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The Brier score over a probability matrix — sklearn.metrics.brier_score_loss with 2-D probabilities.

public static double MultiClass(ReadOnlySpan<int> yTrue, ReadOnlySpan<double> yProba, int classCount, bool scaleByHalf = false, ReadOnlySpan<double> sampleWeight = default)

Parameters — yTrue is the true class index of each sample, in [0, classCount). yProba is the class probabilities row-major. classCount is how many classes each row scores. scaleByHalf halves the sum over classes; false, the default, is what scale_by_half='auto' resolves to for a matrix. sampleWeight is one weight per sample, or empty.

Returns — double, 0 or above. Unlike LogLoss.MultiClass, every column contributes: the score is the squared distance from the one-hot truth across the whole row, so a probability moved between two wrong classes changes it.

Exceptions — ArgumentException when yProba is not yTrue.Length × classCount, when a label is not a class index below classCount, or when a probability falls outside [0, 1]. A sampleWeight holding NaN or an infinity is refused with "Input sample_weight contains NaN." or its infinity counterpart, and one that is zero throughout with "Sample weights must contain at least one non-zero number." — both ArgumentException naming sampleWeight, as scikit-learn's _check_sample_weight refuses them. Weights that merely sum to zero are refused too, with numpy's "Weights sum to zero, can't be normalized." ArgumentOutOfRangeException when classCount is below two.

Example — four samples over three classes.

using Lodestar.Metrics;

int[] truth = [0, 1, 2, 1];
double[] probabilities =
[
    0.7, 0.2, 0.1,
    0.1, 0.8, 0.1,
    0.2, 0.2, 0.6,
    0.3, 0.4, 0.3,
];

double brier = BrierScore.MultiClass(truth, probabilities, classCount: 3);  // => 0.245

Remarks — the default of scaleByHalf is false here and true on BrierScore.Score, deliberately: the reference's 'auto' reads the input's shape rather than the caller's intent, and reproducing it as a default per entry point is what keeps both numbers the reference's. Halving the example above gives 0.1225.

Rows that do not sum to 1 are scored as given, for the reason LogLoss.MultiClass states.

Applies to — net10.0, netstandard2.0.

See also — BrierScore.Score, LogLoss.MultiClass, the Python equivalence table.