalize the causal structural difference among DAGs with distinct nodes and\ncan better consider the uncertainty of causal orders. We rigidly prove our\ndesign's topological interpretation and consistency properties. We conduct\nthorough simulations and one case study to show the effectiveness of our\nMM-DAG. The code is available under https://github.com/Lantian72/MM-DAG\n", "date": "2023-06-05", "categories": []}
{"id": "2306.01638", "title": "Do we become wiser with time? On causal equivalence with tiered\n  background knowledge", "abstract": "  Equivalence classes of DAGs (represented by CPDAGs) may be too large to\nprovide useful causal information. Here, we address incorporating tiered\nbackground knowledge yielding restricted equivalence classes represented by\n'tiered MPDAGs'. Tiered knowledge leads to considerable gains in\ninformativeness and computational efficiency: We show that construction of\ntiered MPDAGs only requires application of Meek's 1st rule, and that tiered\nMPDAGs (unlike general MPDAGs) are chain graphs with chordal components. This\nentails simplifications e.g. of determining valid adjustment sets for causal\neffect estimation. Further, we characterise when one tiered ordering is more\ninformative than another, providing insights into useful aspects of background\nknowledge.\n", "date": "2023-06-02", "categories": []}
{"id": "2210.09054", "title": "On the Identifiability and Estimation of Causal Location-Scale Noise\n  Models", "abstract": "  We study the class of location-scale or heteroscedastic noise models (LSNMs),\nin which the effect $Y$ can be written as a function of the cause $X$ and a\nnoise source $N$ independent of $X$, which may be scaled by a positive function\n$g$ over the cause, i.e., $Y = f(X) + g(X)N$. Despite the generality of the\nmodel class, we show the causal direction is identifiable up to some\npathological cases. To empirically validate these theoretical findings, we\npropose two estimators for LSNMs: an estimator based on (non-linear) feature\nmaps, and one based on neural networks. Both model the conditional distribution\nof $Y$ given $X$ as a Gaussian parameterized by its natural parameters. When\nthe feature maps are correctly specified, we prove that our estimator is\njointly concave, and a consistent estimator for the cause-effect identification\ntask. Although the the neural network does not inherit those guarantees, it can\nfit functions of arbitrary complexity, and reaches state-of-the-art performance\nacross benchmarks.\n", "date": "2022-10-13", "categories": []}
{"id": "2306.00624", "title": "From Temporal to Contemporaneous Iterative Causal Discovery in the\n  Presence of Latent Confounders", "abstract": "  We present a constraint-based algorithm for learning causal structures from\nobservational time-series data, in the presence of latent confounders. We\nassume a discrete-time, stationary structural vector autoregressive process,\nwith both temporal and contemporaneous causal relations. One may ask if\ntemporal and contemporaneous relations should be treated differently. The\npresented algorithm gradually refines a causal graph by learning long-term\ntemporal relations before short-term ones, where contemporaneous relations are\nlearned last. This ordering of causal relations to be learnt leads to a\nreduction in the required number of statistical tests. We validate this\nreduction empirically and demonstrate that it leads to higher accuracy for\nsynthetic data and more plausible causal graphs for real-world data compared to\nstate-of-the-art algorithms.\n", "date": "2023-06-01", "categories": []}
{"id": "2305.19582", "title": "Causal Discovery with Latent Confounders Based on Higher-Order Cumulants", "abstract": "  Causal discovery with latent confounders is an important but challenging task\nin many scientific areas. Despite the success of some overcomplete independent\ncomponent analysis (OICA) based methods in certain domains, they are\ncomputationally expensive and can easily get stuck into local optima. We notice\nthat interestingly, by making use of higher-order cumulants, there exists a\nclosed-form solution to OICA in specific cases, e.g., when the mixing procedure\nfollows the One-Latent-Component structure. In light of the power of the\nclosed-form solution to OICA corresponding to the One-Latent-Component\nstructure, we formulate a way to estimate the mixing matrix using the\nhigher-order cumulants, and further propose the testable One-Latent-Component\ncondition to identify the latent variables and determine causal orders. By\niteratively removing the share identified latent components, we successfully\nextend the results on the One-Latent-Component structure to the\nMulti-Latent-Component structure and finally provide a practical and\nasymptotically correct algorithm to learn the causal structure with latent\nvariables. Experimental results illustrate the asymptotic correctness and\neffectiveness of the proposed method.\n", "date": "2023-05-31", "categories": []}
{"id": "2305.19588", "title": "Active causal structure learning with advice", "abstract": "  We introduce the problem of active causal structure learning with advice. In\nthe typical well-studied setting, the learning algorithm is given the essential\ngraph for the observational distribution and is asked to recover the underlying\ncausal directed acyclic graph (DAG) $G^*$ while minimizing the number of\ninterventions made. In our setting, we are additionally given side information\nabout $G^*$ as advice, e.g. a DAG $G$ purported to be $G^*$. We ask whether the\nlearning algorithm can benefit from the advice when it is close to being\ncorrect, while still having worst-case guarantees even when the advice is\narbitrarily bad. Our work is in the same space as the growing body of research\non algorithms with predictions. When the advice is a DAG $G$, we design an\nadaptive search algorithm to recover $G^*$ whose intervention cost is at most\n$O(\\max\\{1, \\log \\psi\\})$ times the cost for verifying $G^*$; here, $\\psi$ is a\ndistance measure between $G$ and $G^*$ that is upper bounded by the number of\nvariables $n$, and is exactly 0 when $G=G^*$. Our approximation factor matches\nthe state-of-the-art for the advice-less setting.\n", "date": "2023-05-31", "categories": []}
{"id": "2305.19695", "title": "Causal discovery for time series with constraint-based model and PMIME\n  measure", "abstract": "  Causality defines the relationship between cause and effect. In multivariate\ntime series field, this notion allows to characterize the links between several\ntime series considering temporal lags. These phenomena are particularly\nimportant in medicine to analyze the effect of a drug for example, in\nmanufacturing to detect the causes of an anomaly in a complex system or in\nsocial sciences... Most of the time, studying these complex systems is made\nthrough correlation only. But correlation can lead to spurious relationships.\nTo circumvent this problem, we present in this paper a novel approach for\ndiscovering causality in time series data that combines a causal discovery\nalgorithm with an information theoretic-based measure. Hence the proposed\nmethod allows inferring both linear and non-linear relationships and building\nthe underlying causal graph. We evaluate the performance of our approach on\nseveral simulated data sets, showing promising results.\n", "date": "2023-05-31", "categories": []}
{"id": "2305.19802", "title": "Neuro-Causal Factor Analysis", "abstract": "  Factor analysis (FA) is a statistical tool for studying how observed\nvariables with some mutual dependences can be expressed as functions of\nmutually independent unobserved factors, and it is widely applied throughout\nthe psychological, biological, and physical sciences. We revisit this classic\nmethod from the comparatively new perspective given by advancements in causal\ndiscovery and deep learning, introducing a framework for Neuro-Causal Factor\nAnalysis (NCFA). Our approach is fully nonparametric: it identifies factors via\nlatent causal discovery methods and then uses a variational autoencoder (VAE)\nthat is constrained to abide by the Markov factorization of the distribution\nwith respect to the learned graph. We evaluate NCFA on real and synthetic data\nsets, finding that it performs comparably to standard VAEs on data\nreconstruction tasks but with the advantages of sparser architecture, lower\nmodel complexity, and causal interpretability. Unlike traditional FA methods,\nour proposed NCFA method allows learning and reasoning about the latent factors\nunderlying observed data from a justifiably causal perspective, even when the\nrelations between factors and measurements are highly nonlinear.\n", "date": "2023-05-31", "categories": []}
{"id": "2305.20043", "title": "Deception by Omission: Using Adversarial Missingness to Poison Causal\n  Structure Learning", "abstract": "  Inference of causal structures from observational data is a key component of\ncausal machine learning; in practice, this data may be incompletely observed.\nPrior work has demonstrated that adversarial perturbations of completely\nobserved training data may be used to force the learning of inaccurate causal\nstructural models (SCMs). However, when the data can be audited for correctness\n(e.g., it is crytographically signed by its source), this adversarial mechanism\nis invalidated. This work introduces a novel attack methodology wherein the\nadversary deceptively omits a portion of the true training data to bias the\nlearned causal structures in a desired manner. Theoretically sound attack\nmechanisms are derived for the case of arbitrary SCMs, and a sample-efficient\nlearning-based heuristic is given for Gaussian SCMs. Experimental validation of\nthese approaches on real and synthetic data sets demonstrates the effectiveness\nof adversarial missingness attacks at deceiving popular causal structure\nlearning algorithms.\n", "date": "2023-05-31", "categories": []}
{"id": "2305.04445", "title": "New metrics and search algorithms for weighted causal DAGs", "abstract": "  Recovering causal relationships from data is an important problem. Using\nobservational data, one can typically only recover causal graphs up to a Markov\nequivalence class and additional assumptions or interventional data are needed\nfor complete recovery. In this work, under some standard assumptions, we study\ncausal graph discovery via adaptive interventions with node-dependent\ninterventional costs. For this setting, we show that no algorithm can achieve\nan approximation guarantee that is asymptotically better than linear in the\nnumber of vertices with respect to the verification number; a well-established\nbenchmark for adaptive search algorithms. Motivated by this negative result, we\ndefine a new benchmark that captures the worst-case interventional cost for any\nsearch algorithm. Furthermore, with respect to this new benchmark, we provide\nadaptive search algorithms that achieve logarithmic approximations under\nvarious settings: atomic, bounded size interventions and generalized cost\nobjectives.\n", "date": "2023-05-08", "categories": []}
{"id": "2305.18410", "title": "Understanding Breast Cancer Survival: Using Causality and Language\n  Models on Multi-omics Data", "abstract": "  The need for more usable and explainable machine learning models in\nhealthcare increases the importance of developing and utilizing causal\ndiscovery algorithms, which aim to discover causal relations by analyzing\nobservational data. Explainable approaches aid clinicians and biologists in\npredicting the prognosis of diseases and suggesting proper treatments. However,\nvery little research has been conducted at the crossroads between causal\ndiscovery, genomics, and breast cancer, and we aim to bridge this gap.\nMoreover, evaluation of causal discovery methods on real data is in general\nnotoriously difficult because ground-truth causal relations are usually\nunknown, and accordingly, in this paper, we also propose to address the\nevaluation problem with large language models. In particular, we exploit\nsuitable causal discovery algorithms to investigate how various perturbations\nin the genome can affect the survival of patients diagnosed with breast cancer.\nWe used three main causal discovery algorithms: PC, Greedy Equivalence Search\n(GES), and a Generalized Precision Matrix-based one. We experiment with a\nsubset of The Cancer Genome Atlas, which contains information about mutations,\ncopy number variations, protein levels, and gene expressions for 705 breast\ncancer patients. Our findings reveal important factors related to the vital\nstatus of patients using causal discovery algorithms. However, the reliability\nof these results remains a concern in the medical domain. Accordingly, as\nanother contribution of the work, the results are validated through language\nmodels trained on biomedical literature, such as BlueBERT and other large\nlanguage models trained on medical corpora. Our results profess proper\nutilization of causal discovery algorithms and language models for revealing\nreliable causal relations for clinical applications.\n", "date": "2023-05-28", "categories": []}
{"id": "2305.17277", "title": "Optimizing NOTEARS Objectives via Topological Swaps", "abstract": "  Recently, an intriguing class of non-convex optimization problems has emerged\nin the context of learning directed acyclic graphs (DAGs). These problems\ninvolve minimizing a given loss or score function, subject to a non-convex\ncontinuous constraint that penalizes the presence of cycles in a graph. In this\nwork, we delve into the optimization challenges associated with this class of\nnon-convex programs. To address these challenges, we propose a bi-level\nalgorithm that leverages the non-convex constraint in a novel way. The outer\nlevel of the algorithm optimizes over topological orders by iteratively\nswapping pairs of nodes within the topological order of a DAG. A key innovation\nof our approach is the development of an effective method for generating a set\nof candidate swapping pairs for each iteration. At the inner level, given a\ntopological order, we utilize off-the-shelf solvers that can handle linear\nconstraints. The key advantage of our proposed algorithm is that it is\nguaranteed to find a local minimum or a KKT point under weaker conditions\ncompared to previous work and finds solutions with lower scores. Extensive\nexperiments demonstrate that our method outperforms state-of-the-art approaches\nin terms of achieving a better score. Additionally, our method can also be used\nas a post-processing algorithm to significantly improve the score of other\nalgorithms. Code implementing the proposed method is available at\nhttps://github.com/duntrain/topo.\n", "date": "2023-05-26", "categories": []}
{"id": "2305.18210", "title": "Learning Causal Graphs via Monotone Triangular Transport Maps", "abstract": "  We study the problem of causal structure learning from data using optimal\ntransport (OT). Specifically, we first provide a constraint-based method which\nbuilds upon lower-triangular monotone parametric transport maps to design\nconditional independence tests which are agnostic to the noise distribution. We\nprovide an algorithm for causal discovery up to Markov Equivalence with no\nassumptions on the structural equations/noise distributions, which allows for\nsettings with latent variables. Our approach also extends to score-based causal\ndiscovery by providing a novel means for defining scores. This allows us to\nuniquely recover the causal graph under additional identifiability and\nstructural assumptions, such as additive noise or post-nonlinear models. We\nprovide experimental results to compare the proposed approach with the state of\nthe art on both synthetic and real-world datasets.\n", "date": "2023-05-26", "categories": []}
{"id": "2305.13341", "title": "Discovering Causal Relations and Equations from Data", "abstract": "  Physics is a field of science that has traditionally used the scientific\nmethod to answer questions about why natural phenomena occur and to make\ntestable models that explain the phenomena. Discovering equations, laws and\nprinciples that are invariant, robust and causal explanations of the world has\nbeen fundamental in physical sciences throughout the centuries. Discoveries\nemerge from observing the world and, when possible, performing interventional\nstudies in the system under study. With the advent of big data and the use of\ndata-driven methods, causal and equation discovery fields have grown and made\nprogress in computer science, physics, statistics, philosophy, and many applied\nfields. All these domains are intertwined and can be used to discover causal\nrelations, physical laws, and equations from observational data. This paper\nreviews the concepts, methods, and relevant works on causal and equation\ndiscovery in the broad field of Physics and outlines the most important\nchallenges and promising future lines of research. We also provide a taxonomy\nfor observational causal and equation discovery, point out connections, and\nshowcase a complete set of case studies in Earth and climate sciences, fluid\ndynamics and mechanics, and the neurosciences. This review demonstrates that\ndiscovering fundamental laws and causal relations by observing natural\nphenomena is being revolutionised with the efficient exploitation of\nobservational data, modern machine learning algorithms and the interaction with\ndomain knowledge. Exciting times are ahead with many challenges and\nopportunities to improve our understanding of complex systems.\n", "date": "2023-05-21", "categories": []}
{"id": "2305.10041", "title": "Risk Assessment of Lymph Node Metastases in Endometrial Cancer Patients:\n  A Causal Approach", "abstract": "  Assessing the pre-operative risk of lymph node metastases in endometrial\ncancer patients is a complex and challenging task. In principle, machine\nlearning and deep learning models are flexible and expressive enough to capture\nthe dynamics of clinical risk assessment. However, in this setting we are\nlimited to observational data with quality issues, missing values, small sample\nsize and high dimensionality: we cannot reliably learn such models from limited\nobservational data with these sources of bias. Instead, we choose to learn a\ncausal Bayesian network to mitigate the issues above and to leverage the prior\nknowledge on endometrial cancer available from clinicians and physicians. We\nintroduce a causal discovery algorithm for causal Bayesian networks based on\nbootstrap resampling, as opposed to the single imputation used in related\nworks. Moreover, we include a context variable to evaluate whether selection\nbias results in learning spurious associations. Finally, we discuss the\nstrengths and limitations of our findings in light of the presence of missing\ndata that may be missing-not-at-random, which is common in real-world clinical\nsettings.\n", "date": "2023-05-17", "categories": []}
{"id": "2208.09104", "title": "A Causality-Based Learning Approach for Discovering the Underlying\n  Dynamics of Complex Systems from Partial Observations with Stochastic\n  Parameterization", "abstract": "  Discovering the underlying dynamics of complex systems from data is an\nimportant practical topic. Constrained optimization algorithms are widely\nutilized and lead to many successes. Yet, such purely data-driven methods may\nbring about incorrect physics in the presence of random noise and cannot easily\nhandle the situation with incomplete data. In this paper, a new iterative\nlearning algorithm for complex turbulent systems with partial observations is\ndeveloped that alternates between identifying model structures, recovering\nunobserved variables, and estimating parameters. First, a causality-based\nlearning approach is utilized for the sparse identification of model\nstructures, which takes into account certain physics knowledge that is\npre-learned from data. It has unique advantages in coping with indirect\ncoupling between features and is robust to the stochastic noise. A practical\nalgorithm is designed to facilitate the causal inference for high-dimensional\nsystems. Next, a systematic nonlinear stochastic parameterization is built to\ncharacterize the time evolution of the unobserved variables. Closed analytic\nformula via an efficient nonlinear data assimilation is exploited to sample the\ntrajectories of the unobserved variables, which are then treated as synthetic\nobservations to advance a rapid parameter estimation. Furthermore, the\nlocalization of the state variable dependence and the physics constraints are\nincorporated into the learning procedure, which mitigate the curse of\ndimensionality and prevent the finite time blow-up issue. Numerical experiments\nshow that the new algorithm succeeds in identifying the model structure and\nproviding suitable stochastic parameterizations for many complex nonlinear\nsystems with chaotic dynamics, spatiotemporal multiscale structures,\nintermittency, and extreme events.\n", "date": "2022-08-19", "categories": []}
