fix(metrics): correct explained_variance residual-variance term

[teddytennant]

What

SingleTargetRegression::explained_variance computed the residual-variance numerator as diff.mapv_into(|x| x * x).sum() - mean_error, i.e. Σ(diffᵢ²) − mean(diff). That subtracts the raw residual mean (units of y) from a sum of squared residuals (units of y²), which is dimensionally inconsistent.

Explained variance is defined as:

EV = 1 − Var(y_true − y_pred) / Var(y_true)

so the numerator must be the sum of squared deviations of the residuals from their mean, Σ(diffᵢ − mean_error)². mean_error = diff.mean() was already computed but misused. This PR uses it correctly. Numerator and denominator are both sums over the same n samples, so the biased-variance 1/n factors cancel and the existing + 1e-10 denominator guard is preserved.

Why

For y_true = [0, 0.1, 0.2, 0.3, 0.4], y_pred = [0.1, 0.3, 0.2, 0.5, 0.7]:

quantity	value
old explained_variance	0.8 (matches neither R² nor EV)
r2	−0.8
corrected explained_variance	0.48
sklearn.metrics.explained_variance_score	0.48

The old result of 0.8 corresponded to no standard metric. The corrected value matches scikit-learn's reference implementation.

Testing

• Updated test_explained_variance_for_single_targets to assert the corrected value 0.48 (was 0.8), with a comment citing the scikit-learn reference.
• test_same (explained_variance(ones, ones) == 1.0) still passes: diff == 0 ⇒ numerator 0 ⇒ 1 − 0/1e-10 = 1.0.
• cargo test -p linfa explained_variance and the full cargo test -p linfa --lib metrics_regression suite (16 tests) pass.
• cargo fmt --check and cargo clippy -p linfa --lib --tests -- -D warnings are clean.

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[quietlychris]

I'm generally onboard with this change, but when referencing the sklearn implementation, but would like to see a link to the referenced sklearn implementation and docs just to verify alignment there before approving.

[teddytennant]

Links:

• docs: https://scikit-learn.org/stable/modules/generated/sklearn.metrics.explained_variance_score.html
• source: https://github.com/scikit-learn/scikit-learn/blob/53302ff996818d108851e31d38a421425026bba5/sklearn/metrics/_regression.py#L1144-L1152

The part that matters:

y_diff_avg = _average(y_true - y_pred, weights=sample_weight, axis=0, xp=xp)
numerator = _average(
    (y_true - y_pred - y_diff_avg) ** 2, weights=sample_weight, axis=0, xp=xp
)

y_true_avg = _average(y_true, weights=sample_weight, axis=0, xp=xp)
denominator = _average(
    (y_true - y_true_avg) ** 2, weights=sample_weight, axis=0, xp=xp
)

sklearn averages both terms where we sum both terms, so the 1/n cancels and the results agree. Ran it rather than eyeballing it, sklearn 1.9.0 on the test's own data:

>>> explained_variance_score([0.0,0.1,0.2,0.3,0.4], [0.1,0.3,0.2,0.5,0.7])
0.4800000000000002
>>> r2_score([0.0,0.1,0.2,0.3,0.4], [0.1,0.3,0.2,0.5,0.7])
-0.7999999999999994

0.48 is what the test now asserts, and -0.8 is what r2 already returned here before this PR, so the two metrics line up with sklearn on both counts. Put the doc link in the test comment too.

Also rebased on master, it had picked up three commits. cargo test --release --workspace is 547 passed, 0 failed. fmt and clippy clean.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 77.94%. Comparing base (3b411a4) to head (ff0ed3e).

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #447   +/-   ##
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  Coverage   77.93%   77.94%           
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  Files         104      104           
  Lines        7547     7549    +2     
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+ Hits         5882     5884    +2     
  Misses       1665     1665           

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