Metrics explainedvariance varianceweighted

ExplainedVariance.VarianceWeighted

One number, each output counted in proportion to how much its own truth varies.

public static double VarianceWeighted(ReadOnlySpan<double> yTrue, ReadOnlySpan<double> yPred, int outputCount, ReadOnlySpan<double> sampleWeight = default, bool forceFinite = true)

Parameters — yTrue and yPred are the true and predicted values, row-major. outputCount is how many outputs each row holds, and unlike the other two members it has no default — asking for a variance-weighted average of one output is a mistake worth catching at the call site. sampleWeight weights the rows, and forceFinite clamps the zero-variance case.

Returns — double at most 1.

Exceptions — ArgumentException when a length disagrees with the shape, the input is empty, or it holds a non-finite value; ArgumentOutOfRangeException when outputCount is below one.

Example — the same two outputs, the busier one counting for more.

using Lodestar.Metrics;

double[] yTrue = [0.5, 1.0, -1.0, 1.0, 7.0, -6.0];
double[] yPred = [0.0, 2.0, -1.0, 2.0, 8.0, -5.0];

double weighted = ExplainedVariance.VarianceWeighted(yTrue, yPred, outputCount: 2);   // => 0.9830…

Remarks — a plain mean over outputs treats a target that barely moves as equal in importance to one that swings widely, which is rarely what anyone means. This weights each output by the variance of its own truth, so the outputs that carry the information carry the score.

It is a method rather than an outputWeights value you could pass to Score, because the weights are this computation's own per-output variances: they come out of the same pass that produced the scores and cannot be recovered from the scores alone — decision 0021.

The trap is that it is not comparable with Score across datasets. Two models on the same data can be ranked by either, but a variance-weighted number and a uniform-average number are different summaries, and swapping one for the other between two reports invents a change that is not there.

Applies to — net10.0, netstandard2.0.

See also — ExplainedVariance.Score, ExplainedVariance.PerOutput, R2.VarianceWeighted, decision 0021, the Python equivalence table.