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11.7 kB
| """Pre-registered analysis for the v2 harness. | |
| Implements exactly what `PREREGISTRATION.md` commits to: | |
| * primary endpoint: Clotho five-caption T2A R@1; | |
| * secondary: Clotho A2T R@1, AudioCaps T2A R@1, AudioCaps A2T R@1; | |
| * effect: unfused minus fused, paired by query; | |
| * cluster bootstrap that resamples CLIPS (five captions per clip are not | |
| independent), 2000 resamples, fixed seed; | |
| * Holm correction across the four endpoints; | |
| * TOST equivalence at a pre-committed margin, so "no difference" is a claim. | |
| python analysis_v2.py results_v2 --prereg PREREGISTRATION.md | |
| """ | |
| from __future__ import annotations | |
| import argparse | |
| import json | |
| import math | |
| from pathlib import Path | |
| import numpy as np | |
| SEED = 20261027 | |
| N_BOOT = 2000 | |
| EQUIV_MARGIN = 0.03 # pre-registered, do not tune after seeing results | |
| ENDPOINTS = [ | |
| ("clotho5", "t2a", "r@1", "primary"), | |
| ("clotho5", "a2t", "r@1", "secondary"), | |
| ("audiocaps", "t2a", "r@1", "secondary"), | |
| ("audiocaps", "a2t", "r@1", "secondary"), | |
| ] | |
| # ---------------------------------------------------------------- estimators | |
| def _hit(r: int, k: int) -> float: | |
| return 1.0 if r <= k else 0.0 | |
| def cluster_bootstrap_mean(values: np.ndarray, clusters: np.ndarray, stat, | |
| n_boot: int = N_BOOT, seed: int = SEED): | |
| """Resample clusters with replacement; recompute the mean over all their rows.""" | |
| rng = np.random.default_rng(seed) | |
| uniq = np.unique(clusters) | |
| idx_by_cluster = {c: np.flatnonzero(clusters == c) for c in uniq} | |
| draws = np.empty(n_boot) | |
| for i in range(n_boot): | |
| pick = rng.choice(uniq, size=len(uniq), replace=True) | |
| idx = np.concatenate([idx_by_cluster[c] for c in pick]) | |
| draws[i] = stat(values[idx]) | |
| return (float(np.percentile(draws, 2.5)), | |
| float(np.percentile(draws, 97.5)), | |
| float(draws.std(ddof=1))) | |
| def cluster_bootstrap_delta(a: np.ndarray, b: np.ndarray, clusters: np.ndarray, | |
| n_boot: int = N_BOOT, seed: int = SEED): | |
| """Paired bootstrap over clusters: the same resample is applied to both arms.""" | |
| rng = np.random.default_rng(seed) | |
| uniq = np.unique(clusters) | |
| idx_by_cluster = {c: np.flatnonzero(clusters == c) for c in uniq} | |
| draws = np.empty(n_boot) | |
| for i in range(n_boot): | |
| pick = rng.choice(uniq, size=len(uniq), replace=True) | |
| idx = np.concatenate([idx_by_cluster[c] for c in pick]) | |
| draws[i] = b[idx].mean() - a[idx].mean() | |
| return (float(np.percentile(draws, 2.5)), float(np.percentile(draws, 97.5)), | |
| float(draws.std(ddof=1))) | |
| def tost(delta: float, se: float, margin: float = EQUIV_MARGIN, alpha: float = 0.05): | |
| """Two one-sided tests on a paired difference. | |
| Equivalent if the (1 - 2*alpha) CI lies inside [-margin, +margin]. Returned | |
| p-value is the larger of the two one-sided p-values, which is the standard | |
| TOST statistic. Normal approximation, appropriate at these n. | |
| """ | |
| if se <= 0: | |
| return {"equivalent": abs(delta) < margin, "p": 0.0 if abs(delta) < margin else 1.0, | |
| "ci90": [delta, delta]} | |
| z = delta / se | |
| p_lower = 1.0 - _norm_cdf(z + margin / se) # H0: delta <= -margin | |
| p_upper = _norm_cdf(z - margin / se) # H0: delta >= +margin | |
| p = max(p_lower, p_upper) | |
| ci90 = [delta - 1.6448536269514722 * se, delta + 1.6448536269514722 * se] | |
| return {"equivalent": bool(p < alpha), "p": float(p), | |
| "ci90": [float(ci90[0]), float(ci90[1])]} | |
| def _norm_cdf(x: float) -> float: | |
| return 0.5 * (1.0 + math.erf(x / math.sqrt(2.0))) | |
| def cluster_sign_flip(a_hits: np.ndarray, b_hits: np.ndarray, clusters: np.ndarray, | |
| n_perm: int = 10000, seed: int = SEED) -> dict: | |