{"id": "2305.06894", "title": "Reinterpreting causal discovery as the task of predicting unobserved\n  joint statistics", "abstract": "  If $X,Y,Z$ denote sets of random variables, two different data sources may\ncontain samples from $P_{X,Y}$ and $P_{Y,Z}$, respectively. We argue that\ncausal discovery can help inferring properties of the `unobserved joint\ndistributions' $P_{X,Y,Z}$ or $P_{X,Z}$. The properties may be conditional\nindependences (as in `integrative causal inference') or also quantitative\nstatements about dependences.\n  More generally, we define a learning scenario where the input is a subset of\nvariables and the label is some statistical property of that subset. Sets of\njointly observed variables define the training points, while unobserved sets\nare possible test points. To solve this learning task, we infer, as an\nintermediate step, a causal model from the observations that then entails\nproperties of unobserved sets. Accordingly, we can define the VC dimension of a\nclass of causal models and derive generalization bounds for the predictions.\n  Here, causal discovery becomes more modest and better accessible to empirical\ntests than usual: rather than trying to find a causal hypothesis that is `true'\na causal hypothesis is {\\it useful} whenever it correctly predicts statistical\nproperties of unobserved joint distributions. This way, a sparse causal graph\nthat omits weak influences may be more useful than a dense one (despite being\nless accurate) because it is able to reconstruct the full joint distribution\nfrom marginal distributions of smaller subsets.\n  Within such a `pragmatic' application of causal discovery, some popular\nheuristic approaches become justified in retrospect. It is, for instance,\nallowed to infer DAGs from partial correlations instead of conditional\nindependences if the DAGs are only used to predict partial correlations.\n", "date": "2023-05-11", "categories": []}
{"id": "2305.05986", "title": "Structural Hawkes Processes for Learning Causal Structure from\n  Discrete-Time Event Sequences", "abstract": "  Learning causal structure among event types from discrete-time event\nsequences is a particularly important but challenging task. Existing methods,\nsuch as the multivariate Hawkes processes based methods, mostly boil down to\nlearning the so-called Granger causality which assumes that the cause event\nhappens strictly prior to its effect event. Such an assumption is often\nuntenable beyond applications, especially when dealing with discrete-time event\nsequences in low-resolution; and typical discrete Hawkes processes mainly\nsuffer from identifiability issues raised by the instantaneous effect, i.e.,\nthe causal relationship that occurred simultaneously due to the low-resolution\ndata will not be captured by Granger causality. In this work, we propose\nStructure Hawkes Processes (SHPs) that leverage the instantaneous effect for\nlearning the causal structure among events type in discrete-time event\nsequence. The proposed method is featured with the minorization-maximization of\nthe likelihood function and a sparse optimization scheme. Theoretical results\nshow that the instantaneous effect is a blessing rather than a curse, and the\ncausal structure is identifiable under the existence of the instantaneous\neffect. Experiments on synthetic and real-world data verify the effectiveness\nof the proposed method.\n", "date": "2023-05-10", "categories": []}
{"id": "2305.03662", "title": "Causal Discovery with Stage Variables for Health Time Series", "abstract": "  Using observational data to learn causal relationships is essential when\nrandomized experiments are not possible, such as in healthcare. Discovering\ncausal relationships in time-series health data is even more challenging when\nrelationships change over the course of a disease, such as medications that are\nmost effective early on or for individuals with severe disease. Stage variables\nsuch as weeks of pregnancy, disease stages, or biomarkers like HbA1c, can\ninfluence what causal relationships are true for a patient. However, causal\ninference within each stage is often not possible due to limited amounts of\ndata, and combining all data risks incorrect or missed inferences. To address\nthis, we propose Causal Discovery with Stage Variables (CDSV), which uses stage\nvariables to reweight data from multiple time-series while accounting for\ndifferent causal relationships in each stage. In simulated data, CDSV discovers\nmore causes with fewer false discoveries compared to baselines, in eICU it has\na lower FDR than baselines, and in MIMIC-III it discovers more clinically\nrelevant causes of high blood pressure.\n", "date": "2023-05-05", "categories": []}
{"id": "2301.08230", "title": "Score-based Causal Representation Learning with Interventions", "abstract": "  This paper studies the causal representation learning problem when the latent\ncausal variables are observed indirectly through an unknown linear\ntransformation. The objectives are: (i) recovering the unknown linear\ntransformation (up to scaling) and (ii) determining the directed acyclic graph\n(DAG) underlying the latent variables. Sufficient conditions for DAG recovery\nare established, and it is shown that a large class of non-linear models in the\nlatent space (e.g., causal mechanisms parameterized by two-layer neural\nnetworks) satisfy these conditions. These sufficient conditions ensure that the\neffect of an intervention can be detected correctly from changes in the score.\nCapitalizing on this property, recovering a valid transformation is facilitated\nby the following key property: any valid transformation renders latent\nvariables' score function to necessarily have the minimal variations across\ndifferent interventional environments. This property is leveraged for perfect\nrecovery of the latent DAG structure using only \\emph{soft} interventions. For\nthe special case of stochastic \\emph{hard} interventions, with an additional\nhypothesis testing step, one can also uniquely recover the linear\ntransformation up to scaling and a valid causal ordering.\n", "date": "2023-01-19", "categories": []}
{"id": "2304.14109", "title": "The Structurally Complex with Additive Parent Causality (SCARY) Dataset", "abstract": "  Causal datasets play a critical role in advancing the field of causality.\nHowever, existing datasets often lack the complexity of real-world issues such\nas selection bias, unfaithful data, and confounding. To address this gap, we\npropose a new synthetic causal dataset, the Structurally Complex with Additive\npaRent causalitY (SCARY) dataset, which includes the following features. The\ndataset comprises 40 scenarios, each generated with three different seeds,\nallowing researchers to leverage relevant subsets of the dataset. Additionally,\nwe use two different data generation mechanisms for generating the causal\nrelationship between parents and child nodes, including linear and mixed causal\nmechanisms with multiple sub-types. Our dataset generator is inspired by the\nCausal Discovery Toolbox and generates only additive models. The dataset has a\nVarsortability of 0.5. Our SCARY dataset provides a valuable resource for\nresearchers to explore causal discovery under more realistic scenarios. The\ndataset is available at https://github.com/JayJayc/SCARY.\n", "date": "2023-04-27", "categories": []}
{"id": "2304.12523", "title": "CIMLA: Interpretable AI for inference of differential causal networks", "abstract": "  The discovery of causal relationships from high-dimensional data is a major\nopen problem in bioinformatics. Machine learning and feature attribution models\nhave shown great promise in this context but lack causal interpretation. Here,\nwe show that a popular feature attribution model estimates a causal quantity\nreflecting the influence of one variable on another, under certain assumptions.\nWe leverage this insight to implement a new tool, CIMLA, for discovering\ncondition-dependent changes in causal relationships. We then use CIMLA to\nidentify differences in gene regulatory networks between biological conditions,\na problem that has received great attention in recent years. Using extensive\nbenchmarking on simulated data sets, we show that CIMLA is more robust to\nconfounding variables and is more accurate than leading methods. Finally, we\nemploy CIMLA to analyze a previously published single-cell RNA-seq data set\ncollected from subjects with and without Alzheimer's disease (AD), discovering\nseveral potential regulators of AD.\n", "date": "2023-04-25", "categories": []}
{"id": "2301.11336", "title": "Causal Structural Learning from Time Series: A Convex Optimization\n  Approach", "abstract": "  Structural learning, which aims to learn directed acyclic graphs (DAGs) from\nobservational data, is foundational to causal reasoning and scientific\ndiscovery. Recent advancements formulate structural learning into a continuous\noptimization problem; however, DAG learning remains a highly non-convex\nproblem, and there has not been much work on leveraging well-developed convex\noptimization techniques for causal structural learning. We fill this gap by\nproposing a data-adaptive linear approach for causal structural learning from\ntime series data, which can be conveniently cast into a convex optimization\nproblem using a recently developed monotone operator variational inequality\n(VI) formulation. Furthermore, we establish non-asymptotic recovery guarantee\nof the VI-based approach and show the superior performance of our proposed\nmethod on structure recovery over existing methods via extensive numerical\nexperiments.\n", "date": "2023-01-26", "categories": []}
{"id": "2304.05524", "title": "Understanding Causality with Large Language Models: Feasibility and\n  Opportunities", "abstract": "  We assess the ability of large language models (LLMs) to answer causal\nquestions by analyzing their strengths and weaknesses against three types of\ncausal question. We believe that current LLMs can answer causal questions with\nexisting causal knowledge as combined domain experts. However, they are not yet\nable to provide satisfactory answers for discovering new knowledge or for\nhigh-stakes decision-making tasks with high precision. We discuss possible\nfuture directions and opportunities, such as enabling explicit and implicit\ncausal modules as well as deep causal-aware LLMs. These will not only enable\nLLMs to answer many different types of causal questions for greater impact but\nalso enable LLMs to be more trustworthy and efficient in general.\n", "date": "2023-04-11", "categories": []}
{"id": "2304.05823", "title": "DiscoGen: Learning to Discover Gene Regulatory Networks", "abstract": "  Accurately inferring Gene Regulatory Networks (GRNs) is a critical and\nchallenging task in biology. GRNs model the activatory and inhibitory\ninteractions between genes and are inherently causal in nature. To accurately\nidentify GRNs, perturbational data is required. However, most GRN discovery\nmethods only operate on observational data. Recent advances in neural\nnetwork-based causal discovery methods have significantly improved causal\ndiscovery, including handling interventional data, improvements in performance\nand scalability. However, applying state-of-the-art (SOTA) causal discovery\nmethods in biology poses challenges, such as noisy data and a large number of\nsamples. Thus, adapting the causal discovery methods is necessary to handle\nthese challenges. In this paper, we introduce DiscoGen, a neural network-based\nGRN discovery method that can denoise gene expression measurements and handle\ninterventional data. We demonstrate that our model outperforms SOTA neural\nnetwork-based causal discovery methods.\n", "date": "2023-04-12", "categories": []}
{"id": "2304.05976", "title": "Bayesian Causal Inference in Doubly Gaussian DAG-probit Models", "abstract": "  We consider modeling a binary response variable together with a set of\ncovariates for two groups under observational data. The grouping variable can\nbe the confounding variable (the common cause of treatment and outcome),\ngender, case/control, ethnicity, etc. Given the covariates and a binary latent\nvariable, the goal is to construct two directed acyclic graphs (DAGs), while\nsharing some common parameters. The set of nodes, which represent the\nvariables, are the same for both groups but the directed edges between nodes,\nwhich represent the causal relationships between the variables, can be\npotentially different. For each group, we also estimate the effect size for\neach node. We assume that each group follows a Gaussian distribution under its\nDAG. Given the parent nodes, the joint distribution of DAG is conditionally\nindependent due to the Markov property of DAGs. We introduce the concept of\nGaussian DAG-probit model under two groups and hence doubly Gaussian DAG-probit\nmodel. To estimate the skeleton of the DAGs and the model parameters, we took\nsamples from the posterior distribution of doubly Gaussian DAG-probit model via\nMCMC method. We validated the proposed method using a comprehensive simulation\nexperiment and applied it on two real datasets. Furthermore, we validated the\nresults of the real data analysis using well-known experimental studies to show\nthe value of the proposed grouping variable in the causality domain.\n", "date": "2023-04-12", "categories": []}
{"id": "2304.03382", "title": "Scalable Causal Discovery with Score Matching", "abstract": "  This paper demonstrates how to discover the whole causal graph from the\nsecond derivative of the log-likelihood in observational non-linear additive\nGaussian noise models. Leveraging scalable machine learning approaches to\napproximate the score function $\\nabla \\log p(\\mathbf{X})$, we extend the work\nof Rolland et al. (2022) that only recovers the topological order from the\nscore and requires an expensive pruning step removing spurious edges among\nthose admitted by the ordering. Our analysis leads to DAS (acronym for\nDiscovery At Scale), a practical algorithm that reduces the complexity of the\npruning by a factor proportional to the graph size. In practice, DAS achieves\ncompetitive accuracy with current state-of-the-art while being over an order of\nmagnitude faster. Overall, our approach enables principled and scalable causal\ndiscovery, significantly lowering the compute bar.\n", "date": "2023-04-06", "categories": []}
{"id": "2304.03265", "title": "Causal Discovery with Score Matching on Additive Models with Arbitrary\n  Noise", "abstract": "  Causal discovery methods are intrinsically constrained by the set of\nassumptions needed to ensure structure identifiability. Moreover additional\nrestrictions are often imposed in order to simplify the inference task: this is\nthe case for the Gaussian noise assumption on additive non-linear models, which\nis common to many causal discovery approaches. In this paper we show the\nshortcomings of inference under this hypothesis, analyzing the risk of edge\ninversion under violation of Gaussianity of the noise terms. Then, we propose a\nnovel method for inferring the topological ordering of the variables in the\ncausal graph, from data generated according to an additive non-linear model\nwith a generic noise distribution. This leads to NoGAM (Not only Gaussian\nAdditive noise Models), a causal discovery algorithm with a minimal set of\nassumptions and state of the art performance, experimentally benchmarked on\nsynthetic data.\n", "date": "2023-04-06", "categories": []}
{"id": "2304.02286", "title": "A step towards the applicability of algorithms based on invariant causal\n  learning on observational data", "abstract": "  Machine learning can benefit from causal discovery for interpretation and\nfrom causal inference for generalization. In this line of research, a few\ninvariant learning algorithms for out-of-distribution (OOD) generalization have\nbeen proposed by using multiple training environments to find invariant\nrelationships. Some of them are focused on causal discovery as Invariant Causal\nPrediction (ICP), which finds causal parents of a variable of interest, and\nsome directly provide a causal optimal predictor that generalizes well in OOD\nenvironments as Invariant Risk Minimization (IRM). This group of algorithms\nworks under the assumption of multiple environments that represent different\ninterventions in the causal inference context. Those environments are not\nnormally available when working with observational data and real-world\napplications. Here we propose a method to generate them in an efficient way. We\nassess the performance of this unsupervised learning problem by implementing\nICP on simulated data. We also show how to apply ICP efficiently integrated\nwith our method for causal discovery. Finally, we proposed an improved version\nof our method in combination with ICP for datasets with multiple covariates\nwhere ICP and other causal discovery methods normally degrade in performance.\n", "date": "2023-04-05", "categories": []}
{"id": "2303.12703", "title": "Causal Reasoning in the Presence of Latent Confounders via Neural ADMG\n  Learning", "abstract": "  Latent confounding has been a long-standing obstacle for causal reasoning\nfrom observational data. One popular approach is to model the data using\nacyclic directed mixed graphs (ADMGs), which describe ancestral relations\nbetween variables using directed and bidirected edges. However, existing\nmethods using ADMGs are based on either linear functional assumptions or a\ndiscrete search that is complicated to use and lacks computational tractability\nfor large datasets. In this work, we further extend the existing body of work\nand develop a novel gradient-based approach to learning an ADMG with non-linear\nfunctional relations from observational data. We first show that the presence\nof latent confounding is identifiable under the assumptions of bow-free ADMGs\nwith non-linear additive noise models. With this insight, we propose a novel\nneural causal model based on autoregressive flows for ADMG learning. This not\nonly enables us to determine complex causal structural relationships behind the\ndata in the presence of latent confounding, but also estimate their functional\nrelationships (hence treatment effects) simultaneously. We further validate our\napproach via experiments on both synthetic and real-world datasets, and\ndemonstrate the competitive performance against relevant baselines.\n", "date": "2023-03-22", "categories": []}
{"id": "2208.12210", "title": "Learning Relational Causal Models with Cycles through Relational\n  Acyclification", "abstract": "  In real-world phenomena which involve mutual influence or causal effects\nbetween interconnected units, equilibrium states are typically represented with\ncycles in graphical models. An expressive class of graphical models, relational\ncausal models, can represent and reason about complex dynamic systems\nexhibiting such cycles or feedback loops. Existing cyclic causal discovery\nalgorithms for learning causal models from observational data assume that the\ndata instances are independent and identically distributed which makes them\nunsuitable for relational causal models. At the same time, causal discovery\nalgorithms for relational causal models assume acyclicity. In this work, we\nexamine the necessary and sufficient conditions under which a constraint-based\nrelational causal discovery algorithm is sound and complete for cyclic\nrelational causal models. We introduce relational acyclification, an operation\nspecifically designed for relational models that enables reasoning about the\nidentifiability of cyclic relational causal models. We show that under the\nassumptions of relational acyclification and $\\sigma$-faithfulness, the\nrelational causal discovery algorithm RCD (Maier et al. 2013) is sound and\ncomplete for cyclic models. We present experimental results to support our\nclaim.\n", "date": "2022-08-25", "categories": []}
