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The mean of the squared differences of log(1 + y).

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, and every value must be above −1. 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 squared log units, which are not the target's units and not a fraction either.

Exceptions — ArgumentException when a length disagrees with the shape, the input is empty, it holds a non-finite value, or either array holds a value at or below −1; ArgumentOutOfRangeException when outputCount is below one. 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 — four counts, one of them predicted 60% high.

using Lodestar.Metrics;

double[] yTrue = [3.0, 5.0, 2.5, 7.0];
double[] yPred = [2.5, 5.0, 4.0, 8.0];

double error = MeanSquaredLogError.Score(yTrue, yPred);   // => 0.0397…

Remarks — taking the logarithm first turns a ratio into a difference, so this charges "predicted twice the truth" the same whether the truth was 10 or 10 000. That makes it the natural metric for counts, demand, page views — anything that grows multiplicatively and where the small values are as interesting as the large ones. MeanSquaredError.Score on such a target is decided entirely by the largest few samples.

It is also asymmetric on purpose, and this is the reason to choose it over MeanAbsolutePercentageError.Score: because log compresses upward, under-predicting is charged more than over-predicting by the same factor. If running out of stock is worse than holding too much, that asymmetry is the feature.

Two traps. The units are not interpretable — 0.0397… is neither a count nor a percentage — so report RootMeanSquaredLogError.Score if a human is going to read it, and even then it is a log ratio. And negative targets are refused, not clamped: any value at or below −1 raises ArgumentException, because log(1 + y) is undefined there. The exception additionally names which side the offending value was on, which scikit-learn's does not.

The logarithm is numpy's log1p, reached through Kahan's identity rather than Math.Log(1.0 + x). That is not decoration: on targets around 1e-9 the naive spelling is out by 1.7e-8 relative, where this agrees with scikit-learn to a unit in the last place, because log(1 + x) · x / ((1 + x) − 1) divides out the rounding the addition made.

Applies to — net10.0, netstandard2.0.

See also — MeanSquaredLogError.PerOutput, RootMeanSquaredLogError.Score, MeanAbsolutePercentageError.Score, the Python equivalence table.