| """Permutation test at the clip level. | |
| McNemar assumes independent pairs, but five captions of one clip share their | |
| audio, so those five pairs are correlated and McNemar's p is anti-conservative. | |
| Here the labels are swapped *per cluster*: under the null the two checkpoints are | |
| exchangeable within a clip, so each clip contributes either +d or -d, where d is | |
| that clip's (b - a) contribution. Captions never move independently. | |
| """ | |
| uniq, inv = np.unique(clusters, return_inverse=True) | |
| sa = np.bincount(inv, weights=a_hits.astype(float), minlength=len(uniq)) | |
| sb = np.bincount(inv, weights=b_hits.astype(float), minlength=len(uniq)) | |
| d = sb - sa | |
| total = float(len(a_hits)) | |
| obs = float(d.sum() / total) | |
| rng = np.random.default_rng(seed) | |
| hits = 0 | |
| done = 0 | |
| while done < n_perm: | |
| chunk = min(1000, n_perm - done) | |
| signs = rng.choice(np.array([-1.0, 1.0]), size=(chunk, len(uniq))) | |
| sims = signs @ d / total | |
| hits += int(np.sum(np.abs(sims) >= abs(obs) - 1e-15)) | |
| done += chunk | |
| p = (1.0 + hits) / (n_perm + 1.0) | |
| return {"delta": obs, "p_cluster_perm": float(p), | |
| "n_permutations": n_perm, "n_clusters": int(len(uniq))} | |
| def mcnemar_exact(a_hits: np.ndarray, b_hits: np.ndarray) -> tuple[float, int, int]: | |
| """Exact two-sided McNemar on paired binary outcomes. | |
| Returns (p, b_only, a_only) where b_only counts queries only b gets right. | |
| This is the difference test; TOST answers a different question and must not be | |
| substituted for it. | |
| """ | |
| n01 = int((~a_hits & b_hits).sum()) | |
| n10 = int((a_hits & ~b_hits).sum()) | |
| m = n01 + n10 | |
| if m == 0: | |
| return 1.0, n01, n10 | |
| tail = sum(math.comb(m, i) for i in range(0, min(n01, n10) + 1)) / 2 ** m | |
| return min(1.0, 2 * tail), n01, n10 | |
| def holm(pvals: dict[str, float], alpha: float = 0.05) -> dict[str, float]: | |
| """Holm-Bonferroni step-down. Returns adjusted p-values, monotone in the input.""" | |
| items = sorted(pvals.items(), key=lambda kv: kv[1]) | |
| m = len(items) | |
| adj, running = {}, 0.0 | |
| for i, (name, p) in enumerate(items): | |
| val = min(1.0, (m - i) * p) | |
| running = max(running, val) | |
| adj[name] = running | |
| return adj | |
| def mdd(se: float, alpha: float = 0.05, power: float = 0.8) -> float: | |
| """Minimum detectable difference at the given power (normal approximation).""" | |
| return float((1.959963984540054 + 0.8416212335729143) * se) | |
| # ---------------------------------------------------------------- loading | |
| def load_cell(path: Path) -> dict: | |
| d = json.loads(path.read_text(encoding="utf-8")) | |
| need = ("first_hit_rank", "cluster") | |
| if d["metrics"]["t2a"].get("cluster") is None: | |
| raise SystemExit(f"{path.name}: missing per-query clusters; rerun the cell") | |
| return d | |
| def arm(d: dict, direction: str, k: int): | |
| m = d["metrics"][direction] | |
| ranks = np.asarray(m["first_hit_rank"], dtype=np.int64) | |
| clusters = np.asarray(m["cluster"], dtype=np.int64) | |
| return np.array([_hit(r, k) for r in ranks]), clusters | |
| def summarise(d: dict, direction: str, k: int) -> dict: | |
| hits, clusters = arm(d, direction, k) | |
| lo, hi, se = cluster_bootstrap_mean(hits, clusters, lambda v: float(v.mean())) | |
| return {"value": float(hits.mean()), "ci95": [lo, hi], "se_cluster": se, | |
| "n_queries": int(len(hits)), "n_clusters": int(clusters.max() + 1)} | |
| def main() -> int: | |
| ap = argparse.ArgumentParser() | |
| ap.add_argument("dir", nargs="?", default="results_v2") | |
| ap.add_argument("--out", default="analysis_v2.json") | |
| ap.add_argument("--prereg", default="PREREGISTRATION.md") | |
| args = ap.parse_args() | |
| if not Path(args.prereg).exists(): | |
| raise SystemExit("PREREGISTRATION.md missing: analysis must follow a committed plan") | |