{"id": "2303.08572", "title": "Distinguishing Cause from Effect on Categorical Data: The Uniform\n  Channel Model", "abstract": "  Distinguishing cause from effect using observations of a pair of random\nvariables is a core problem in causal discovery. Most approaches proposed for\nthis task, namely additive noise models (ANM), are only adequate for\nquantitative data. We propose a criterion to address the cause-effect problem\nwith categorical variables (living in sets with no meaningful order), inspired\nby seeing a conditional probability mass function (pmf) as a discrete\nmemoryless channel. We select as the most likely causal direction the one in\nwhich the conditional pmf is closer to a uniform channel (UC). The rationale is\nthat, in a UC, as in an ANM, the conditional entropy (of the effect given the\ncause) is independent of the cause distribution, in agreement with the\nprinciple of independence of cause and mechanism. Our approach, which we call\nthe uniform channel model (UCM), thus extends the ANM rationale to categorical\nvariables. To assess how close a conditional pmf (estimated from data) is to a\nUC, we use statistical testing, supported by a closed-form estimate of a UC\nchannel. On the theoretical front, we prove identifiability of the UCM and show\nits equivalence with a structural causal model with a low-cardinality exogenous\nvariable. Finally, the proposed method compares favorably with recent\nstate-of-the-art alternatives in experiments on synthetic, benchmark, and real\ndata.\n", "date": "2023-03-14", "categories": []}
{"id": "2303.07774", "title": "Testing Causality for High Dimensional Data", "abstract": "  Determining causal relationship between high dimensional observations are\namong the most important tasks in scientific discoveries. In this paper, we\nrevisited the \\emph{linear trace method}, a technique proposed\nin~\\citep{janzing2009telling,zscheischler2011testing} to infer the causal\ndirection between two random variables of high dimensions. We strengthen the\nexisting results significantly by providing an improved tail analysis in\naddition to extending the results to nonlinear trace functionals with sharper\nconfidence bounds under certain distributional assumptions. We obtain our\nresults by interpreting the trace estimator in the causal regime as a function\nover random orthogonal matrices, where the concentration of Lipschitz functions\nover such space could be applied. We additionally propose a novel\nridge-regularized variant of the estimator in \\cite{zscheischler2011testing},\nand give provable bounds relating the ridge-estimated terms to their\nground-truth counterparts. We support our theoretical results with encouraging\nexperiments on synthetic datasets, more prominently, under high-dimension low\nsample size regime.\n", "date": "2023-03-14", "categories": []}
{"id": "2303.06423", "title": "Learning interpretable causal networks from very large datasets,\n  application to 400,000 medical records of breast cancer patients", "abstract": "  Discovering causal effects is at the core of scientific investigation but\nremains challenging when only observational data is available. In practice,\ncausal networks are difficult to learn and interpret, and limited to relatively\nsmall datasets. We report a more reliable and scalable causal discovery method\n(iMIIC), based on a general mutual information supremum principle, which\ngreatly improves the precision of inferred causal relations while\ndistinguishing genuine causes from putative and latent causal effects. We\nshowcase iMIIC on synthetic and real-life healthcare data from 396,179 breast\ncancer patients from the US Surveillance, Epidemiology, and End Results\nprogram. More than 90\\% of predicted causal effects appear correct, while the\nremaining unexpected direct and indirect causal effects can be interpreted in\nterms of diagnostic procedures, therapeutic timing, patient preference or\nsocio-economic disparity. iMIIC's unique capabilities open up new avenues to\ndiscover reliable and interpretable causal networks across a range of research\nfields.\n", "date": "2023-03-11", "categories": []}
{"id": "2303.06556", "title": "DOMINO: Visual Causal Reasoning with Time-Dependent Phenomena", "abstract": "  Current work on using visual analytics to determine causal relations among\nvariables has mostly been based on the concept of counterfactuals. As such the\nderived static causal networks do not take into account the effect of time as\nan indicator. However, knowing the time delay of a causal relation can be\ncrucial as it instructs how and when actions should be taken. Yet, similar to\nstatic causality, deriving causal relations from observational time-series\ndata, as opposed to designed experiments, is not a straightforward process. It\ncan greatly benefit from human insight to break ties and resolve errors. We\nhence propose a set of visual analytics methods that allow humans to\nparticipate in the discovery of causal relations associated with windows of\ntime delay. Specifically, we leverage a well-established method, logic-based\ncausality, to enable analysts to test the significance of potential causes and\nmeasure their influences toward a certain effect. Furthermore, since an effect\ncan be a cause of other effects, we allow users to aggregate different temporal\ncause-effect relations found with our method into a visual flow diagram to\nenable the discovery of temporal causal networks. To demonstrate the\neffectiveness of our methods we constructed a prototype system named DOMINO and\nshowcase it via a number of case studies using real-world datasets. Finally, we\nalso used DOMINO to conduct several evaluations with human analysts from\ndifferent science domains in order to gain feedback on the utility of our\nsystem in practical scenarios.\n", "date": "2023-03-12", "categories": []}
{"id": "2210.08185", "title": "GFlowCausal: Generative Flow Networks for Causal Discovery", "abstract": "  Causal discovery aims to uncover causal structure among a set of variables.\nScore-based approaches mainly focus on searching for the best Directed Acyclic\nGraph (DAG) based on a predefined score function. However, most of them are not\napplicable on a large scale due to the limited searchability. Inspired by the\nactive learning in generative flow networks, we propose a novel approach to\nlearning a DAG from observational data called GFlowCausal. It converts the\ngraph search problem to a generation problem, in which direct edges are added\ngradually. GFlowCausal aims to learn the best policy to generate high-reward\nDAGs by sequential actions with probabilities proportional to predefined\nrewards. We propose a plug-and-play module based on transitive closure to\nensure efficient sampling. Theoretical analysis shows that this module could\nguarantee acyclicity properties effectively and the consistency between final\nstates and fully-connected graphs. We conduct extensive experiments on both\nsynthetic and real datasets, and results show the proposed approach to be\nsuperior and also performs well in a large-scale setting.\n", "date": "2022-10-15", "categories": []}
{"id": "2206.06169", "title": "Causal Representation Learning for Instantaneous and Temporal Effects in\n  Interactive Systems", "abstract": "  Causal representation learning is the task of identifying the underlying\ncausal variables and their relations from high-dimensional observations, such\nas images. Recent work has shown that one can reconstruct the causal variables\nfrom temporal sequences of observations under the assumption that there are no\ninstantaneous causal relations between them. In practical applications,\nhowever, our measurement or frame rate might be slower than many of the causal\neffects. This effectively creates \"instantaneous\" effects and invalidates\nprevious identifiability results. To address this issue, we propose iCITRIS, a\ncausal representation learning method that allows for instantaneous effects in\nintervened temporal sequences when intervention targets can be observed, e.g.,\nas actions of an agent. iCITRIS identifies the potentially multidimensional\ncausal variables from temporal observations, while simultaneously using a\ndifferentiable causal discovery method to learn their causal graph. In\nexperiments on three datasets of interactive systems, iCITRIS accurately\nidentifies the causal variables and their causal graph.\n", "date": "2022-06-13", "categories": []}
{"id": "2303.02833", "title": "eCDANs: Efficient Temporal Causal Discovery from Autocorrelated and\n  Non-stationary Data (Student Abstract)", "abstract": "  Conventional temporal causal discovery (CD) methods suffer from high\ndimensionality, fail to identify lagged causal relationships, and often ignore\ndynamics in relations. In this study, we present a novel constraint-based CD\napproach for autocorrelated and non-stationary time series data (eCDANs)\ncapable of detecting lagged and contemporaneous causal relationships along with\ntemporal changes. eCDANs addresses high dimensionality by optimizing the\nconditioning sets while conducting conditional independence (CI) tests and\nidentifies the changes in causal relations by introducing a surrogate variable\nto represent time dependency. Experiments on synthetic and real-world data show\nthat eCDANs can identify time influence and outperform the baselines.\n", "date": "2023-03-06", "categories": []}
{"id": "2303.03187", "title": "Boosting Differentiable Causal Discovery via Adaptive Sample Reweighting", "abstract": "  Under stringent model type and variable distribution assumptions,\ndifferentiable score-based causal discovery methods learn a directed acyclic\ngraph (DAG) from observational data by evaluating candidate graphs over an\naverage score function. Despite great success in low-dimensional linear\nsystems, it has been observed that these approaches overly exploit\neasier-to-fit samples, thus inevitably learning spurious edges. Worse still,\ninherent mostly in these methods the common homogeneity assumption can be\neasily violated, due to the widespread existence of heterogeneous data in the\nreal world, resulting in performance vulnerability when noise distributions\nvary. We propose a simple yet effective model-agnostic framework to boost\ncausal discovery performance by dynamically learning the adaptive weights for\nthe Reweighted Score function, ReScore for short, where the weights tailor\nquantitatively to the importance degree of each sample. Intuitively, we\nleverage the bilevel optimization scheme to \\wx{alternately train a standard\nDAG learner and reweight samples -- that is, upweight the samples the learner\nfails to fit and downweight the samples that the learner easily extracts the\nspurious information from. Extensive experiments on both synthetic and\nreal-world datasets are carried out to validate the effectiveness of ReScore.\nWe observe consistent and significant boosts in structure learning performance.\nFurthermore, we visualize that ReScore concurrently mitigates the influence of\nspurious edges and generalizes to heterogeneous data. Finally, we perform the\ntheoretical analysis to guarantee the structure identifiability and the weight\nadaptive properties of ReScore in linear systems. Our codes are available at\nhttps://github.com/anzhang314/ReScore.\n", "date": "2023-03-06", "categories": []}
{"id": "2302.14386", "title": "Practical Algorithms for Orientations of Partially Directed Graphical\n  Models", "abstract": "  In observational studies, the true causal model is typically unknown and\nneeds to be estimated from available observational and limited experimental\ndata. In such cases, the learned causal model is commonly represented as a\npartially directed acyclic graph (PDAG), which contains both directed and\nundirected edges indicating uncertainty of causal relations between random\nvariables. The main focus of this paper is on the maximal orientation task,\nwhich, for a given PDAG, aims to orient the undirected edges maximally such\nthat the resulting graph represents the same Markov equivalent DAGs as the\ninput PDAG. This task is a subroutine used frequently in causal discovery, e.\ng., as the final step of the celebrated PC algorithm. Utilizing connections to\nthe problem of finding a consistent DAG extension of a PDAG, we derive faster\nalgorithms for computing the maximal orientation by proposing two novel\napproaches for extending PDAGs, both constructed with an emphasis on simplicity\nand practical effectiveness.\n", "date": "2023-02-28", "categories": []}
{"id": "2206.01665", "title": "BaCaDI: Bayesian Causal Discovery with Unknown Interventions", "abstract": "  Inferring causal structures from experimentation is a central task in many\ndomains. For example, in biology, recent advances allow us to obtain\nsingle-cell expression data under multiple interventions such as drugs or gene\nknockouts. However, the targets of the interventions are often uncertain or\nunknown and the number of observations limited. As a result, standard causal\ndiscovery methods can no longer be reliably used. To fill this gap, we propose\na Bayesian framework (BaCaDI) for discovering and reasoning about the causal\nstructure that underlies data generated under various unknown experimental or\ninterventional conditions. BaCaDI is fully differentiable, which allows us to\ninfer the complex joint posterior over the intervention targets and the causal\nstructure via efficient gradient-based variational inference. In experiments on\nsynthetic causal discovery tasks and simulated gene-expression data, BaCaDI\noutperforms related methods in identifying causal structures and intervention\ntargets.\n", "date": "2022-06-03", "categories": []}
{"id": "2207.08457", "title": "A Meta-Reinforcement Learning Algorithm for Causal Discovery", "abstract": "  Causal discovery is a major task with the utmost importance for machine\nlearning since causal structures can enable models to go beyond pure\ncorrelation-based inference and significantly boost their performance. However,\nfinding causal structures from data poses a significant challenge both in\ncomputational effort and accuracy, let alone its impossibility without\ninterventions in general. In this paper, we develop a meta-reinforcement\nlearning algorithm that performs causal discovery by learning to perform\ninterventions such that it can construct an explicit causal graph. Apart from\nbeing useful for possible downstream applications, the estimated causal graph\nalso provides an explanation for the data-generating process. In this article,\nwe show that our algorithm estimates a good graph compared to the SOTA\napproaches, even in environments whose underlying causal structure is\npreviously unseen. Further, we make an ablation study that shows how learning\ninterventions contribute to the overall performance of our approach. We\nconclude that interventions indeed help boost the performance, efficiently\nyielding an accurate estimate of the causal structure of a possibly unseen\nenvironment.\n", "date": "2022-07-18", "categories": []}
{"id": "2302.06804", "title": "Discovering Optimal Scoring Mechanisms in Causal Strategic Prediction", "abstract": "  Faced with data-driven policies, individuals will manipulate their features\nto obtain favorable decisions. While earlier works cast these manipulations as\nundesirable gaming, recent works have adopted a more nuanced causal framing in\nwhich manipulations can improve outcomes of interest, and setting coherent\nmechanisms requires accounting for both predictive accuracy and improvement of\nthe outcome. Typically, these works focus on known causal graphs, consisting\nonly of an outcome and its parents. In this paper, we introduce a general\nframework in which an outcome and n observed features are related by an\narbitrary unknown graph and manipulations are restricted by a fixed budget and\ncost structure. We develop algorithms that leverage strategic responses to\ndiscover the causal graph in a finite number of steps. Given this graph\nstructure, we can then derive mechanisms that trade off between accuracy and\nimprovement. Altogether, our work deepens links between causal discovery and\nincentive design and provides a more nuanced view of learning under causal\nstrategic prediction.\n", "date": "2023-02-14", "categories": []}
{"id": "2302.10804", "title": "GDBN: a Graph Neural Network Approach to Dynamic Bayesian Network", "abstract": "  Identifying causal relations among multi-variate time series is one of the\nmost important elements towards understanding the complex mechanisms underlying\nthe dynamic system. It provides critical tools for forecasting, simulations and\ninterventions in science and business analytics. In this paper, we proposed a\ngraph neural network approach with score-based method aiming at learning a\nsparse DAG that captures the causal dependencies in a discretized time temporal\ngraph. We demonstrate methods with graph neural network significantly\noutperformed other state-of-the-art methods with dynamic bayesian networking\ninference. In addition, from the experiments, the structural causal model can\nbe more accurate than a linear SCM discovered by the methods such as Notears.\n", "date": "2023-01-28", "categories": []}
{"id": "2210.16535", "title": "Causal Discovery of Dynamic Models for Predicting Human Spatial\n  Interactions", "abstract": "  Exploiting robots for activities in human-shared environments, whether\nwarehouses, shopping centres or hospitals, calls for such robots to understand\nthe underlying physical interactions between nearby agents and objects. In\nparticular, modelling cause-and-effect relations between the latter can help to\npredict unobserved human behaviours and anticipate the outcome of specific\nrobot interventions. In this paper, we propose an application of causal\ndiscovery methods to model human-robot spatial interactions, trying to\nunderstand human behaviours from real-world sensor data in two possible\nscenarios: humans interacting with the environment, and humans interacting with\nobstacles. New methods and practical solutions are discussed to exploit, for\nthe first time, a state-of-the-art causal discovery algorithm in some\nchallenging human environments, with potential application in many service\nrobotics scenarios. To demonstrate the utility of the causal models obtained\nfrom real-world datasets, we present a comparison between causal and non-causal\nprediction approaches. Our results show that the causal model correctly\ncaptures the underlying interactions of the considered scenarios and improves\nits prediction accuracy.\n", "date": "2022-10-29", "categories": []}
{"id": "2209.02946", "title": "On the Sparse DAG Structure Learning Based on Adaptive Lasso", "abstract": "  Learning the underlying Bayesian Networks (BNs), represented by directed\nacyclic graphs (DAGs), of the concerned events from purely-observational data\nis a crucial part of evidential reasoning. This task remains challenging due to\nthe large and discrete search space. A recent flurry of developments followed\nNOTEARS[1] recast this combinatorial problem into a continuous optimization\nproblem by leveraging an algebraic equality characterization of acyclicity.\nHowever, the continuous optimization methods suffer from obtaining non-spare\ngraphs after the numerical optimization, which leads to the inflexibility to\nrule out the potentially cycle-inducing edges or false discovery edges with\nsmall values. To address this issue, in this paper, we develop a completely\ndata-driven DAG structure learning method without a predefined value to\npost-threshold small values. We name our method NOTEARS with adaptive Lasso\n(NOTEARS-AL), which is achieved by applying the adaptive penalty method to\nensure the sparsity of the estimated DAG. Moreover, we show that NOTEARS-AL\nalso inherits the oracle properties under some specific conditions. Extensive\nexperiments on both synthetic and a real-world dataset demonstrate that our\nmethod consistently outperforms NOTEARS.\n", "date": "2022-09-07", "categories": []}
{"id": "2302.07458", "title": "CUTS: Neural Causal Discovery from Irregular Time-Series Data", "abstract": "  Causal discovery from time-series data has been a central task in machine\nlearning. Recently, Granger causality inference is gaining momentum due to its\ngood explainability and high compatibility with emerging deep neural networks.\nHowever, most existing methods assume structured input data and degenerate\ngreatly when encountering data with randomly missing entries or non-uniform\nsampling frequencies, which hampers their applications in real scenarios. To\naddress this issue, here we present CUTS, a neural Granger causal discovery\nalgorithm to jointly impute unobserved data points and build causal graphs, via\nplugging in two mutually boosting modules in an iterative framework: (i) Latent\ndata prediction stage: designs a Delayed Supervision Graph Neural Network\n(DSGNN) to hallucinate and register unstructured data which might be of high\ndimension and with complex distribution; (ii) Causal graph fitting stage:\nbuilds a causal adjacency matrix with imputed data under sparse penalty.\nExperiments show that CUTS effectively infers causal graphs from unstructured\ntime-series data, with significantly superior performance to existing methods.\nOur approach constitutes a promising step towards applying causal discovery to\nreal applications with non-ideal observations.\n", "date": "2023-02-15", "categories": []}
