fix(naive-bayes): GaussianNB var_smoothing = var_smoothing*max_var (sklearn parity) — F-GAUSSIANNB-EPSILON-003 (PMAT-890)

[noahgift]

PMAT-890 — Pillar-1 GaussianNB var_smoothing parity (F-GAUSSIANNB-EPSILON-003)

LIVE wrong-answer bug vs scikit-learn (the provably-correct reference).

Defect

GaussianNB::fit (in crates/aprender-core/src/classification/linear_svm.rs) added a raw additive var_smoothing (default 1e-9) directly to each per-class feature variance:

*variance_val = sum_sq_diff / n_class_samples + self.var_smoothing;

scikit-learn instead defines the smoothing as a single scalar scaled by the largest feature variance:

epsilon = var_smoothing * X.var(axis=0).max()

added uniformly to every per-class feature variance. On a mixed-scale dataset (one feature var ~3.25e6, another ~1e-4) the raw additive constant makes the smoothed variance for the small feature ~33.5× too small, mis-scaling the Gaussian log-likelihood / Mahalanobis term — able to flip predict.

Fix

Compute max_feature_var = max_j Var(X[:,j]) over all training rows (biased/population variance, matching the existing convention), set epsilon = var_smoothing * max_feature_var, add that single epsilon to every per-class feature variance. var_smoothing stays configurable (default 1e-9).

RED → GREEN evidence

Falsifier test_gaussian_nb_var_smoothing_scaled_by_max_feature_var (no Python/sklearn required; closed-form sklearn reference):

• RED (main, buggy): stored=1.000009943e-4 vs sklearn_expected=3.350000000e-3 (epsilon=3.25e-3), rel_err=0.97 → FAIL
• GREEN (fixed): passes; predict_proba rows finite and sum to ~1

Full crate tests

cargo test -p aprender-core --lib → 13955 passed; 0 failed; 2 ignored (no sibling test encoded the old raw-1e-9 behavior). cargo fmt --all --check clean, cargo clippy -p aprender-core -- -D warnings clean.

Contract

F-GAUSSIANNB-EPSILON-003 proof_obligation + single-line cargo test falsifier added to contracts/naive-bayes-v1.yaml. pv lint contracts/ → PASS (0 errors).

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