docs/algorithms/README.md

Core Algorithm Specifications & Mathematical Foundations

Privacy-Preserving Collaborative Financial Crime Intelligence Platform (CF-Intelligence)

This directory contains the authoritative mathematical, algorithmic, and implementation specifications for the core machine learning, privacy, security, and graph intelligence algorithms employed across CF-Intelligence.

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Algorithmic Architecture Index

Algorithm	Primary Reference	Domain / Problem Solved	Implementation Module	Test Harness
FedAvg	McMahan et al., 2017	Distributed parameter optimization	backend/app/application/services/fl_engine.py	test_fl_engine.py
FedProx	Li et al., 2020	Non-IID label skew & straggler robustness	backend/app/application/services/fl_engine.py	test_fl_engine.py
SCAFFOLD	Karimireddy et al., 2020	Client drift correction via control variates	backend/app/application/services/fl_engine.py	test_fl_engine.py
Differential Privacy & RDP	Mironov, 2017; Abadi et al., 2016	Information bounding & membership defense	backend/app/application/services/privacy_service.py	test_privacy_service.py
Curve25519 SecAgg	Bonawitz et al., 2017	Pairwise zero-sum update blinding	backend/app/infrastructure/security/p2p_secagg_driver.py	test_p2p_secagg_driver.py
Byzantine Robustness (Krum/Bulyan)	Blanchard et al., 2017; Guerraoui et al., 2018	Poisoned / adversarial weight filtering	backend/app/domain/byzantine_defense.py	test_byzantine_defense_branches.py
GraphSAGE	Hamilton et al., 2017	Inductive multi-hop transaction graph embeddings	backend/app/application/services/graph_embedding_model.py	test_graph_embedding.py
MinHash LSH Fuzzy PSI	Broder, 1997	Cross-bank entity matching without raw identifier exposure	backend/app/domain/minhash_lsh.py, graph_engine.py	test_minhash_psi.py, test_graph_engine.py
SHAP KernelExplainer	Lundberg & Lee, 2017	Local cooperative game theory feature attribution	backend/app/application/services/explainability_service.py	test_explainability_service.py

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Design Invariants Across All Implementations

1. Zero Raw PII Transmission: No raw customer names, account numbers, or plain transaction amounts leave local banking nodes.
2. Deterministic Seed Control: All randomized mechanisms (Gaussian DP, Shamir secret sharing, stochastic mini-batching) support explicit seed initialization for reproducible testing.
3. Explicit Threat Boundaries: Every algorithm document details the specific mathematical adversarial budget ($f < \frac{n-2}{2}$, $\epsilon \le \epsilon_{\max}$, $\delta = 10^{-5}$) under which guarantees hold.

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Mathematical & Empirical Evaluation Metric Standards

All quantitative evaluations and model risk validations across these algorithms strictly adhere to the unified standard defined in docs/METRICS.md:

Metric Category	Standard Metrics	Formal Mathematical Target	Applicable Governance Framework
Imbalance Detection	$\mathrm{PR\text{-}AUC}$ (Average Precision), $\mathrm{Recall@0.1%FPR}$	$\mathrm{PR\text{-}AUC} \ge 0.75$, $\mathrm{Recall@0.1%FPR} \ge 0.60$	Federal Reserve SR 11-7 / OCC 2011-12
Probability Calibration	$\mathrm{ECE}$ ($M=10$ bins), $\mathrm{BS}$ (Brier Score)	$\mathrm{ECE} \le 0.030$, $\mathrm{BS} \le 0.020$	EU AI Act Art. 15 (Accuracy & Robustness)
Population Drift	$\mathrm{PSI}$ (Traffic-light matrix), $\mathrm{JSD}$ (Symmetric KL)	$\mathrm{PSI} < 0.10$ (stable), $\mathrm{JSD} \le 0.15$	Basel Committee BCBS 32 Model Risk
Economic & Fairness	$\mathcal{L}{\mathrm{financial}}$ ($C{\mathrm{FN}}=850$, $C_{\mathrm{FP}}=25$), $\mathrm{DIR}$	$\theta^*_{\mathrm{cost}} = \arg\min \mathcal{L}$, $0.80 \le \mathrm{DIR} \le 1.25$	ECOA Reg B / EEOC 80% Rule