Metrics meansquarederror score

Development build. This page describes main, not a released package. The latest published Lodestar.Metrics is 0.3.0 — read its documentation.

MeanSquaredError.Score

The mean of the squared 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, 0 only for an exact prediction. In the square of the target's 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.

Example — the same four predictions MeanAbsoluteError.Score scores 0.5.

using Lodestar.Metrics;

double[] yTrue = [3.0, -0.5, 2.0, 7.0];
double[] yPred = [2.5, 0.0, 2.0, 8.0];

double error = MeanSquaredError.Score(yTrue, yPred);   // => 0.375

Remarks — squaring is the whole design, and it has two consequences that pull in opposite directions. It makes the metric differentiable everywhere, which is why almost every regression model minimises it during training. And it makes one bad prediction count out of all proportion: on [1, 2, 3, 100] against [1, 2, 3, 4] this is 2304 where MeanAbsoluteError.Score is 24. If your costs really do grow faster than the error does — a bridge, a dosage — that is the right behaviour. If they do not, it is a metric that will let one bad label decide which model you ship.

The trap is the units. This is in the square of the target's units, so a mean squared error of 0.375 on a target measured in metres is 0.375 square metres, which is not a distance and is not comparable to a mean absolute error of 0.5. RootMeanSquaredError.Score puts it back into metres, and is what you should report to anyone who is going to read the number rather than optimise it.

The accumulation is Neumaier-compensated, at least as accurate as numpy's pairwise reduction rather than merely close to it — decision 0033.

Applies to — net10.0, netstandard2.0.

See also — MeanSquaredError.PerOutput, RootMeanSquaredError.Score, MeanAbsoluteError.Score, R2.Score, the Python equivalence table.