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One median absolute error per output, unreduced.

public static double[] PerOutput(ReadOnlySpan<double> yTrue, ReadOnlySpan<double> yPred, int outputCount = 1, ReadOnlySpan<double> sampleWeight = default)

Parameters — yTrue and yPred are the true and predicted values, row-major. outputCount is how many outputs each row holds, and sampleWeight weights the rows.

Returns — a fresh double[] of outputCount entries, in column order.

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 — three samples, two outputs; each column's median is taken separately.

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[] perOutput = MedianAbsoluteError.PerOutput(yTrue, yPred, outputCount: 2);
double first = perOutput[0];    // => 0.5
double second = perOutput[1];   // => 1

Remarks — the median is taken per column, which is the only definition that makes sense and is worth stating because it is not what "the median of a matrix" would mean. Each output is sorted on its own and its own middle value taken.

The trap is that a median does not decompose the way a mean does. The mean of the per-output medians that Score returns is not the median of anything, so it is a summary of summaries rather than a statistic of the data. On multioutput targets, read the array.

Internally each column is selected rather than fully sorted, which is what keeps this from costing an n log n per output — the selection rule. Nothing about the answer depends on it.

Applies to — net10.0, netstandard2.0.

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