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The median of the absolute residuals.

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

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 weights the rows, and outputWeights weights the outputs in the reduction.

Returns — double, never negative, in the target's own units.

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. outputWeights are refused with an ArgumentException too, in scikit-learn's words, in three cases:

• holding NaN or an infinity — "Input contains NaN." or its infinity counterpart (#1461);
• given for a single output — "Custom weights are useful only in multi-output cases." (#1533);
• summing to zero, such as [0, 0] or [-1, 1] — "Weights sum to zero, can't be normalized", where scikit-learn raises ZeroDivisionError (#1588).

Example — three exact predictions and one catastrophic one. MeanAbsoluteError.Score on this data is 24.

using Lodestar.Metrics;

double[] yTrue = [1.0, 2.0, 3.0, 100.0];
double[] yPred = [1.0, 2.0, 3.0, 4.0];

double typical = MedianAbsoluteError.Score(yTrue, yPred);   // => 0

Remarks — reach for this when your data has outliers you do not believe in — mistyped labels, a sensor that dropped out, a fraud in the training set. Its breakdown point is 50%: half your samples can be arbitrarily wrong and this number does not move. That is a genuinely different question from the one MeanAbsoluteError.Score answers, and reporting the two side by side is the fastest way to see whether a dataset has a tail.

Which is the trap, stated as bluntly as the example above puts it: 0 here does not mean the model is good. It means at least half the predictions are exact, and says nothing about the other half. Never report this alone; pair it with MeanAbsoluteError.Score or MaxError.Score.

Under sampleWeight this stops being the value at the halfway point. scikit-learn takes an averaged weighted percentile — the mean of the first value whose cumulative weight reaches half the total and the one just past the last that comes within one machine epsilon of it — and that tolerance is load-bearing rather than decoration: a uniform weight is usually the ordinary median and not always. Measured, [0.7] * 10 gives 5.0 on the weighted path against 4.5 unweighted, while [0.1] * 10 gives 4.5 on both. Both agree with scikit-learn, whose _weighted_percentile compares against np.finfo(np.float64).eps rather than zero.

Negative weights are read as scikit-learn reads them. A negative weight makes the cumulative weight fall as well as rise, and the halfway point is then found by numpy 2.5's own searchsorted, whose branchless halving lands where a textbook binary search does not: sampleWeight: [1, -1, 0] on [1, 2, 3] against [1, 2, 4] gives 1.0, as scikit-learn does (#1546). One case stays out of reach: equal errors carrying different weights, where the result follows the order numpy's argsort leaves them in, which is not stable and depends on the CPU's vector units. sampleWeight: [-2, 0, 2, -1] on [2, 2, 0, 1] against zeros gives 0.0 there and 2.0 here. Measured, 1 random case in 2,000 with continuous errors and about 5 % with tied integer errors, both under negative weights; with non-negative weights that order changes nothing.

Applies to — net10.0, netstandard2.0.

See also — MedianAbsoluteError.PerOutput, MeanAbsoluteError.Score, MaxError.Score, the Python equivalence table.