Bug: OvO Multi-class `coef_` Diverges from sklearn `OneVsOneClassifier` Despite Matching Accuracy

[statmlben]

@Leona-LYT

When using plq_Ridge_Classifier with multi_class='ovo', the fitted coefficients (coef_) diverge significantly from those produced by sklearn's OneVsOneClassifier(LinearSVC(...)), even though both classifiers achieve identical test accuracy. The maximum per-coefficient absolute difference reaches 4.24 (far above the expected tolerance of 1e-3), indicating a numerical or algorithmic discrepancy in the OvO subproblem setup.

Steps to Reproduce

python tests/_test_multiclass.py

Maybe there is some post-processing on solution for LinearSVC; please fix/figure it.

[Leona-LYT]

The root cause is a sign convention mismatch in the OvO label encoding.

In _fit_multiclass, each OvO subproblem was encoded as cls_i → +1, cls_j → -1. However, sklearn's LinearSVC internally uses LabelEncoder, which sorts classes before encoding, so it always maps the lower class to -1 and the higher class to +1. Since combinations() yields sorted pairs, cls_i < cls_j is always true, meaning sklearn's convention is cls_i → -1, cls_j → +1 — the opposite of what we had.

This sign flip on y causes the solver to find β_rehline = -β_sklearn, which explains the large coefficient differences (max diff ~4.24). Predictions appeared correct because the two errors cancelled out — the voting logic was also reversed in the same direction.

Fix: Two changes are required together:

1. In _fit_multiclass: change np.where(y[mask] == cls_i, 1, -1) to np.where(y[mask] == cls_j, 1, -1)
2. In predict: update the voting logic so that a positive score votes for cls_j instead of cls_i

Both changes must be applied together. After the fix, OvO coef_ matches sklearn within tol=1e-3.