F
faithfulness | \(F = \rho_{\mathrm{Pearson}}\!\left(\mathrm{attr},\ |\Delta y(u)|\right)\) | Raw Pearson correlation between the method's per-cause attribution magnitudes and the oracle's true absolute causal effects |Delta_y(u)|, scored separately for the content and position output regimes. | ✓ matches kernelshap.jl: SHAP map per cause, F = pearson(shap_attr, oracle_abs_delta); triad_extra_dict(f.pearson, attr, f.oracle_abs_delta). Record: out/kernelshap_air_raid_content.json (metric_name=pearson_corr_with_oracle, value=0.79). Scorer pilot_ig_vs_oracle.jl pearson() (raw Statistics.cor, zero-variance->0); F = pearson(attr, oracle_abs_delta) where oracle_abs_delta = abs.(cmap.delta) (true |Delta_y| per cause). Also reports spearman, precision@k, deletion/insertion AUC (paper's auxiliary F metrics). Per-regime split: separate *_content.json and *_position.json records, each carrying its own extra.triad.{F,S,M}. |
S
sufficiency | \(S = \dfrac{\#\{\,u_{\mathrm{held}}:\ |\hat{y}-y|\le\varepsilon\,\}}{|\mathrm{held\text{-}out}|}\in[0,1]\) | Fit Delta_y = a*attr + b on a calibration half of the do(u) causes, predict the disjoint held-out half, and report the fraction of held-out causes whose predicted output lands within an epsilon band of the oracle's bit-exact re-run. | ✓ matches common/triad_sm.jl sufficiency_score() (interleaved calib/held split by seed, least-squares 1-D fit Delta_y~a*attr+b on calib, epsilon = max(0.5, 0.10*heldout_spread)); assembled in triad_extra_dict(). The new §3 (sec:triad) admits the fraction-within-tolerance [0,1] special case of the held-out predictive test, which this held-out do(u) fit-then-predict estimator satisfies, so it matches. (Detail: epsilon is a self-scaled band 0.10*spread; the [-1,1] correlation form is available but this method reports the [0,1] hit fraction.)how it's measured — call stack:- sufficiency_score: fit Δy=a·attr+b on a calib half, predict held-out within ε —
triad_sm.jl:111 - assemble the F∧S∧M triad record (calls sufficiency_score) —
triad_sm.jl:173 - true causal effect Δy(u) by bit-exact re-run —
oracle_intervene.jl:242
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M
minimality | \(M = |U^{\star}| / |\hat{U}| \in (0,1]\quad U^{\star}=\{u:\Delta y(u)>0\},\ \hat{U}=\{u:|\mathrm{attr}(u)|>\tau\}\) | Ratio of the number of oracle causal movers (causes with nonzero true Delta_y) to the number of cells the method names above 1e-6 of its own max attribution; null when the oracle finds no mover or the method names nothing. | ✓ matches common/triad_sm.jl minimality_score() with name_frac=1e-6, mover_floor=0.0; the above-threshold named set is used (topk kept but not passed), see triad_extra_dict(). This is the paper's M = |U*|/|U_hat| in (0,1] (standardized everywhere), so it matches the new §3. (Detail: |U*| is taken as all oracle movers with Delta_y>0, an upper bound on the strictly-smallest reproducing subset, so M can be optimistic.) |