{"id": "2301.11898", "title": "DAG Learning on the Permutahedron", "abstract": "  We propose a continuous optimization framework for discovering a latent\ndirected acyclic graph (DAG) from observational data. Our approach optimizes\nover the polytope of permutation vectors, the so-called Permutahedron, to learn\na topological ordering. Edges can be optimized jointly, or learned conditional\non the ordering via a non-differentiable subroutine. Compared to existing\ncontinuous optimization approaches our formulation has a number of advantages\nincluding: 1. validity: optimizes over exact DAGs as opposed to other\nrelaxations optimizing approximate DAGs; 2. modularity: accommodates any\nedge-optimization procedure, edge structural parameterization, and optimization\nloss; 3. end-to-end: either alternately iterates between node-ordering and\nedge-optimization, or optimizes them jointly. We demonstrate, on real-world\ndata problems in protein-signaling and transcriptional network discovery, that\nour approach lies on the Pareto frontier of two key metrics, the SID and SHD.\n", "date": "2023-01-27", "categories": []}
{"id": "2301.13819", "title": "Causal-Discovery Performance of ChatGPT in the context of Neuropathic\n  Pain Diagnosis", "abstract": "  ChatGPT has demonstrated exceptional proficiency in natural language\nconversation, e.g., it can answer a wide range of questions while no previous\nlarge language models can. Thus, we would like to push its limit and explore\nits ability to answer causal discovery questions by using a medical benchmark\n(Tu et al. 2019) in causal discovery.\n", "date": "2023-01-24", "categories": []}
{"id": "2302.01987", "title": "Hierarchical Graph Neural Networks for Causal Discovery and Root Cause\n  Localization", "abstract": "  In this paper, we propose REASON, a novel framework that enables the\nautomatic discovery of both intra-level (i.e., within-network) and inter-level\n(i.e., across-network) causal relationships for root cause localization. REASON\nconsists of Topological Causal Discovery and Individual Causal Discovery. The\nTopological Causal Discovery component aims to model the fault propagation in\norder to trace back to the root causes. To achieve this, we propose novel\nhierarchical graph neural networks to construct interdependent causal networks\nby modeling both intra-level and inter-level non-linear causal relations. Based\non the learned interdependent causal networks, we then leverage random walks\nwith restarts to model the network propagation of a system fault. The\nIndividual Causal Discovery component focuses on capturing abrupt change\npatterns of a single system entity. This component examines the temporal\npatterns of each entity's metric data (i.e., time series), and estimates its\nlikelihood of being a root cause based on the Extreme Value theory. Combining\nthe topological and individual causal scores, the top K system entities are\nidentified as root causes. Extensive experiments on three real-world datasets\nwith case studies demonstrate the effectiveness and superiority of the proposed\nframework.\n", "date": "2023-02-03", "categories": []}
{"id": "2302.02160", "title": "Directed Acyclic Graphs With Tears", "abstract": "  Bayesian network is a frequently-used method for fault detection and\ndiagnosis in industrial processes. The basis of Bayesian network is structure\nlearning which learns a directed acyclic graph (DAG) from data. However, the\nsearch space will scale super-exponentially with the increase of process\nvariables, which makes the data-driven structure learning a challenging\nproblem. To this end, the DAGs with NOTEARs methods are being well studied not\nonly for their conversion of the discrete optimization into continuous\noptimization problem but also their compatibility with deep learning framework.\nNevertheless, there still remain challenges for NOTEAR-based methods: 1) the\ninfeasible solution results from the gradient descent-based optimization\nparadigm; 2) the truncation operation to promise the learned graph acyclic. In\nthis work, the reason for challenge 1) is analyzed theoretically, and a novel\nmethod named DAGs with Tears method is proposed based on mix-integer\nprogramming to alleviate challenge 2). In addition, prior knowledge is able to\nincorporate into the new proposed method, making structure learning more\npractical and useful in industrial processes. Finally, a numerical example and\nan industrial example are adopted as case studies to demonstrate the\nsuperiority of the developed method.\n", "date": "2023-02-04", "categories": []}
{"id": "2301.11197", "title": "Causal Graph Discovery from Self and Mutually Exciting Time Series", "abstract": "  We present a generalized linear structural causal model, coupled with a novel\ndata-adaptive linear regularization, to recover causal directed acyclic graphs\n(DAGs) from time series. By leveraging a recently developed stochastic monotone\nVariational Inequality (VI) formulation, we cast the causal discovery problem\nas a general convex optimization. Furthermore, we develop a non-asymptotic\nrecovery guarantee and quantifiable uncertainty by solving a linear program to\nestablish confidence intervals for a wide range of non-linear monotone link\nfunctions. We validate our theoretical results and show the competitive\nperformance of our method via extensive numerical experiments. Most\nimportantly, we demonstrate the effectiveness of our approach in recovering\nhighly interpretable causal DAGs over Sepsis Associated Derangements (SADs)\nwhile achieving comparable prediction performance to powerful ``black-box''\nmodels such as XGBoost. Thus, the future adoption of our proposed method to\nconduct continuous surveillance of high-risk patients by clinicians is much\nmore likely.\n", "date": "2023-01-26", "categories": []}
{"id": "2209.08037", "title": "DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity\n  Characterization", "abstract": "  The combinatorial problem of learning directed acyclic graphs (DAGs) from\ndata was recently framed as a purely continuous optimization problem by\nleveraging a differentiable acyclicity characterization of DAGs based on the\ntrace of a matrix exponential function. Existing acyclicity characterizations\nare based on the idea that powers of an adjacency matrix contain information\nabout walks and cycles. In this work, we propose a new acyclicity\ncharacterization based on the log-determinant (log-det) function, which\nleverages the nilpotency property of DAGs. To deal with the inherent\nasymmetries of a DAG, we relate the domain of our log-det characterization to\nthe set of $\\textit{M-matrices}$, which is a key difference to the classical\nlog-det function defined over the cone of positive definite matrices. Similar\nto acyclicity functions previously proposed, our characterization is also exact\nand differentiable. However, when compared to existing characterizations, our\nlog-det function: (1) Is better at detecting large cycles; (2) Has\nbetter-behaved gradients; and (3) Its runtime is in practice about an order of\nmagnitude faster. From the optimization side, we drop the typically used\naugmented Lagrangian scheme and propose DAGMA ($\\textit{DAGs via M-matrices for\nAcyclicity}$), a method that resembles the central path for barrier methods.\nEach point in the central path of DAGMA is a solution to an unconstrained\nproblem regularized by our log-det function, then we show that at the limit of\nthe central path the solution is guaranteed to be a DAG. Finally, we provide\nextensive experiments for $\\textit{linear}$ and $\\textit{nonlinear}$ SEMs and\nshow that our approach can reach large speed-ups and smaller structural Hamming\ndistances against state-of-the-art methods. Code implementing the proposed\nmethod is open-source and publicly available at\nhttps://github.com/kevinsbello/dagma.\n", "date": "2022-09-16", "categories": []}
{"id": "2301.06300", "title": "Sensor data-driven analysis for identification of causal relationships\n  between exposure to air pollution and respiratory rate in asthmatics", "abstract": "  According to the Lancet report on the global burden of disease published in\nOctober 2020, air pollution is among the five highest risk factors for global\nhealth, reducing life expectancy on average by 20 months. This paper describes\na data-driven method for establishing causal relationships within and between\ntwo multivariate time series data streams derived from wearable sensors:\npersonal exposure to airborne particulate matter of aerodynamic sizes less than\n2.5um (PM2.5) gathered from the Airspeck monitor worn on the person and\ncontinuous respiratory rate (breaths per minute) measured by the Respeck\nmonitor worn as a plaster on the chest. Results are presented for a cohort of\n113 asthmatic adolescents using the PCMCI+ algorithm to learn the short-term\ncausal relationships between lags of \\pm exposure and respiratory rate. We\nconsider causal effects up to a maximum delay of 8 hours, using data at both a\n1 minute and 15 minute resolution in different experiments. For the first time\na personalised exposure-response relationship between PM2.5 exposure and\nrespiratory rate has been demonstrated to exist for short-term effects in\nasthmatic adolescents during their everyday lives. Our results lead to\nrecommendations for work on specific open problems in causal discovery, to\nincrease the feasibility of this approach for similar epidemiology studies in\nthe future.\n", "date": "2023-01-16", "categories": []}
{"id": "2301.06574", "title": "Causal Recurrent Variational Autoencoder for Medical Time Series\n  Generation", "abstract": "  We propose causal recurrent variational autoencoder (CR-VAE), a novel\ngenerative model that is able to learn a Granger causal graph from a\nmultivariate time series x and incorporates the underlying causal mechanism\ninto its data generation process. Distinct to the classical recurrent VAEs, our\nCR-VAE uses a multi-head decoder, in which the $p$-th head is responsible for\ngenerating the $p$-th dimension of $\\mathbf{x}$ (i.e., $\\mathbf{x}^p$). By\nimposing a sparsity-inducing penalty on the weights (of the decoder) and\nencouraging specific sets of weights to be zero, our CR-VAE learns a sparse\nadjacency matrix that encodes causal relations between all pairs of variables.\nThanks to this causal matrix, our decoder strictly obeys the underlying\nprinciples of Granger causality, thereby making the data generating process\ntransparent. We develop a two-stage approach to train the overall objective.\nEmpirically, we evaluate the behavior of our model in synthetic data and two\nreal-world human brain datasets involving, respectively, the\nelectroencephalography (EEG) signals and the functional magnetic resonance\nimaging (fMRI) data. Our model consistently outperforms state-of-the-art time\nseries generative models both qualitatively and quantitatively. Moreover, it\nalso discovers a faithful causal graph with similar or improved accuracy over\nexisting Granger causality-based causal inference methods. Code of CR-VAE is\npublicly available at https://github.com/hongmingli1995/CR-VAE.\n", "date": "2023-01-16", "categories": []}
{"id": "2301.01817", "title": "Evaluation of Induced Expert Knowledge in Causal Structure Learning by\n  NOTEARS", "abstract": "  Causal modeling provides us with powerful counterfactual reasoning and\ninterventional mechanism to generate predictions and reason under various\nwhat-if scenarios. However, causal discovery using observation data remains a\nnontrivial task due to unobserved confounding factors, finite sampling, and\nchanges in the data distribution. These can lead to spurious cause-effect\nrelationships. To mitigate these challenges in practice, researchers augment\ncausal learning with known causal relations. The goal of the paper is to study\nthe impact of expert knowledge on causal relations in the form of additional\nconstraints used in the formulation of the nonparametric NOTEARS. We provide a\ncomprehensive set of comparative analyses of biasing the model using different\ntypes of knowledge. We found that (i) knowledge that corrects the mistakes of\nthe NOTEARS model can lead to statistically significant improvements, (ii)\nconstraints on active edges have a larger positive impact on causal discovery\nthan inactive edges, and surprisingly, (iii) the induced knowledge does not\ncorrect on average more incorrect active and/or inactive edges than expected.\nWe also demonstrate the behavior of the model and the effectiveness of domain\nknowledge on a real-world dataset.\n", "date": "2023-01-04", "categories": []}
{"id": "2301.01849", "title": "NODAGS-Flow: Nonlinear Cyclic Causal Structure Learning", "abstract": "  Learning causal relationships between variables is a well-studied problem in\nstatistics, with many important applications in science. However, modeling\nreal-world systems remain challenging, as most existing algorithms assume that\nthe underlying causal graph is acyclic. While this is a convenient framework\nfor developing theoretical developments about causal reasoning and inference,\nthe underlying modeling assumption is likely to be violated in real systems,\nbecause feedback loops are common (e.g., in biological systems). Although a few\nmethods search for cyclic causal models, they usually rely on some form of\nlinearity, which is also limiting, or lack a clear underlying probabilistic\nmodel. In this work, we propose a novel framework for learning nonlinear cyclic\ncausal graphical models from interventional data, called NODAGS-Flow. We\nperform inference via direct likelihood optimization, employing techniques from\nresidual normalizing flows for likelihood estimation. Through synthetic\nexperiments and an application to single-cell high-content perturbation\nscreening data, we show significant performance improvements with our approach\ncompared to state-of-the-art methods with respect to structure recovery and\npredictive performance.\n", "date": "2023-01-04", "categories": []}
{"id": "2301.01110", "title": "Causal Discovery for Gene Regulatory Network Prediction", "abstract": "  Biological systems and processes are networks of complex nonlinear regulatory\ninteractions between nucleic acids, proteins, and metabolites. A natural way in\nwhich to represent these interaction networks is through the use of a graph. In\nthis formulation, each node represents a nucleic acid, protein, or metabolite\nand edges represent intermolecular interactions (inhibition, regulation,\npromotion, coexpression, etc.). In this work, a novel algorithm for the\ndiscovery of latent graph structures given experimental data is presented.\n", "date": "2023-01-03", "categories": []}
{"id": "2301.00629", "title": "Learning and interpreting asymmetry-labeled DAGs: a case study on\n  COVID-19 fear", "abstract": "  Bayesian networks are widely used to learn and reason about the dependence\nstructure of discrete variables. However, they are only capable of formally\nencoding symmetric conditional independence, which in practice is often too\nstrict to hold. Asymmetry-labeled DAGs have been recently proposed to both\nextend the class of Bayesian networks by relaxing the symmetric assumption of\nindependence and denote the type of dependence existing between the variables\nof interest. Here, we introduce novel structural learning algorithms for this\nclass of models which, whilst being efficient, allow for a straightforward\ninterpretation of the underlying dependence structure. A comprehensive\ncomputational study highlights the efficiency of the algorithms. A real-world\ndata application using data from the Fear of COVID-19 Scale collected in Italy\nshowcases their use in practice.\n", "date": "2023-01-02", "categories": []}
{"id": "2212.14133", "title": "Investigating Sindy As a Tool For Causal Discovery In Time Series\n  Signals", "abstract": "  The SINDy algorithm has been successfully used to identify the governing\nequations of dynamical systems from time series data. In this paper, we argue\nthat this makes SINDy a potentially useful tool for causal discovery and that\nexisting tools for causal discovery can be used to dramatically improve the\nperformance of SINDy as tool for robust sparse modeling and system\nidentification. We then demonstrate empirically that augmenting the SINDy\nalgorithm with tools from causal discovery can provides engineers with a tool\nfor learning causally robust governing equations.\n", "date": "2022-12-29", "categories": []}
{"id": "2208.14571", "title": "Truncated Matrix Power Iteration for Differentiable DAG Learning", "abstract": "  Recovering underlying Directed Acyclic Graph (DAG) structures from\nobservational data is highly challenging due to the combinatorial nature of the\nDAG-constrained optimization problem. Recently, DAG learning has been cast as a\ncontinuous optimization problem by characterizing the DAG constraint as a\nsmooth equality one, generally based on polynomials over adjacency matrices.\nExisting methods place very small coefficients on high-order polynomial terms\nfor stabilization, since they argue that large coefficients on the higher-order\nterms are harmful due to numeric exploding. On the contrary, we discover that\nlarge coefficients on higher-order terms are beneficial for DAG learning, when\nthe spectral radiuses of the adjacency matrices are small, and that larger\ncoefficients for higher-order terms can approximate the DAG constraints much\nbetter than the small counterparts. Based on this, we propose a novel DAG\nlearning method with efficient truncated matrix power iteration to approximate\ngeometric series based DAG constraints. Empirically, our DAG learning method\noutperforms the previous state-of-the-arts in various settings, often by a\nfactor of $3$ or more in terms of structural Hamming distance.\n", "date": "2022-08-30", "categories": []}
{"id": "2206.01152", "title": "Causal Structure Learning: a Combinatorial Perspective", "abstract": "  In this review, we discuss approaches for learning causal structure from\ndata, also called causal discovery. In particular, we focus on approaches for\nlearning directed acyclic graphs (DAGs) and various generalizations which allow\nfor some variables to be unobserved in the available data. We devote special\nattention to two fundamental combinatorial aspects of causal structure\nlearning. First, we discuss the structure of the search space over causal\ngraphs. Second, we discuss the structure of equivalence classes over causal\ngraphs, i.e., sets of graphs which represent what can be learned from\nobservational data alone, and how these equivalence classes can be refined by\nadding interventional data.\n", "date": "2022-06-02", "categories": []}
{"id": "2209.08579", "title": "Bivariate Causal Discovery for Categorical Data via Classification with\n  Optimal Label Permutation", "abstract": "  Causal discovery for quantitative data has been extensively studied but less\nis known for categorical data. We propose a novel causal model for categorical\ndata based on a new classification model, termed classification with optimal\nlabel permutation (COLP). By design, COLP is a parsimonious classifier, which\ngives rise to a provably identifiable causal model. A simple learning algorithm\nvia comparing likelihood functions of causal and anti-causal models suffices to\nlearn the causal direction. Through experiments with synthetic and real data,\nwe demonstrate the favorable performance of the proposed COLP-based causal\nmodel compared to state-of-the-art methods. We also make available an\naccompanying R package COLP, which contains the proposed causal discovery\nalgorithm and a benchmark dataset of categorical cause-effect pairs.\n", "date": "2022-09-18", "categories": []}
