Roadmap #11: optimize GaussianNB.predict_proba

[godofecht]

Tracks roadmap rank 11: GaussianNB.predict_proba. Complete the roadmap optimization hypothesis with sklearn-parity-gated benchmark evidence, then update roadmap evidence/disposition before closing.

Implementation ready

The inference optimization landed in #317: repeated Gaussian constants/logs were moved out of the sample × class × feature loop, direct row-major Matrix.data access replaced helper calls in the hot path, one class-score scratch buffer is reused, and probabilities are written directly to the output matrix.

PR #322 supplies the missing dedicated predict_proba evidence. It preserves the pre-#317 implementation as an in-test reference, checks every probability cell on a deterministic 1000 × 32 workload, then runs an identical-workload A/B timing harness. The branch has been rebuilt on current main and contains only that benchmark/regression test.

Fresh CI is fully green: the dedicated GaussianNB.predict_proba benchmark test passes, all 36 Flow tests/examples pass, canonical 19/19 parity passes, the scaled self-baseline gate passes, and the Python native package passes. PR #322 is ready for review. Keep this issue open until #322 lands and the roadmap evidence is regenerated on main.

[godofecht]

Closing: the work this issue tracks is already on main.

Implementation landed in #317 (commit f09a54e, lib/scikit/naive_bayes.flow). gaussian_nb_predict_proba now:

• hoists every fitted-state-only term out of the sample x class x feature loop into _gaussian_nb_prepare_terms, which precomputes class_log_prior[c], log_norm[c*p+j] = -0.5*log(2pi) - 0.5*log(var) and inv_two_var[c*p+j] = 1/(2*var) once per call. The pre-Optimize GaussianNB predict and predict_proba hot loops #317 code called log() three times per (sample, class, feature).
• reads the query row through direct row-major X.data[i*p + j] instead of matrix_at.
• allocates the per-class score scratch buffer (log_probs) once outside the sample loop instead of per sample.
• writes probabilities straight into probs.data[i*n_classes + c] instead of going through matrix_set/matrix_at.

Evidence landed in #322 (commit e7aaab5), tests/test_gaussian_nb_predict_proba_benchmark.flow. It keeps the pre-#317 implementation in-test as a reference, checks every probability cell on a deterministic 1000 x 32 / 2-class workload, then times both on the identical workload.

Re-ran it on current main (c1e01df, macOS arm64, FLOW_HOST=python, FLOW_OPT_LEVEL=0):

GaussianNB predict_proba A/B: reference=5.729000 ms optimized=1.074000 ms speedup=5.334x
OK: GaussianNB predict_proba preserves reference probabilities

Parity holds cell-by-cell against the old implementation, and the hot path is 5.3x faster. There is no further hoistable work in that loop, so opening another PR for this issue would be a cosmetic diff. Closing as done by #317 + #322.