| root = Path(args.dir) | |
| cells = {} | |
| for f in sorted(root.glob("*__canon.json")): | |
| d = load_cell(f) | |
| cells[(d["dataset"], d["model"])] = d | |
| models = sorted({m for (_, m) in cells}) | |
| if len(models) != 2: | |
| raise SystemExit(f"expected two checkpoints, found {models}") | |
| report = {"prereg": args.prereg, "equivalence_margin": EQUIV_MARGIN, | |
| "cells": {}, "endpoints": {}} | |
| for ds in sorted({d for (d, _) in cells}): | |
| for m in models: | |
| key = f"{m}|{ds}" | |
| report["cells"][key] = { | |
| "t2a_r1": summarise(cells[(ds, m)], "t2a", 1), | |
| "a2t_r1": summarise(cells[(ds, m)], "a2t", 1), | |
| "t2a_mrr": summarise_rank(cells[(ds, m)], "t2a"), | |
| "a2t_map": summarise_ap(cells[(ds, m)]), | |
| } | |
| fused = next(m for m in models if m.endswith("fused")) | |
| unfused = next(m for m in models if m.endswith("unfused")) | |
| pvals = {} | |
| for ds, direction, metric, role in ENDPOINTS: | |
| if (ds, fused) not in cells or (ds, unfused) not in cells: | |
| continue | |
| k = int(metric.split("@")[1]) | |
| a, clusters = arm(cells[(ds, fused)], direction, k) | |
| b, _ = arm(cells[(ds, unfused)], direction, k) | |
| delta = float(b.mean() - a.mean()) | |
| lo, hi, se = cluster_bootstrap_delta(a, b, clusters) | |
| eq = tost(delta, se) | |
| # difference test at the clip level: captions within a clip are correlated, | |
| # so McNemar's independent-pairs p is reported only for reference | |
| perm = cluster_sign_flip(a > 0.5, b > 0.5, clusters) | |
| mcn_p, n01, n10 = mcnemar_exact(a > 0.5, b > 0.5) | |
| name = f"{ds}_{direction}_{metric}" | |
| pvals[name] = perm["p_cluster_perm"] | |
| report["endpoints"][name] = { | |
| "role": role, "dataset": ds, "direction": direction, "metric": metric, | |
| "delta_unfused_minus_fused": delta, | |
| "ci95": [lo, hi], "se_cluster": se, "mdd80": mdd(se), | |
| "p_cluster_perm": perm["p_cluster_perm"], | |
| "n_permutations": perm["n_permutations"], | |
| "mcnemar_p_reference_only": mcn_p, "b_only": n01, "a_only": n10, | |
| "tost_p": eq["p"], "equivalent_at_margin": eq["equivalent"], | |
| "ci90_for_tost": eq["ci90"], | |
| } | |
| holm_adj = holm(pvals) | |
| for name, adj in holm_adj.items(): | |
| report["endpoints"][name]["holm_adjusted_p"] = adj | |
| report["endpoints"][name]["significant_after_holm"] = bool(adj < 0.05) | |
| Path(args.out).write_text(json.dumps(report, indent=2), encoding="utf-8", | |
| newline="\n") | |
| print(f"{'endpoint':<24}{'delta':>8} {'95% CI':<19}{'perm p':>9}{'Holm':>8}" | |
| f"{'TOST':>8} verdict") | |
| for name, e in report["endpoints"].items(): | |
| ci = f"[{e['ci95'][0]:+.3f}, {e['ci95'][1]:+.3f}]" | |
| if e["significant_after_holm"]: | |
| verdict = "difference" | |
| elif e["equivalent_at_margin"]: | |
| verdict = "equivalent within +/-0.03" | |
| else: | |
| verdict = "inconclusive" | |
| print(f"{name:<24}{e['delta_unfused_minus_fused']:>+8.3f} {ci:<19}" | |
| f"{e['p_cluster_perm']:>9.2g}{e['holm_adjusted_p']:>8.2g}" | |
| f"{e['tost_p']:>8.2g} {verdict}") | |
| print(f"\nwrote {args.out}") | |
| return 0 | |
| def summarise_rank(d: dict, direction: str) -> dict: | |
| m = d["metrics"][direction] | |
| ranks = np.asarray(m["first_hit_rank"], dtype=np.float64) | |
| clusters = np.asarray(m["cluster"], dtype=np.int64) | |
| lo, hi, se = cluster_bootstrap_mean(ranks, clusters, lambda v: float((1.0 / v).mean())) | |
| return {"value": float((1.0 / ranks).mean()), "ci95": [lo, hi], "se_cluster": se} | |
| def summarise_ap(d: dict) -> dict: | |
| m = d["metrics"]["a2t"] | |
| ap = np.asarray(m["ap"], dtype=np.float64) | |
| clusters = np.asarray(m["cluster"], dtype=np.int64) | |
| lo, hi, se = cluster_bootstrap_mean(ap, clusters, lambda v: float(v.mean())) | |
| return {"value": float(ap.mean()), "ci95": [lo, hi], "se_cluster": se} | |
| if __name__ == "__main__": | |
| raise SystemExit(main()) | |