{"id": "2212.04866", "title": "Deep Learning of Causal Structures in High Dimensions", "abstract": "  Recent years have seen rapid progress at the intersection between causality\nand machine learning. Motivated by scientific applications involving\nhigh-dimensional data, in particular in biomedicine, we propose a deep neural\narchitecture for learning causal relationships between variables from a\ncombination of empirical data and prior causal knowledge. We combine\nconvolutional and graph neural networks within a causal risk framework to\nprovide a flexible and scalable approach. Empirical results include linear and\nnonlinear simulations (where the underlying causal structures are known and can\nbe directly compared against), as well as a real biological example where the\nmodels are applied to high-dimensional molecular data and their output compared\nagainst entirely unseen validation experiments. These results demonstrate the\nfeasibility of using deep learning approaches to learn causal networks in\nlarge-scale problems spanning thousands of variables.\n", "date": "2022-12-09", "categories": []}
{"id": "2212.04235", "title": "A probabilistic autoencoder for causal discovery", "abstract": "  The paper addresses the problem of finding the causal direction between two\nassociated variables. The proposed solution is to build an autoencoder of their\njoint distribution and to maximize its estimation capacity relative to both the\nmarginal distributions. It is shown that the resulting two capacities cannot,\nin general, be equal. This leads to a new criterion for causal discovery: the\nhigher capacity is consistent with the unconstrained choice of a distribution\nrepresenting the cause while the lower capacity reflects the constraints\nimposed by the mechanism on the distribution of the effect. Estimation capacity\nis defined as the ability of the auto-encoder to represent arbitrary datasets.\nA regularization term forces it to decide which one of the variables to model\nin a more generic way i.e., while maintaining higher model capacity. The causal\ndirection is revealed by the constraints encountered while encoding the data\ninstead of being measured as a property of the data itself. The idea is\nimplemented and tested using a restricted Boltzmann machine.\n", "date": "2022-12-08", "categories": []}
{"id": "2212.02435", "title": "Observational and Interventional Causal Learning for Regret-Minimizing\n  Control", "abstract": "  We explore how observational and interventional causal discovery methods can\nbe combined. A state-of-the-art observational causal discovery algorithm for\ntime series capable of handling latent confounders and contemporaneous effects,\ncalled LPCMCI, is extended to profit from casual constraints found through\nrandomized control trials. Numerical results show that, given perfect\ninterventional constraints, the reconstructed structural causal models (SCMs)\nof the extended LPCMCI allow 84.6% of the time for the optimal prediction of\nthe target variable. The implementation of interventional and observational\ncausal discovery is modular, allowing causal constraints from other sources.\n  The second part of this thesis investigates the question of regret minimizing\ncontrol by simultaneously learning a causal model and planning actions through\nthe causal model. The idea is that an agent to optimize a measured variable\nfirst learns the system's mechanics through observational causal discovery. The\nagent then intervenes on the most promising variable with randomized values\nallowing for the exploitation and generation of new interventional data. The\nagent then uses the interventional data to enhance the causal model further,\nallowing improved actions the next time.\n  The extended LPCMCI can be favorable compared to the original LPCMCI\nalgorithm. The numerical results show that detecting and using interventional\nconstraints leads to reconstructed SCMs that allow 60.9% of the time for the\noptimal prediction of the target variable in contrast to the baseline of 53.6%\nwhen using the original LPCMCI algorithm. Furthermore, the induced average\nregret decreases from 1.2 when using the original LPCMCI algorithm to 1.0 when\nusing the extended LPCMCI algorithm with interventional discovery.\n", "date": "2022-12-05", "categories": []}
{"id": "2212.00911", "title": "Navigating causal deep learning", "abstract": "  Causal deep learning (CDL) is a new and important research area in the larger\nfield of machine learning. With CDL, researchers aim to structure and encode\ncausal knowledge in the extremely flexible representation space of deep\nlearning models. Doing so will lead to more informed, robust, and general\npredictions and inference -- which is important! However, CDL is still in its\ninfancy. For example, it is not clear how we ought to compare different methods\nas they are so different in their output, the way they encode causal knowledge,\nor even how they represent this knowledge. This is a living paper that\ncategorises methods in causal deep learning beyond Pearl's ladder of causation.\nWe refine the rungs in Pearl's ladder, while also adding a separate dimension\nthat categorises the parametric assumptions of both input and representation,\narriving at the map of causal deep learning. Our map covers machine learning\ndisciplines such as supervised learning, reinforcement learning, generative\nmodelling and beyond. Our paradigm is a tool which helps researchers to: find\nbenchmarks, compare methods, and most importantly: identify research gaps. With\nthis work we aim to structure the avalanche of papers being published on causal\ndeep learning. While papers on the topic are being published daily, our map\nremains fixed. We open-source our map for others to use as they see fit:\nperhaps to offer guidance in a related works section, or to better highlight\nthe contribution of their paper.\n", "date": "2022-12-01", "categories": []}
{"id": "2212.01279", "title": "Initial Results for Pairwise Causal Discovery Using Quantitative\n  Information Flow", "abstract": "  Pairwise Causal Discovery is the task of determining causal, anticausal,\nconfounded or independence relationships from pairs of variables. Over the last\nfew years, this challenging task has promoted not only the discovery of novel\nmachine learning models aimed at solving the task, but also discussions on how\nlearning the causal direction of variables may benefit machine learning\noverall. In this paper, we show that Quantitative Information Flow (QIF), a\nmeasure usually employed for measuring leakages of information from a system to\nan attacker, shows promising results as features for the task. In particular,\nexperiments with real-world datasets indicate that QIF is statistically tied to\nthe state of the art. Our initial results motivate further inquiries on how QIF\nrelates to causality and what are its limitations.\n", "date": "2022-12-02", "categories": []}
{"id": "2211.13800", "title": "Estimation of a Causal Directed Acyclic Graph Process using\n  Non-Gaussianity", "abstract": "  Numerous approaches have been proposed to discover causal dependencies in\nmachine learning and data mining; among them, the state-of-the-art VAR-LiNGAM\n(short for Vector Auto-Regressive Linear Non-Gaussian Acyclic Model) is a\ndesirable approach to reveal both the instantaneous and time-lagged\nrelationships. However, all the obtained VAR matrices need to be analyzed to\ninfer the final causal graph, leading to a rise in the number of parameters. To\naddress this issue, we propose the CGP-LiNGAM (short for Causal Graph\nProcess-LiNGAM), which has significantly fewer model parameters and deals with\nonly one causal graph for interpreting the causal relations by exploiting Graph\nSignal Processing (GSP).\n", "date": "2022-11-24", "categories": []}
{"id": "2211.12983", "title": "Causal Analysis of the TOPCAT Trial: Spironolactone for Preserved\n  Cardiac Function Heart Failure", "abstract": "  We describe the results of applying causal discovery methods on the data from\na multi-site clinical trial, on the Treatment of Preserved Cardiac Function\nHeart Failure with an Aldosterone Antagonist (TOPCAT). The trial was\ninconclusive, with no clear benefits consistently shown for the whole cohort.\nHowever, there were questions regarding the reliability of the diagnosis and\ntreatment protocol for a geographic subgroup of the cohort. With the inclusion\nof medical context in the form of domain knowledge, causal discovery is used to\ndemonstrate regional discrepancies and to frame the regional transportability\nof the results. Furthermore, we show that, globally and especially for some\nsubgroups, the treatment has significant causal effects, thus offering a more\nrefined view of the trial results.\n", "date": "2022-11-23", "categories": []}
{"id": "2211.12016", "title": "Variation-based Cause Effect Identification", "abstract": "  Mining genuine mechanisms underlying the complex data generation process in\nreal-world systems is a fundamental step in promoting interpretability of, and\nthus trust in, data-driven models. Therefore, we propose a variation-based\ncause effect identification (VCEI) framework for causal discovery in bivariate\nsystems from a single observational setting. Our framework relies on the\nprinciple of independence of cause and mechanism (ICM) under the assumption of\nan existing acyclic causal link, and offers a practical realization of this\nprinciple. Principally, we artificially construct two settings in which the\nmarginal distributions of one covariate, claimed to be the cause, are\nguaranteed to have non-negligible variations. This is achieved by re-weighting\nsamples of the marginal so that the resultant distribution is notably distinct\nfrom this marginal according to some discrepancy measure. In the causal\ndirection, such variations are expected to have no impact on the effect\ngeneration mechanism. Therefore, quantifying the impact of these variations on\nthe conditionals reveals the genuine causal direction. Moreover, we formulate\nour approach in the kernel-based maximum mean discrepancy, lifting all\nconstraints on the data types of cause-and-effect covariates, and rendering\nsuch artificial interventions a convex optimization problem. We provide a\nseries of experiments on real and synthetic data showing that VCEI is, in\nprinciple, competitive to other cause effect identification frameworks.\n", "date": "2022-11-22", "categories": []}
{"id": "2211.12151", "title": "Reinforcement Causal Structure Learning on Order Graph", "abstract": "  Learning directed acyclic graph (DAG) that describes the causality of\nobserved data is a very challenging but important task. Due to the limited\nquantity and quality of observed data, and non-identifiability of causal graph,\nit is almost impossible to infer a single precise DAG. Some methods approximate\nthe posterior distribution of DAGs to explore the DAG space via Markov chain\nMonte Carlo (MCMC), but the DAG space is over the nature of super-exponential\ngrowth, accurately characterizing the whole distribution over DAGs is very\nintractable. In this paper, we propose {Reinforcement Causal Structure Learning\non Order Graph} (RCL-OG) that uses order graph instead of MCMC to model\ndifferent DAG topological orderings and to reduce the problem size. RCL-OG\nfirst defines reinforcement learning with a new reward mechanism to approximate\nthe posterior distribution of orderings in an efficacy way, and uses deep\nQ-learning to update and transfer rewards between nodes. Next, it obtains the\nprobability transition model of nodes on order graph, and computes the\nposterior probability of different orderings. In this way, we can sample on\nthis model to obtain the ordering with high probability. Experiments on\nsynthetic and benchmark datasets show that RCL-OG provides accurate posterior\nprobability approximation and achieves better results than competitive causal\ndiscovery algorithms.\n", "date": "2022-11-22", "categories": []}
{"id": "2209.11497", "title": "Time Series Causal Link Estimation under Hidden Confounding using\n  Knockoff Interventions", "abstract": "  Latent variables often mask cause-effect relationships in observational data\nwhich provokes spurious links that may be misinterpreted as causal. This\nproblem sparks great interest in the fields such as climate science and\neconomics. We propose to estimate confounded causal links of time series using\nSequential Causal Effect Variational Autoencoder (SCEVAE) while applying\nKnockoff interventions. Knockoff variables have the same distribution as the\noriginals and preserve the correlation to other variables. This allows for\ncounterfactuals that are more faithful to the observational distribution. We\nshow the advantage of Knockoff interventions by applying SCEVAE to synthetic\ndatasets with both linear and nonlinear causal links. Moreover, we apply SCEVAE\nwith Knockoffs to real aerosol-cloud-climate observational time series data. We\ncompare our results on synthetic data to those of a time series deconfounding\nmethod both with and without estimated confounders. We show that our method\noutperforms this benchmark by comparing both methods to the ground truth. For\nthe real data analysis, we rely on expert knowledge of causal links and\ndemonstrate how using suitable proxy variables improves the causal link\nestimation in the presence of hidden confounders.\n", "date": "2022-09-23", "categories": []}
{"id": "2211.08883", "title": "Identifying the Causes of Pyrocumulonimbus (PyroCb)", "abstract": "  A first causal discovery analysis from observational data of pyroCb (storm\nclouds generated from extreme wildfires) is presented. Invariant Causal\nPrediction was used to develop tools to understand the causal drivers of pyroCb\nformation. This includes a conditional independence test for testing $Y$\nconditionally independent of $E$ given $X$ for binary variable $Y$ and\nmultivariate, continuous variables $X$ and $E$, and a greedy-ICP search\nalgorithm that relies on fewer conditional independence tests to obtain a\nsmaller more manageable set of causal predictors. With these tools, we\nidentified a subset of seven causal predictors which are plausible when\ncontrasted with domain knowledge: surface sensible heat flux, relative humidity\nat $850$ hPa, a component of wind at $250$ hPa, $13.3$ micro-meters, thermal\nemissions, convective available potential energy, and altitude.\n", "date": "2022-11-16", "categories": []}
{"id": "2211.09024", "title": "Phenomenological Causality", "abstract": "  Discussions on causal relations in real life often consider variables for\nwhich the definition of causality is unclear since the notion of interventions\non the respective variables is obscure. Asking 'what qualifies an action for\nbeing an intervention on the variable X' raises the question whether the action\nimpacted all other variables only through X or directly, which implicitly\nrefers to a causal model.\n  To avoid this known circularity, we instead suggest a notion of\n'phenomenological causality' whose basic concept is a set of elementary\nactions. Then the causal structure is defined such that elementary actions\nchange only the causal mechanism at one node (e.g. one of the causal\nconditionals in the Markov factorization). This way, the Principle of\nIndependent Mechanisms becomes the defining property of causal structure in\ndomains where causality is a more abstract phenomenon rather than being an\nobjective fact relying on hard-wired causal links between tangible objects. We\ndescribe this phenomenological approach to causality for toy and hypothetical\nreal-world examples and argue that it is consistent with the causal Markov\ncondition when the system under consideration interacts with other variables\nthat control the elementary actions.\n", "date": "2022-11-15", "categories": []}
{"id": "2211.06536", "title": "Improving the Efficiency of the PC Algorithm by Using Model-Based\n  Conditional Independence Tests", "abstract": "  Learning causal structure is useful in many areas of artificial intelligence,\nincluding planning, robotics, and explanation. Constraint-based structure\nlearning algorithms such as PC use conditional independence (CI) tests to infer\ncausal structure. Traditionally, constraint-based algorithms perform CI tests\nwith a preference for smaller-sized conditioning sets, partially because the\nstatistical power of conventional CI tests declines rapidly as the size of the\nconditioning set increases. However, many modern conditional independence tests\nare model-based, and these tests use well-regularized models that maintain\nstatistical power even with very large conditioning sets. This suggests an\nintriguing new strategy for constraint-based algorithms which may result in a\nreduction of the total number of CI tests performed: Test variable pairs with\nlarge conditioning sets first, as a pre-processing step that finds some\nconditional independencies quickly, before moving on to the more conventional\nstrategy that favors small conditioning sets. We propose such a pre-processing\nstep for the PC algorithm which relies on performing CI tests on a few randomly\nselected large conditioning sets. We perform an empirical analysis on directed\nacyclic graphs (DAGs) that correspond to real-world systems and both empirical\nand theoretical analyses for Erd\\H{o}s-Renyi DAGs. Our results show that\nPre-Processing Plus PC (P3PC) performs far fewer CI tests than the original PC\nalgorithm, between 0.5% to 36%, and often less than 10%, of the CI tests that\nthe PC algorithm alone performs. The efficiency gains are particularly\nsignificant for the DAGs corresponding to real-world systems.\n", "date": "2022-11-12", "categories": []}
{"id": "2211.03984", "title": "Causal Discovery in Linear Latent Variable Models Subject to Measurement\n  Error", "abstract": "  We focus on causal discovery in the presence of measurement error in linear\nsystems where the mixing matrix, i.e., the matrix indicating the independent\nexogenous noise terms pertaining to the observed variables, is identified up to\npermutation and scaling of the columns. We demonstrate a somewhat surprising\nconnection between this problem and causal discovery in the presence of\nunobserved parentless causes, in the sense that there is a mapping, given by\nthe mixing matrix, between the underlying models to be inferred in these\nproblems. Consequently, any identifiability result based on the mixing matrix\nfor one model translates to an identifiability result for the other model. We\ncharacterize to what extent the causal models can be identified under a\ntwo-part faithfulness assumption. Under only the first part of the assumption\n(corresponding to the conventional definition of faithfulness), the structure\ncan be learned up to the causal ordering among an ordered grouping of the\nvariables but not all the edges across the groups can be identified. We further\nshow that if both parts of the faithfulness assumption are imposed, the\nstructure can be learned up to a more refined ordered grouping. As a result of\nthis refinement, for the latent variable model with unobserved parentless\ncauses, the structure can be identified. Based on our theoretical results, we\npropose causal structure learning methods for both models, and evaluate their\nperformance on synthetic data.\n", "date": "2022-11-08", "categories": []}
{"id": "2211.04312", "title": "From Causal Pairs to Causal Graphs", "abstract": "  Causal structure learning from observational data remains a non-trivial task\ndue to various factors such as finite sampling, unobserved confounding factors,\nand measurement errors. Constraint-based and score-based methods tend to suffer\nfrom high computational complexity due to the combinatorial nature of\nestimating the directed acyclic graph (DAG). Motivated by the `Cause-Effect\nPair' NIPS 2013 Workshop on Causality Challenge, in this paper, we take a\ndifferent approach and generate a probability distribution over all possible\ngraphs informed by the cause-effect pair features proposed in response to the\nworkshop challenge. The goal of the paper is to propose new methods based on\nthis probabilistic information and compare their performance with traditional\nand state-of-the-art approaches. Our experiments, on both synthetic and real\ndatasets, show that our proposed methods not only have statistically similar or\nbetter performances than some traditional approaches but also are\ncomputationally faster.\n", "date": "2022-11-08", "categories": []}
