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The fraction of absolute error explained — sklearn.metrics.d2_absolute_error_score.

public static double Score(ReadOnlySpan<double> yTrue, ReadOnlySpan<double> yPred, int outputCount = 1, ReadOnlySpan<double> sampleWeight = default, ReadOnlySpan<double> outputWeights = default, ZeroDivision zeroDivision = ZeroDivision.NaN)

Parameters — yTrue and yPred are the true and predicted values, row-major when there is more than one output. outputCount is how many outputs each row holds. sampleWeight is one weight per row — per sample, not per value. outputWeights is a weight per output, multioutput=[…]; omit it for multioutput="uniform_average". zeroDivision decides the answer for fewer than two samples.

Returns — double. 1 for a perfect prediction, 0 for one no better than always predicting the weighted median, and negative below that.

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. UndefinedMetricException when there are fewer than two samples and zeroDivision is ZeroDivision.Throw. outputWeights holding NaN or an infinity is ArgumentException too, with scikit-learn's "Input contains NaN." or its infinity counterpart (#1461), and so is any outputWeights on a single output, with "Custom weights are useful only in multi-output cases." (#1533).

Example — the worked case, and the same weights read differently.

using Lodestar.Metrics;

double[] truth = [1.0, 2.0, 3.0, 4.0];
double[] predicted = [1.5, 2.5, 2.0, 4.5];

double explained = D2AbsoluteError.Score(truth, predicted);  // => 0.375

using Lodestar.Metrics;

double[] truth = [1.0, 2.0, 3.0, 4.0];
double[] predicted = [1.5, 2.5, 2.0, 4.5];
double[] weights = [1.0, 2.0, 3.0, 4.0];

double weighted = D2AbsoluteError.Score(truth, predicted, 1, weights);  // => 0.1875

Weighting the later samples more halves the score, because the third prediction — the worst of the four — is where most of the weight now sits.

Remarks — D2Pinball.Score at alpha: 0.5, asserted across the whole frozen corpus rather than on one pair, since the two reach their baseline through different code.

A truth that never varies answers 0 rather than raising: the reference masks that denominator here, where d2_tweedie_score divides by it — D2Tweedie.Score reproduces that side of the split.

Applies to — net10.0, netstandard2.0.

See also — D2AbsoluteError.PerOutput, D2Pinball.Score, R2.Score, MeanAbsoluteError.Score, the Python equivalence table.