0026 r2 and explainedvariance split their undefined cases differently

0026 — R² and ExplainedVariance split their undefined cases differently

Status: accepted · Date: 2026-08-14

Context

R2.Score and ExplainedVariance.Score both divide by the variance of yTrue, both take forceFinite, and both were assumed — before this was checked against scikit-learn 1.9.0 rather than read off its source — to handle a zero denominator the same way. They do not.

sklearn.metrics.r2_score carries an explicit n < 2 check ahead of the division: with fewer than two samples the variance of yTrue is not just zero, it is not a defined quantity at all, and the function returns nan regardless of force_finite, with a warning. explained_variance_score carries no such check. A single sample still has a variance — zero, by the definition of variance over one point — so it reaches the same zero-denominator branch a constant multi-sample target would, and force_finite decides it exactly as it would for any other zero variance.

R2.cs reproduces the split with two independent knobs: forceFinite answers the zero-variance-over-two-or-more-samples branch, and ZeroDivision answers the fewer-than-two-samples branch, which is nan under either setting of forceFinite and therefore is not forceFinite's case at all. ExplainedVariance.cs takes only forceFinite, because it has no second branch to route — routing R2's fewer-than-two-samples case through ExplainedVariance's forceFinite would already be correct, since that case does not exist for this metric.

Decision

Case	R²	ExplainedVariance
Fewer than 2 samples	ZeroDivision's case: nan under either forceFinite setting	Not a separate case — one sample has zero variance by definition and falls into the row below
Zero variance, 2+ samples (or the 1-sample case, for ExplainedVariance)	forceFinite's case: 1 if the numerator also vanished, 0 otherwise, or unclamped nan/-inf	Same

The two R² branches must not be merged: routing the fewer-than-two-samples case through forceFinite would return -inf where scikit-learn returns nan. Not on every fixture that reaches it with forceFinite: false, though — the forceFinite: false branch is perfect ? nan : -inf (src/DataNet.Metrics/R2.cs:337-343), so a single sample predicted exactly right already yields nan and would hide the merge. Only a single wrong sample exposes it.

Consequences

• R2.Resolve and ExplainedVariance.Resolve carry the full per-branch reasoning at the point that implements it; the class-level <remarks> on R2 and ExplainedVariance point here instead of repeating it.
• Verified by R2Tests.Fewer_than_two_samples_is_zeroDivisions_case_and_not_forceFinites, R2Tests.Zero_variance_over_two_samples_is_forceFinites_case_and_not_zeroDivisions and R2Tests.Explained_variance_is_one_on_a_single_wrong_sample.
• A metric added later that divides by a variance-like denominator should check scikit-learn's own source for an equivalent early-exit before assuming its zero-denominator handling matches either of these two.