{"id": "2210.11275", "title": "Causal Structural Hypothesis Testing and Data Generation Models", "abstract": "  A vast amount of expert and domain knowledge is captured by causal structural\npriors, yet there has been little research on testing such priors for\ngeneralization and data synthesis purposes. We propose a novel model\narchitecture, Causal Structural Hypothesis Testing, that can use nonparametric,\nstructural causal knowledge and approximate a causal model's functional\nrelationships using deep neural networks. We use these architectures for\ncomparing structural priors, akin to hypothesis testing, using a deliberate\n(non-random) split of training and testing data. Extensive simulations\ndemonstrate the effectiveness of out-of-distribution generalization error as a\nproxy for causal structural prior hypothesis testing and offers a statistical\nbaseline for interpreting results. We show that the variational version of the\narchitecture, Causal Structural Variational Hypothesis Testing can improve\nperformance in low SNR regimes. Due to the simplicity and low parameter count\nof the models, practitioners can test and compare structural prior hypotheses\non small dataset and use the priors with the best generalization capacity to\nsynthesize much larger, causally-informed datasets. Finally, we validate our\nmethods on a synthetic pendulum dataset, and show a use-case on a real-world\ntrauma surgery ground-level falls dataset.\n", "date": "2022-10-20", "categories": []}
{"id": "2211.00486", "title": "Causal DAG extraction from a library of books or videos/movies", "abstract": "  Determining a causal DAG (directed acyclic graph) for a problem under\nconsideration, is a major roadblock when doing Judea Pearl's Causal Inference\n(CI) in Statistics. The same problem arises when doing CI in Artificial\nIntelligence (AI) and Machine Learning (ML). As with many problems in Science,\nwe think Nature has found an effective solution to this problem. We argue that\nhuman and animal brains contain an explicit engine for doing CI, and that such\nan engine uses as input an atlas (i.e., collection) of causal DAGs. We propose\na simple algorithm for constructing such an atlas from a library of books or\nvideos/movies. We illustrate our method by applying it to a database of\nrandomly generated Tic-Tac-Toe games. The software used to generate this\nTic-Tac-Toe example is open source and available at GitHub.\n", "date": "2022-10-29", "categories": []}
{"id": "2210.16775", "title": "Nonlinear Causal Discovery via Kernel Anchor Regression", "abstract": "  Learning causal relationships is a fundamental problem in science. Anchor\nregression has been developed to address this problem for a large class of\ncausal graphical models, though the relationships between the variables are\nassumed to be linear. In this work, we tackle the nonlinear setting by\nproposing kernel anchor regression (KAR). Beyond the natural formulation using\na classic two-stage least square estimator, we also study an improved variant\nthat involves nonparametric regression in three separate stages. We provide\nconvergence results for the proposed KAR estimators and the identifiability\nconditions for KAR to learn the nonlinear structural equation models (SEM).\nExperimental results demonstrate the superior performances of the proposed KAR\nestimators over existing baselines.\n", "date": "2022-10-30", "categories": []}
{"id": "2210.15353", "title": "Learning Discrete Directed Acyclic Graphs via Backpropagation", "abstract": "  Recently continuous relaxations have been proposed in order to learn Directed\nAcyclic Graphs (DAGs) from data by backpropagation, instead of using\ncombinatorial optimization. However, a number of techniques for fully discrete\nbackpropagation could instead be applied. In this paper, we explore that\ndirection and propose DAG-DB, a framework for learning DAGs by Discrete\nBackpropagation. Based on the architecture of Implicit Maximum Likelihood\nEstimation [I-MLE, arXiv:2106.01798], DAG-DB adopts a probabilistic approach to\nthe problem, sampling binary adjacency matrices from an implicit probability\ndistribution. DAG-DB learns a parameter for the distribution from the loss\nincurred by each sample, performing competitively using either of two fully\ndiscrete backpropagation techniques, namely I-MLE and Straight-Through\nEstimation.\n", "date": "2022-10-27", "categories": []}
{"id": "2210.14573", "title": "Learning Causal Graphs in Manufacturing Domains using Structural\n  Equation Models", "abstract": "  Many production processes are characterized by numerous and complex\ncause-and-effect relationships. Since they are only partially known they pose a\nchallenge to effective process control. In this work we present how Structural\nEquation Models can be used for deriving cause-and-effect relationships from\nthe combination of prior knowledge and process data in the manufacturing\ndomain. Compared to existing applications, we do not assume linear\nrelationships leading to more informative results.\n", "date": "2022-10-26", "categories": []}
{"id": "2210.14706", "title": "Rhino: Deep Causal Temporal Relationship Learning With History-dependent\n  Noise", "abstract": "  Discovering causal relationships between different variables from time series\ndata has been a long-standing challenge for many domains such as climate\nscience, finance, and healthcare. Given the complexity of real-world\nrelationships and the nature of observations in discrete time, causal discovery\nmethods need to consider non-linear relations between variables, instantaneous\neffects and history-dependent noise (the change of noise distribution due to\npast actions). However, previous works do not offer a solution addressing all\nthese problems together. In this paper, we propose a novel causal relationship\nlearning framework for time-series data, called Rhino, which combines vector\nauto-regression, deep learning and variational inference to model non-linear\nrelationships with instantaneous effects while allowing the noise distribution\nto be modulated by historical observations. Theoretically, we prove the\nstructural identifiability of Rhino. Our empirical results from extensive\nsynthetic experiments and two real-world benchmarks demonstrate better\ndiscovery performance compared to relevant baselines, with ablation studies\nrevealing its robustness under model misspecification.\n", "date": "2022-10-26", "categories": []}
{"id": "2210.13583", "title": "Learning Latent Structural Causal Models", "abstract": "  Causal learning has long concerned itself with the accurate recovery of\nunderlying causal mechanisms. Such causal modelling enables better explanations\nof out-of-distribution data. Prior works on causal learning assume that the\nhigh-level causal variables are given. However, in machine learning tasks, one\noften operates on low-level data like image pixels or high-dimensional vectors.\nIn such settings, the entire Structural Causal Model (SCM) -- structure,\nparameters, \\textit{and} high-level causal variables -- is unobserved and needs\nto be learnt from low-level data. We treat this problem as Bayesian inference\nof the latent SCM, given low-level data. For linear Gaussian additive noise\nSCMs, we present a tractable approximate inference method which performs joint\ninference over the causal variables, structure and parameters of the latent SCM\nfrom random, known interventions. Experiments are performed on synthetic\ndatasets and a causally generated image dataset to demonstrate the efficacy of\nour approach. We also perform image generation from unseen interventions,\nthereby verifying out of distribution generalization for the proposed causal\nmodel.\n", "date": "2022-10-24", "categories": []}
{"id": "2210.13647", "title": "Temporally Disentangled Representation Learning", "abstract": "  Recently in the field of unsupervised representation learning, strong\nidentifiability results for disentanglement of causally-related latent\nvariables have been established by exploiting certain side information, such as\nclass labels, in addition to independence. However, most existing work is\nconstrained by functional form assumptions such as independent sources or\nfurther with linear transitions, and distribution assumptions such as\nstationary, exponential family distribution. It is unknown whether the\nunderlying latent variables and their causal relations are identifiable if they\nhave arbitrary, nonparametric causal influences in between. In this work, we\nestablish the identifiability theories of nonparametric latent causal processes\nfrom their nonlinear mixtures under fixed temporal causal influences and\nanalyze how distribution changes can further benefit the disentanglement. We\npropose \\textbf{\\texttt{TDRL}}, a principled framework to recover time-delayed\nlatent causal variables and identify their relations from measured sequential\ndata under stationary environments and under different distribution shifts.\nSpecifically, the framework can factorize unknown distribution shifts into\ntransition distribution changes under fixed and time-varying latent causal\nrelations, and under observation changes in observation. Through experiments,\nwe show that time-delayed latent causal influences are reliably identified and\nthat our approach considerably outperforms existing baselines that do not\ncorrectly exploit this modular representation of changes. Our code is available\nat: \\url{https://github.com/weirayao/tdrl}.\n", "date": "2022-10-24", "categories": []}
{"id": "2210.11021", "title": "Independence Testing-Based Approach to Causal Discovery under\n  Measurement Error and Linear Non-Gaussian Models", "abstract": "  Causal discovery aims to recover causal structures generating the\nobservational data. Despite its success in certain problems, in many real-world\nscenarios the observed variables are not the target variables of interest, but\nthe imperfect measures of the target variables. Causal discovery under\nmeasurement error aims to recover the causal graph among unobserved target\nvariables from observations made with measurement error. We consider a specific\nformulation of the problem, where the unobserved target variables follow a\nlinear non-Gaussian acyclic model, and the measurement process follows the\nrandom measurement error model. Existing methods on this formulation rely on\nnon-scalable over-complete independent component analysis (OICA). In this work,\nwe propose the Transformed Independent Noise (TIN) condition, which checks for\nindependence between a specific linear transformation of some measured\nvariables and certain other measured variables. By leveraging the\nnon-Gaussianity and higher-order statistics of data, TIN is informative about\nthe graph structure among the unobserved target variables. By utilizing TIN,\nthe ordered group decomposition of the causal model is identifiable. In other\nwords, we could achieve what once required OICA to achieve by only conducting\nindependence tests. Experimental results on both synthetic and real-world data\ndemonstrate the effectiveness and reliability of our method.\n", "date": "2022-10-20", "categories": []}
{"id": "2210.10256", "title": "Causal Structure Learning with Recommendation System", "abstract": "  A fundamental challenge of recommendation systems (RS) is understanding the\ncausal dynamics underlying users' decision making. Most existing literature\naddresses this problem by using causal structures inferred from domain\nknowledge. However, there are numerous phenomenons where domain knowledge is\ninsufficient, and the causal mechanisms must be learnt from the feedback data.\nDiscovering the causal mechanism from RS feedback data is both novel and\nchallenging, since RS itself is a source of intervention that can influence\nboth the users' exposure and their willingness to interact. Also for this\nreason, most existing solutions become inappropriate since they require data\ncollected free from any RS. In this paper, we first formulate the underlying\ncausal mechanism as a causal structural model and describe a general causal\nstructure learning framework grounded in the real-world working mechanism of\nRS. The essence of our approach is to acknowledge the unknown nature of RS\nintervention. We then derive the learning objective from our framework and\npropose an augmented Lagrangian solver for efficient optimization. We conduct\nboth simulation and real-world experiments to demonstrate how our approach\ncompares favorably to existing solutions, together with the empirical analysis\nfrom sensitivity and ablation studies.\n", "date": "2022-10-19", "categories": []}
{"id": "2206.02013", "title": "Causal Discovery in Heterogeneous Environments Under the Sparse\n  Mechanism Shift Hypothesis", "abstract": "  Machine learning approaches commonly rely on the assumption of independent\nand identically distributed (i.i.d.) data. In reality, however, this assumption\nis almost always violated due to distribution shifts between environments.\nAlthough valuable learning signals can be provided by heterogeneous data from\nchanging distributions, it is also known that learning under arbitrary\n(adversarial) changes is impossible. Causality provides a useful framework for\nmodeling distribution shifts, since causal models encode both observational and\ninterventional distributions. In this work, we explore the sparse mechanism\nshift hypothesis, which posits that distribution shifts occur due to a small\nnumber of changing causal conditionals. Motivated by this idea, we apply it to\nlearning causal structure from heterogeneous environments, where i.i.d. data\nonly allows for learning an equivalence class of graphs without restrictive\nassumptions. We propose the Mechanism Shift Score (MSS), a score-based approach\namenable to various empirical estimators, which provably identifies the entire\ncausal structure with high probability if the sparse mechanism shift hypothesis\nholds. Empirically, we verify behavior predicted by the theory and compare\nmultiple estimators and score functions to identify the best approaches in\npractice. Compared to other methods, we show how MSS bridges a gap by both\nbeing nonparametric as well as explicitly leveraging sparse changes.\n", "date": "2022-06-04", "categories": []}
{"id": "2206.02063", "title": "Active Bayesian Causal Inference", "abstract": "  Causal discovery and causal reasoning are classically treated as separate and\nconsecutive tasks: one first infers the causal graph, and then uses it to\nestimate causal effects of interventions. However, such a two-stage approach is\nuneconomical, especially in terms of actively collected interventional data,\nsince the causal query of interest may not require a fully-specified causal\nmodel. From a Bayesian perspective, it is also unnatural, since a causal query\n(e.g., the causal graph or some causal effect) can be viewed as a latent\nquantity subject to posterior inference -- other unobserved quantities that are\nnot of direct interest (e.g., the full causal model) ought to be marginalized\nout in this process and contribute to our epistemic uncertainty. In this work,\nwe propose Active Bayesian Causal Inference (ABCI), a fully-Bayesian active\nlearning framework for integrated causal discovery and reasoning, which jointly\ninfers a posterior over causal models and queries of interest. In our approach\nto ABCI, we focus on the class of causally-sufficient, nonlinear additive noise\nmodels, which we model using Gaussian processes. We sequentially design\nexperiments that are maximally informative about our target causal query,\ncollect the corresponding interventional data, and update our beliefs to choose\nthe next experiment. Through simulations, we demonstrate that our approach is\nmore data-efficient than several baselines that only focus on learning the full\ncausal graph. This allows us to accurately learn downstream causal queries from\nfewer samples while providing well-calibrated uncertainty estimates for the\nquantities of interest.\n", "date": "2022-06-04", "categories": []}
{"id": "2210.04958", "title": "Mining Causality from Continuous-time Dynamics Models: An Application to\n  Tsunami Forecasting", "abstract": "  Continuous-time dynamics models, such as neural ordinary differential\nequations, have enabled the modeling of underlying dynamics in time-series data\nand accurate forecasting. However, parameterization of dynamics using a neural\nnetwork makes it difficult for humans to identify causal structures in the\ndata. In consequence, this opaqueness hinders the use of these models in the\ndomains where capturing causal relationships carries the same importance as\naccurate predictions, e.g., tsunami forecasting. In this paper, we address this\nchallenge by proposing a mechanism for mining causal structures from\ncontinuous-time models. We train models to capture the causal structure by\nenforcing sparsity in the weights of the input layers of the dynamics models.\nWe first verify the effectiveness of our method in the scenario where the exact\ncausal-structures of time-series are known as a priori. We next apply our\nmethod to a real-world problem, namely tsunami forecasting, where the exact\ncausal-structures are difficult to characterize. Experimental results show that\nthe proposed method is effective in learning physically-consistent causal\nrelationships while achieving high forecasting accuracy.\n", "date": "2022-10-10", "categories": []}
{"id": "2206.07824", "title": "Large-Scale Differentiable Causal Discovery of Factor Graphs", "abstract": "  A common theme in causal inference is learning causal relationships between\nobserved variables, also known as causal discovery. This is usually a daunting\ntask, given the large number of candidate causal graphs and the combinatorial\nnature of the search space. Perhaps for this reason, most research has so far\nfocused on relatively small causal graphs, with up to hundreds of nodes.\nHowever, recent advances in fields like biology enable generating experimental\ndata sets with thousands of interventions followed by rich profiling of\nthousands of variables, raising the opportunity and urgent need for large\ncausal graph models. Here, we introduce the notion of factor directed acyclic\ngraphs (f-DAGs) as a way to restrict the search space to non-linear low-rank\ncausal interaction models. Combining this novel structural assumption with\nrecent advances that bridge the gap between causal discovery and continuous\noptimization, we achieve causal discovery on thousands of variables.\nAdditionally, as a model for the impact of statistical noise on this estimation\nprocedure, we study a model of edge perturbations of the f-DAG skeleton based\non random graphs and quantify the effect of such perturbations on the f-DAG\nrank. This theoretical analysis suggests that the set of candidate f-DAGs is\nmuch smaller than the whole DAG space and thus may be more suitable as a search\nspace in the high-dimensional regime where the underlying skeleton is hard to\nassess. We propose Differentiable Causal Discovery of Factor Graphs (DCD-FG), a\nscalable implementation of -DAG constrained causal discovery for\nhigh-dimensional interventional data. DCD-FG uses a Gaussian non-linear\nlow-rank structural equation model and shows significant improvements compared\nto state-of-the-art methods in both simulations as well as a recent large-scale\nsingle-cell RNA sequencing data set with hundreds of genetic interventions.\n", "date": "2022-06-15", "categories": []}
{"id": "2206.15374", "title": "Verification and search algorithms for causal DAGs", "abstract": "  We study two problems related to recovering causal graphs from interventional\ndata: (i) $\\textit{verification}$, where the task is to check if a purported\ncausal graph is correct, and (ii) $\\textit{search}$, where the task is to\nrecover the correct causal graph. For both, we wish to minimize the number of\ninterventions performed. For the first problem, we give a characterization of a\nminimal sized set of atomic interventions that is necessary and sufficient to\ncheck the correctness of a claimed causal graph. Our characterization uses the\nnotion of $\\textit{covered edges}$, which enables us to obtain simple proofs\nand also easily reason about earlier known results. We also generalize our\nresults to the settings of bounded size interventions and node-dependent\ninterventional costs. For all the above settings, we provide the first known\nprovable algorithms for efficiently computing (near)-optimal verifying sets on\ngeneral graphs. For the second problem, we give a simple adaptive algorithm\nbased on graph separators that produces an atomic intervention set which fully\norients any essential graph while using $\\mathcal{O}(\\log n)$ times the optimal\nnumber of interventions needed to $\\textit{verify}$ (verifying size) the\nunderlying DAG on $n$ vertices. This approximation is tight as $\\textit{any}$\nsearch algorithm on an essential line graph has worst case approximation ratio\nof $\\Omega(\\log n)$ with respect to the verifying size. With bounded size\ninterventions, each of size $\\leq k$, our algorithm gives an $\\mathcal{O}(\\log\nn \\cdot \\log k)$ factor approximation. Our result is the first known algorithm\nthat gives a non-trivial approximation guarantee to the verifying size on\ngeneral unweighted graphs and with bounded size interventions.\n", "date": "2022-06-30", "categories": []}
