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The binary cross-entropy — sklearn.metrics.log_loss.

public static double Score(ReadOnlySpan<int> yTrue, ReadOnlySpan<double> yProba, int posLabel = 1, bool normalize = true, ReadOnlySpan<double> sampleWeight = default)

Parameters — yTrue is the true labels, one per sample. yProba is the probability of posLabel for each sample, in [0, 1]. posLabel is the label that probability is about, 1 by default. normalize divides by the total weight; pass false for the sum, which is normalize=False. sampleWeight is one weight per sample, or empty — the default.

Returns — double, 0 or above and unbounded. A perfect prediction scores 2.2204460492503136e-16 rather than 0, because the clip applies at the top end too.

Exceptions — ArgumentException when the lengths disagree, the input is empty, or a probability falls outside [0, 1]. The message is the reference's — "y_prob contains values greater than 1: 1.5" above, and "y_prob contains values lower than 0: -0.1" below. BrierScore.Score words that second one as less than, which is its own reference's wording rather than an inconsistency here. yTrue holding more than two distinct labels is refused as log_loss refuses it, "y_true and y_prob contain different number of classes: 3 vs 2.", rather than counting the third as negative — LogLoss.MultiClass scores it. 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." — only while normalize is true.

Example — four samples, well calibrated.

using Lodestar.Metrics;

int[] truth = [0, 1, 1, 0];
double[] confidence = [0.1, 0.9, 0.8, 0.3];

double loss = LogLoss.Score(truth, confidence);  // => 0.1976…

One confident mistake is what the metric is built to punish:

using Lodestar.Metrics;

int[] truth = [1, 0];
double[] certainAndWrong = [0.0, 0.5];

double punished = LogLoss.Score(truth, certainAndWrong);  // => 18.3684…

Remarks — posLabel is a widening. log_loss has no such parameter: a one-dimensional probability column always describes the greater of the two labels present, and passing labels in the other order does not change that — measured, it warns and returns the same number. Scoring about the other class is the same call on the complement, which is what this parameter reaches, and the frozen corpus pins that equivalence.

The clip is machine epsilon; the type page has what that decides.

Applies to — net10.0, netstandard2.0.

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