{"id": "2210.01798", "title": "Latent Hierarchical Causal Structure Discovery with Rank Constraints", "abstract": "  Most causal discovery procedures assume that there are no latent confounders\nin the system, which is often violated in real-world problems. In this paper,\nwe consider a challenging scenario for causal structure identification, where\nsome variables are latent and they form a hierarchical graph structure to\ngenerate the measured variables; the children of latent variables may still be\nlatent and only leaf nodes are measured, and moreover, there can be multiple\npaths between every pair of variables (i.e., it is beyond tree structure). We\npropose an estimation procedure that can efficiently locate latent variables,\ndetermine their cardinalities, and identify the latent hierarchical structure,\nby leveraging rank deficiency constraints over the measured variables. We show\nthat the proposed algorithm can find the correct Markov equivalence class of\nthe whole graph asymptotically under proper restrictions on the graph\nstructure.\n", "date": "2022-10-01", "categories": []}
{"id": "2209.06367", "title": "A Review and Roadmap of Deep Learning Causal Discovery in Different\n  Variable Paradigms", "abstract": "  Understanding causality helps to structure interventions to achieve specific\ngoals and enables predictions under interventions. With the growing importance\nof learning causal relationships, causal discovery tasks have transitioned from\nusing traditional methods to infer potential causal structures from\nobservational data to the field of pattern recognition involved in deep\nlearning. The rapid accumulation of massive data promotes the emergence of\ncausal search methods with brilliant scalability. Existing summaries of causal\ndiscovery methods mainly focus on traditional methods based on constraints,\nscores and FCMs, there is a lack of perfect sorting and elaboration for deep\nlearning-based methods, also lacking some considers and exploration of causal\ndiscovery methods from the perspective of variable paradigms. Therefore, we\ndivide the possible causal discovery tasks into three types according to the\nvariable paradigm and give the definitions of the three tasks respectively,\ndefine and instantiate the relevant datasets for each task and the final causal\nmodel constructed at the same time, then reviews the main existing causal\ndiscovery methods for different tasks. Finally, we propose some roadmaps from\ndifferent perspectives for the current research gaps in the field of causal\ndiscovery and point out future research directions.\n", "date": "2022-09-14", "categories": []}
{"id": "2209.03427", "title": "Causal discovery for time series with latent confounders", "abstract": "  Reconstructing the causal relationships behind the phenomena we observe is a\nfundamental challenge in all areas of science. Discovering causal relationships\nthrough experiments is often infeasible, unethical, or expensive in complex\nsystems. However, increases in computational power allow us to process the\never-growing amount of data that modern science generates, leading to an\nemerging interest in the causal discovery problem from observational data. This\nwork evaluates the LPCMCI algorithm, which aims to find generators compatible\nwith a multi-dimensional, highly autocorrelated time series while some\nvariables are unobserved. We find that LPCMCI performs much better than a\nrandom algorithm mimicking not knowing anything but is still far from optimal\ndetection. Furthermore, LPCMCI performs best on auto-dependencies, then\ncontemporaneous dependencies, and struggles most with lagged dependencies. The\nsource code of this project is available online.\n", "date": "2022-09-07", "categories": []}
{"id": "2209.01547", "title": "Conditional Independence Testing via Latent Representation Learning", "abstract": "  Detecting conditional independencies plays a key role in several statistical\nand machine learning tasks, especially in causal discovery algorithms. In this\nstudy, we introduce LCIT (Latent representation based Conditional Independence\nTest)-a novel non-parametric method for conditional independence testing based\non representation learning. Our main contribution involves proposing a\ngenerative framework in which to test for the independence between X and Y\ngiven Z, we first learn to infer the latent representations of target variables\nX and Y that contain no information about the conditioning variable Z. The\nlatent variables are then investigated for any significant remaining\ndependencies, which can be performed using the conventional partial correlation\ntest. The empirical evaluations show that LCIT outperforms several\nstate-of-the-art baselines consistently under different evaluation metrics, and\nis able to adapt really well to both non-linear and high-dimensional settings\non a diverse collection of synthetic and real data sets.\n", "date": "2022-09-04", "categories": []}
{"id": "2208.12610", "title": "NeurIPS Competition Instructions and Guide: Causal Insights for Learning\n  Paths in Education", "abstract": "  In this competition, participants will address two fundamental causal\nchallenges in machine learning in the context of education using time-series\ndata. The first is to identify the causal relationships between different\nconstructs, where a construct is defined as the smallest element of learning.\nThe second challenge is to predict the impact of learning one construct on the\nability to answer questions on other constructs. Addressing these challenges\nwill enable optimisation of students' knowledge acquisition, which can be\ndeployed in a real edtech solution impacting millions of students. Participants\nwill run these tasks in an idealised environment with synthetic data and a\nreal-world scenario with evaluation data collected from a series of A/B tests.\n", "date": "2022-08-17", "categories": []}
{"id": "2208.08345", "title": "Discovering Agents", "abstract": "  Causal models of agents have been used to analyse the safety aspects of\nmachine learning systems. But identifying agents is non-trivial -- often the\ncausal model is just assumed by the modeler without much justification -- and\nmodelling failures can lead to mistakes in the safety analysis. This paper\nproposes the first formal causal definition of agents -- roughly that agents\nare systems that would adapt their policy if their actions influenced the world\nin a different way. From this we derive the first causal discovery algorithm\nfor discovering agents from empirical data, and give algorithms for translating\nbetween causal models and game-theoretic influence diagrams. We demonstrate our\napproach by resolving some previous confusions caused by incorrect causal\nmodelling of agents.\n", "date": "2022-08-17", "categories": []}
{"id": "2206.05490", "title": "Discovery and density estimation of latent confounders in Bayesian\n  networks with evidence lower bound", "abstract": "  Discovering and parameterising latent confounders represent important and\nchallenging problems in causal structure learning and density estimation\nrespectively. In this paper, we focus on both discovering and learning the\ndistribution of latent confounders. This task requires solutions that come from\ndifferent areas of statistics and machine learning. We combine elements of\nvariational Bayesian methods, expectation-maximisation, hill-climbing search,\nand structure learning under the assumption of causal insufficiency. We propose\ntwo learning strategies; one that maximises model selection accuracy, and\nanother that improves computational efficiency in exchange for minor reductions\nin accuracy. The former strategy is suitable for small networks and the latter\nfor moderate size networks. Both learning strategies perform well relative to\nexisting solutions.\n", "date": "2022-06-11", "categories": []}
{"id": "2208.08247", "title": "Domain Knowledge in A*-Based Causal Discovery", "abstract": "  Causal discovery has become a vital tool for scientists and practitioners\nwanting to discover causal relationships from observational data. While most\nprevious approaches to causal discovery have implicitly assumed that no expert\ndomain knowledge is available, practitioners can often provide such domain\nknowledge from prior experience. Recent work has incorporated domain knowledge\ninto constraint-based causal discovery. The majority of such constraint-based\nmethods, however, assume causal faithfulness, which has been shown to be\nfrequently violated in practice. Consequently, there has been renewed attention\ntowards exact-search score-based causal discovery methods, which do not assume\ncausal faithfulness, such as A*-based methods. However, there has been no\nconsideration of these methods in the context of domain knowledge. In this\nwork, we focus on efficiently integrating several types of domain knowledge\ninto A*-based causal discovery. In doing so, we discuss and explain how domain\nknowledge can reduce the graph search space and then provide an analysis of the\npotential computational gains. We support these findings with experiments on\nsynthetic and real data, showing that even small amounts of domain knowledge\ncan dramatically speed up A*-based causal discovery and improve its performance\nand practicality.\n", "date": "2022-08-17", "categories": []}
{"id": "2208.06701", "title": "Learning Linear Non-Gaussian Polytree Models", "abstract": "  In the context of graphical causal discovery, we adapt the versatile\nframework of linear non-Gaussian acyclic models (LiNGAMs) to propose new\nalgorithms to efficiently learn graphs that are polytrees. Our approach\ncombines the Chow--Liu algorithm, which first learns the undirected tree\nstructure, with novel schemes to orient the edges. The orientation schemes\nassess algebraic relations among moments of the data-generating distribution\nand are computationally inexpensive. We establish high-dimensional consistency\nresults for our approach and compare different algorithmic versions in\nnumerical experiments.\n", "date": "2022-08-13", "categories": []}
{"id": "2208.06935", "title": "Novel Ordering-based Approaches for Causal Structure Learning in the\n  Presence of Unobserved Variables", "abstract": "  We propose ordering-based approaches for learning the maximal ancestral graph\n(MAG) of a structural equation model (SEM) up to its Markov equivalence class\n(MEC) in the presence of unobserved variables. Existing ordering-based methods\nin the literature recover a graph through learning a causal order (c-order). We\nadvocate for a novel order called removable order (r-order) as they are\nadvantageous over c-orders for structure learning. This is because r-orders are\nthe minimizers of an appropriately defined optimization problem that could be\neither solved exactly (using a reinforcement learning approach) or\napproximately (using a hill-climbing search). Moreover, the r-orders (unlike\nc-orders) are invariant among all the graphs in a MEC and include c-orders as a\nsubset. Given that set of r-orders is often significantly larger than the set\nof c-orders, it is easier for the optimization problem to find an r-order\ninstead of a c-order. We evaluate the performance and the scalability of our\nproposed approaches on both real-world and randomly generated networks.\n", "date": "2022-08-14", "categories": []}
{"id": "2207.05723", "title": "Latent Variable Models for Bayesian Causal Discovery", "abstract": "  Learning predictors that do not rely on spurious correlations involves\nbuilding causal representations. However, learning such a representation is\nvery challenging. We, therefore, formulate the problem of learning a causal\nrepresentation from high dimensional data and study causal recovery with\nsynthetic data. This work introduces a latent variable decoder model, Decoder\nBCD, for Bayesian causal discovery and performs experiments in mildly\nsupervised and unsupervised settings. We present a series of synthetic\nexperiments to characterize important factors for causal discovery and show\nthat using known intervention targets as labels helps in unsupervised Bayesian\ninference over structure and parameters of linear Gaussian additive noise\nlatent structural causal models.\n", "date": "2022-07-12", "categories": []}
{"id": "2208.01529", "title": "CIPCaD-Bench: Continuous Industrial Process datasets for benchmarking\n  Causal Discovery methods", "abstract": "  Causal relationships are commonly examined in manufacturing processes to\nsupport faults investigations, perform interventions, and make strategic\ndecisions. Industry 4.0 has made available an increasing amount of data that\nenable data-driven Causal Discovery (CD). Considering the growing number of\nrecently proposed CD methods, it is necessary to introduce strict benchmarking\nprocedures on publicly available datasets since they represent the foundation\nfor a fair comparison and validation of different methods. This work introduces\ntwo novel public datasets for CD in continuous manufacturing processes. The\nfirst dataset employs the well-known Tennessee Eastman simulator for fault\ndetection and process control. The second dataset is extracted from an\nultra-processed food manufacturing plant, and it includes a description of the\nplant, as well as multiple ground truths. These datasets are used to propose a\nbenchmarking procedure based on different metrics and evaluated on a wide\nselection of CD algorithms. This work allows testing CD methods in realistic\nconditions enabling the selection of the most suitable method for specific\ntarget applications. The datasets are available at the following link:\nhttps://github.com/giovanniMen\n", "date": "2022-08-02", "categories": []}
{"id": "2207.07908", "title": "Multiscale Causal Structure Learning", "abstract": "  The inference of causal structures from observed data plays a key role in\nunveiling the underlying dynamics of the system. This paper exposes a novel\nmethod, named Multiscale-Causal Structure Learning (MS-CASTLE), to estimate the\nstructure of linear causal relationships occurring at different time scales.\nDifferently from existing approaches, MS-CASTLE takes explicitly into account\ninstantaneous and lagged inter-relations between multiple time series,\nrepresented at different scales, hinging on stationary wavelet transform and\nnon-convex optimization. MS-CASTLE incorporates, as a special case, a\nsingle-scale version named SS-CASTLE, which compares favorably in terms of\ncomputational efficiency, performance and robustness with respect to the state\nof the art onto synthetic data. We used MS-CASTLE to study the multiscale\ncausal structure of the risk of 15 global equity markets, during covid-19\npandemic, illustrating how MS-CASTLE can extract meaningful information thanks\nto its multiscale analysis, outperforming SS-CASTLE. We found that the most\npersistent and strongest interactions occur at mid-term time resolutions.\nMoreover, we identified the stock markets that drive the risk during the\nconsidered period: Brazil, Canada and Italy. The proposed approach can be\nexploited by financial investors who, depending to their investment horizon,\ncan manage the risk within equity portfolios from a causal perspective.\n", "date": "2022-07-16", "categories": []}
{"id": "2207.08365", "title": "CausNet : Generational orderings based search for optimal Bayesian\n  networks via dynamic programming with parent set constraints", "abstract": "  Finding a globally optimal Bayesian Network using exhaustive search is a\nproblem with super-exponential complexity, which severely restricts the number\nof variables that it can work for. We implement a dynamic programming based\nalgorithm with built-in dimensionality reduction and parent set identification.\nThis reduces the search space drastically and can be applied to\nlarge-dimensional data. We use what we call generational orderings based search\nfor optimal networks, which is a novel way to efficiently search the space of\npossible networks given the possible parent sets. The algorithm supports both\ncontinuous and categorical data, and categorical as well as survival outcomes.\nWe demonstrate the efficacy of our algorithm on both synthetic and real data.\nIn simulations, our algorithm performs better than three state-of-art\nalgorithms that are currently used extensively. We then apply it to an Ovarian\nCancer gene expression dataset with 513 genes and a survival outcome. Our\nalgorithm is able to find an optimal network describing the disease pathway\nconsisting of 6 genes leading to the outcome node in a few minutes on a basic\ncomputer. Our generational orderings based search for optimal networks, is both\nefficient and highly scalable approach to finding optimal Bayesian Networks,\nthat can be applied to 1000s of variables. Using specifiable parameters -\ncorrelation, FDR cutoffs, and in-degree - one can increase or decrease the\nnumber of nodes and density of the networks. Availability of two scoring\noption-BIC and Bge-and implementation of survival outcomes and mixed data types\nmakes our algorithm very suitable for many types of high dimensional biomedical\ndata to find disease pathways.\n", "date": "2022-07-18", "categories": []}
{"id": "2207.04055", "title": "Causal Discovery using Model Invariance through Knockoff Interventions", "abstract": "  Cause-effect analysis is crucial to understand the underlying mechanism of a\nsystem. We propose to exploit model invariance through interventions on the\npredictors to infer causality in nonlinear multivariate systems of time series.\nWe model nonlinear interactions in time series using DeepAR and then expose the\nmodel to different environments using Knockoffs-based interventions to test\nmodel invariance. Knockoff samples are pairwise exchangeable, in-distribution\nand statistically null variables generated without knowing the response. We\ntest model invariance where we show that the distribution of the response\nresidual does not change significantly upon interventions on non-causal\npredictors. We evaluate our method on real and synthetically generated time\nseries. Overall our method outperforms other widely used causality methods,\ni.e, VAR Granger causality, VARLiNGAM and PCMCI+.\n", "date": "2022-07-08", "categories": []}
{"id": "2206.09777", "title": "Actively learning to learn causal relationships", "abstract": "  How do people actively learn to learn? That is, how and when do people choose\nactions that facilitate long-term learning and choosing future actions that are\nmore informative? We explore these questions in the domain of active causal\nlearning. We propose a hierarchical Bayesian model that goes beyond past models\nby predicting that people pursue information not only about the causal\nrelationship at hand but also about causal\noverhypotheses$\\unicode{x2014}$abstract beliefs about causal relationships that\nspan multiple situations and constrain how we learn the specifics in each\nsituation. In two active \"blicket detector\" experiments with 14\nbetween-subjects manipulations, our model was supported by both qualitative\ntrends in participant behavior and an individual-differences-based model\ncomparison. Our results suggest when there are abstract similarities across\nactive causal learning problems, people readily learn and transfer\noverhypotheses about these similarities. Moreover, people exploit these\noverhypotheses to facilitate long-term active learning.\n", "date": "2022-06-20", "categories": []}
{"id": "2206.08448", "title": "Empirical Bayesian Approaches for Robust Constraint-based Causal\n  Discovery under Insufficient Data", "abstract": "  Causal discovery is to learn cause-effect relationships among variables given\nobservational data and is important for many applications. Existing causal\ndiscovery methods assume data sufficiency, which may not be the case in many\nreal world datasets. As a result, many existing causal discovery methods can\nfail under limited data. In this work, we propose Bayesian-augmented\nfrequentist independence tests to improve the performance of constraint-based\ncausal discovery methods under insufficient data: 1) We firstly introduce a\nBayesian method to estimate mutual information (MI), based on which we propose\na robust MI based independence test; 2) Secondly, we consider the Bayesian\nestimation of hypothesis likelihood and incorporate it into a well-defined\nstatistical test, resulting in a robust statistical testing based independence\ntest. We apply proposed independence tests to constraint-based causal discovery\nmethods and evaluate the performance on benchmark datasets with insufficient\nsamples. Experiments show significant performance improvement in terms of both\naccuracy and efficiency over SOTA methods.\n", "date": "2022-06-16", "categories": []}
{"id": "2206.08531", "title": "Reframed GES with a Neural Conditional Dependence Measure", "abstract": "  In a nonparametric setting, the causal structure is often identifiable only\nup to Markov equivalence, and for the purpose of causal inference, it is useful\nto learn a graphical representation of the Markov equivalence class (MEC). In\nthis paper, we revisit the Greedy Equivalence Search (GES) algorithm, which is\nwidely cited as a score-based algorithm for learning the MEC of the underlying\ncausal structure. We observe that in order to make the GES algorithm consistent\nin a nonparametric setting, it is not necessary to design a scoring metric that\nevaluates graphs. Instead, it suffices to plug in a consistent estimator of a\nmeasure of conditional dependence to guide the search. We therefore present a\nreframing of the GES algorithm, which is more flexible than the standard\nscore-based version and readily lends itself to the nonparametric setting with\na general measure of conditional dependence. In addition, we propose a neural\nconditional dependence (NCD) measure, which utilizes the expressive power of\ndeep neural networks to characterize conditional independence in a\nnonparametric manner. We establish the optimality of the reframed GES algorithm\nunder standard assumptions and the consistency of using our NCD estimator to\ndecide conditional independence. Together these results justify the proposed\napproach. Experimental results demonstrate the effectiveness of our method in\ncausal discovery, as well as the advantages of using our NCD measure over\nkernel-based measures.\n", "date": "2022-06-17", "categories": []}
{"id": "2206.07195", "title": "Tearing Apart NOTEARS: Controlling the Graph Prediction via Variance\n  Manipulation", "abstract": "  Simulations are ubiquitous in machine learning. Especially in graph learning,\nsimulations of Directed Acyclic Graphs (DAG) are being deployed for evaluating\nnew algorithms. In the literature, it was recently argued that\ncontinuous-optimization approaches to structure discovery such as NOTEARS might\nbe exploiting the sortability of the variable's variances in the available data\ndue to their use of least square losses. Specifically, since structure\ndiscovery is a key problem in science and beyond, we want to be invariant to\nthe scale being used for measuring our data (e.g. meter versus centimeter\nshould not affect the causal direction inferred by the algorithm). In this\nwork, we further strengthen this initial, negative empirical suggestion by both\nproving key results in the multivariate case and corroborating with further\nempirical evidence. In particular, we show that we can control the resulting\ngraph with our targeted variance attacks, even in the case where we can only\npartially manipulate the variances of the data.\n", "date": "2022-06-14", "categories": []}
{"id": "2206.06469", "title": "Invariant Structure Learning for Better Generalization and Causal\n  Explainability", "abstract": "  Learning the causal structure behind data is invaluable for improving\ngeneralization and obtaining high-quality explanations. We propose a novel\nframework, Invariant Structure Learning (ISL), that is designed to improve\ncausal structure discovery by utilizing generalization as an indication. ISL\nsplits the data into different environments, and learns a structure that is\ninvariant to the target across different environments by imposing a consistency\nconstraint. An aggregation mechanism then selects the optimal classifier based\non a graph structure that reflects the causal mechanisms in the data more\naccurately compared to the structures learnt from individual environments.\nFurthermore, we extend ISL to a self-supervised learning setting where accurate\ncausal structure discovery does not rely on any labels. This self-supervised\nISL utilizes invariant causality proposals by iteratively setting different\nnodes as targets. On synthetic and real-world datasets, we demonstrate that ISL\naccurately discovers the causal structure, outperforms alternative methods, and\nyields superior generalization for datasets with significant distribution\nshifts.\n", "date": "2022-06-13", "categories": []}
{"id": "2206.06685", "title": "Causal Discovery for Fairness", "abstract": "  It is crucial to consider the social and ethical consequences of AI and ML\nbased decisions for the safe and acceptable use of these emerging technologies.\nFairness, in particular, guarantees that the ML decisions do not result in\ndiscrimination against individuals or minorities. Identifying and measuring\nreliably fairness/discrimination is better achieved using causality which\nconsiders the causal relation, beyond mere association, between the sensitive\nattribute (e.g. gender, race, religion, etc.) and the decision (e.g. job\nhiring, loan granting, etc.). The big impediment to the use of causality to\naddress fairness, however, is the unavailability of the causal model (typically\nrepresented as a causal graph). Existing causal approaches to fairness in the\nliterature do not address this problem and assume that the causal model is\navailable. In this paper, we do not make such assumption and we review the\nmajor algorithms to discover causal relations from observable data. This study\nfocuses on causal discovery and its impact on fairness. In particular, we show\nhow different causal discovery approaches may result in different causal models\nand, most importantly, how even slight differences between causal models can\nhave significant impact on fairness/discrimination conclusions. These results\nare consolidated by empirical analysis using synthetic and standard fairness\nbenchmark datasets. The main goal of this study is to highlight the importance\nof the causal discovery step to appropriately address fairness using causality.\n", "date": "2022-06-14", "categories": []}
{"id": "2206.05421", "title": "Greedy Relaxations of the Sparsest Permutation Algorithm", "abstract": "  There has been an increasing interest in methods that exploit permutation\nreasoning to search for directed acyclic causal models, including the \"Ordering\nSearch\" of Teyssier and Kohler and GSP of Solus, Wang and Uhler. We extend the\nmethods of the latter by a permutation-based operation, tuck, and develop a\nclass of algorithms, namely GRaSP, that are efficient and pointwise consistent\nunder increasingly weaker assumptions than faithfulness. The most relaxed form\nof GRaSP outperforms many state-of-the-art causal search algorithms in\nsimulation, allowing efficient and accurate search even for dense graphs and\ngraphs with more than 100 variables.\n", "date": "2022-06-11", "categories": []}
{"id": "2206.06124", "title": "Causal Discovery in Hawkes Processes by Minimum Description Length", "abstract": "  Hawkes processes are a special class of temporal point processes which\nexhibit a natural notion of causality, as occurrence of events in the past may\nincrease the probability of events in the future. Discovery of the underlying\ninfluence network among the dimensions of multi-dimensional temporal processes\nis of high importance in disciplines where a high-frequency data is to model,\ne.g. in financial data or in seismological data. This paper approaches the\nproblem of learning Granger-causal network in multi-dimensional Hawkes\nprocesses. We formulate this problem as a model selection task in which we\nfollow the minimum description length (MDL) principle. Moreover, we propose a\ngeneral algorithm for MDL-based inference using a Monte-Carlo method and we use\nit for our causal discovery problem. We compare our algorithm with the\nstate-of-the-art baseline methods on synthetic and real-world financial data.\nThe synthetic experiments demonstrate superiority of our method incausal graph\ndiscovery compared to the baseline methods with respect to the size of the\ndata. The results of experiments with the G-7 bonds price data are consistent\nwith the experts knowledge.\n", "date": "2022-06-10", "categories": []}
{"id": "2206.01496", "title": "Causality Learning With Wasserstein Generative Adversarial Networks", "abstract": "  Conventional methods for causal structure learning from data face significant\nchallenges due to combinatorial search space. Recently, the problem has been\nformulated into a continuous optimization framework with an acyclicity\nconstraint to learn Directed Acyclic Graphs (DAGs). Such a framework allows the\nutilization of deep generative models for causal structure learning to better\ncapture the relations between data sample distributions and DAGs. However, so\nfar no study has experimented with the use of Wasserstein distance in the\ncontext of causal structure learning. Our model named DAG-WGAN combines the\nWasserstein-based adversarial loss with an acyclicity constraint in an\nauto-encoder architecture. It simultaneously learns causal structures while\nimproving its data generation capability. We compare the performance of\nDAG-WGAN with other models that do not involve the Wasserstein metric in order\nto identify its contribution to causal structure learning. Our model performs\nbetter with high cardinality data according to our experiments.\n", "date": "2022-06-03", "categories": []}
{"id": "2606.21212", "title": "DCD-PFN: A Decoupling-Aware Foundation Model for Causal Discovery", "abstract": "Causal discovery is critical for understanding complex data-generating mechanisms, yet traditional algorithms often struggle with highly non-linear and noisy systems, or suffer from severe computational bottlenecks. Recent tabular foundation models based on Prior-Data Fitted Networks (PFNs) have demonstrated remarkable zero-shot inference capabilities, but their potential for explicit structural causal discovery remains underexplored. To bridge this gap, we propose DCD-PFN, a decoupling-aware foundation model for causal discovery. Instead of directly amortizing global graph reconstruction, DCD-PFN focuses on local causal discovery through a decoupling-based paradigm. Through pre-training on diverse synthetic Structural Causal Models (SCMs), the model learns sample-wise decoupling weights that enable Markov boundary (MB) identification. Furthermore, by leveraging parallelized local discovery, DCD-PFN efficiently reconstructs global causal graphs while remaining grounded in the theoretical foundations of decoupling-based causal discovery. Experiments demonstrate that our foundation model achieves robust zero-shot generalization.", "date": "2026-06-19", "categories": []}
{"id": "2606.21668", "title": "A Framework for Directed Acyclic Hypergraph Learning", "abstract": "Continuous optimization methods for learning Directed Acyclic Graphs (DAGs) operate on weighted adjacency matrices and are therefore limited to pairwise causal relationships. We propose a framework for learning Directed Acyclic Hypergraphs (DAHGs) from observational data, capturing joint parental influences that pairwise models cannot represent. Our approach rests on three components: (i) a generalized linear structural equation model (SEM) with multiplicative interaction terms whose non-zero weights correspond one-to-one with directed hyperedges; (ii) a weighted adjacency tensor representation whose acyclicity is characterized via nilpotency under the tensor t-product; and (iii) a differentiable acyclicity constraint derived through the Fourier decomposition of the t-product, which reduces tensor nilpotency to slice-wise matrix nilpotency and enables least-squares learning via the augmented Lagrangian method.", "date": "2026-06-19", "categories": []}
{"id": "2606.23608", "title": "Causal Discovery in the Era of Agents", "abstract": "Recent attempts to combine large language models (LLMs) with causal discovery ask models to infer pairwise directions, propose graph structures, or inject language-model outputs as priors and constraints. These approaches promise faster analysis, but they also obscure whether a causal evidence is supported by data and assumptions or by textual associations, prompt artifacts and hallucinated mechanisms. We argue for a different role for agents in causal discovery. Agents should inspect data, retrieve context, explain method assumptions and clarify graph outputs, but they should not supply edges, orientations, priors, constraints or causal conclusions. We propose the principle that agents assist the workflow, while causal claims remain grounded in data, explicit assumptions, formal algorithms, diagnostics and user or domain-expert decisions. We instantiate this principle in causal-learn+, an online platform that coordinates data analysis, preprocessing, method recommendation, expert-knowledge incorporation, formal discovery and interpretation around the algorithmic ecosystem of causal-learn. A case study on Big Five personality data illustrates agent-assisted pipeline of causal discovery without turning language-model unreliability into causal evidence. The platform is available at causallearn.com.", "date": "2026-06-22", "categories": []}
{"id": "2606.23767", "title": "One Ruler: A Same-Hands Re-Evaluation of Bivariate Causal Direction on Tuebingen, with a Parameter-Free Compression Baseline", "abstract": "Headline accuracies on the Tuebingen cause-effect pairs are routinely compared across papers even though each is measured under its authors' own protocol -- different pair subsets, weightings, model-selection, and decision rates. We argue this is the wrong comparison and run the right one: a same-hands re-evaluation in which every method is run by us on the identical 102 pairs, with one strict rule -- no tuning and a decision forced on every pair. As a clean reference point we introduce a deliberately minimal baseline: sorted-conditional compression, which feeds quantized, sorted, first-differenced data to an off-the-shelf compressor (bz2) and has zero fitted parameters. Under the common ruler the ranking differs sharply from the literature. Our baseline reaches 74.7% weighted accuracy (p = 3.7e-7); on the same 100 pairs that SLOPE is evaluated on it scores 76.0%, a 1.2-point gap below the authors' own forced-decision SLOPE (77.2%) that is well inside noise (McNemar p = 0.39). A faithful re-run of RECI lands at 70.7% -- inside the original authors' reported error bar, not the 77.5% often quoted (which we trace to a mis-copied cell). SLOPE's published 82.4% is a decided-subset figure: scoring the authors' own stored output only on the pairs its significance test chose to answer reproduces 81.7%. Under the common ruler the methods cluster in the low-to-mid 70s and the zero-parameter compressor ties the strongest of them. We document the mechanisms that inflate published figures (test-set model selection, significance-gated abstention) and contribute two further results: compression score magnitude is a model-free confounding flag (p = 2.8e-68), and a pre-registered falsification test fails in an instructive way that bounds the method's theoretical interpretation. Code, pre-registrations, and per-pair outputs are released.", "date": "2026-06-22", "categories": []}
{"id": "2606.23880", "title": "GRACE: Gated Refinement for Accurate Causal Edge Discovery in High-Dimensional Time Series", "abstract": "From climate teleconnections to gene regulation, modern time-series datasets encompass tens or hundreds of interacting variables, making causal discovery increasingly challenging. Constraint-based methods offer statistical rigor but their nonlinear CI tests are infeasible at scale, while score-based alternatives avoid CI testing but require arbitrary thresholds to binarize continuous edge scores. We propose GRACE ($\\textbf{G}$ated $\\textbf{R}$efinement for $\\textbf{A}$ccurate $\\textbf{C}$ausal $\\textbf{E}$dge discovery), which refines constraint-based discovery using Hard Concrete gates with $L_0$ regularization: each candidate edge has an independent gate whose values concentrate near 0 or 1, yielding a clean bimodal separation that makes the binary decision robust, unlike the narrow, overlapping score distributions produced by $L_1$ and attention-based methods. A fast linear CI skeleton provides high-recall candidates; a single gated model then prunes false positives by learning which edges genuinely improve prediction, with automatic regularization adapted to problem dimensions and skeleton density. Systematic experiments on synthetic benchmarks, spanning diverse graph topologies (scale-free, Erd\\H{o}s-R'enyi, small-world) and dimensionalities up to $d=100$, show that GRACE substantially improves F1 over its base CI method while maintaining high precision, and outperforms attention-based and score-based alternatives. GRACE matches or exceeds expensive nonlinear CI tests at a fraction of the cost ($75\\times$ faster). On a real-world river flow dataset, where rainfall confounders, variable propagation lags, and distributional shifts violate standard assumptions, a temporal bootstrap variant of GRACE recovers 9 of 11 causal edges along the Elbe River with only 1 false positive ($F_1 = 0.86$, AUROC${} = 0.99$), reducing the skeleton's 106 false positives by 99%.", "date": "2026-06-22", "categories": []}
{"id": "2606.24488", "title": "RetiSEM: Generalising Causal Models for Fragmented Biomedical Data", "abstract": "Learning causal models from fragmented biomedical data is challenging because clinical, molecular, and imaging variables are often incomplete or not jointly observed. We propose RetiSEM, a domain-constrained structural equation modelling (SEM) framework for causal graph recovery and mediation analysis under limited multimodal resources. This proposed work organises variables into biologically informed blocks, applies forbidden-edge constraints, and decomposes pathway-level effects into TE, NDE, and NIE components. We evaluate RetiSEM across ten synthetic benchmark scenarios that vary in dimensionality, nonlinearity, causal depth, and pathway structure, together with a fragmented real-world setting that combines NHANES clinical variables with externally derived retinal representations. This approach achieves lower structural error and higher causal accuracy than unconstrained baselines across the synthetic benchmarks. In the real-data analysis, retinal variables behave mainly as downstream biomarker-like indicators, with smaller but detectable indirect effects. These findings support our strategy as an interpretable framework for testing structured causal hypotheses in limited-resource biomedical AI. The code and resources for this work are publicly available at: https://github.com/Inamullah-Colab/ReitSEM.", "date": "2026-06-23", "categories": []}
{"id": "2606.26467", "title": "A Causal Foundation Model for Structure and Outcome Prediction", "abstract": "We introduce TabPFN-CFM, a causal foundation model that can handle multiple causal problems. TabPFN-CFM predicts both causal structure and outcomes from observational data, supports queries on all three levels of Pearl's Causal Hierarchy and uses known graph structure when available to improve predictions. TabPFN-CFM is trained on synthetic datasets, and generalises to real datasets, demonstrating improved performance over both structural and outcome prediction baselines.", "date": "2026-06-25", "categories": []}
{"id": "2606.30467", "title": "Non-parametric recovery of causal diffusion mechanisms from steady-state observations", "abstract": "We consider sparse multivariate stochastic systems that evolve in continuous time according to a causal mechanism and present methodology to recover the system's time-infinitesimal transition mechanism from mere cross-sectional data. This observational paradigm is motivated by applications such as gene expression analysis, where destructive experimental techniques may only allow recording data once over a cell's lifetime. Precisely, we assume the system follows a time-homogeneous diffusion process that has reached an equilibrium distribution at observation time. Further, we assume the causal mechanism is fully described by the diffusion drift, is acyclic, and its causal structure graph is known. In this setting, we prove that the full causal mechanism, i.e., the drift function, can be non-parametrically identified under a weak non-explosion criterion. We derive a non-parametric kernel estimator for this challenging inverse problem and prove its consistency. Moreover, we propose a cross-validation scheme for hyperparameter tuning, illustrate the behavior of our estimator in simulations, and we discuss connections with irreversible generative diffusion models and low-frequency sampled data.", "date": "2026-06-29", "categories": []}