Metrics logloss

LogLoss

The cross-entropy of a probabilistic prediction: how surprised the model should be by what actually happened. 0 is perfect and it is unbounded above — one confident mistake dominates the whole average, which is the property the metric exists for.

Three questions, three metrics. Accuracy asks whether the prediction was right. RocAuc asks whether the ranking was right. This asks whether the confidence was honest, and it is the one to read before choosing a threshold.

The clip is the specification

A predicted 0 for the class that actually occurred would make the logarithm infinite, so the reference clips every probability into [eps, 1 - eps]. That bound is machine epsilon, 2.220446049250313e-16 — measured against scikit-learn 1.9.0 rather than assumed, because it has changed across versions, and it is what decides the number in exactly the cases a caller cares about.

Three consequences worth knowing:

• A predicted 0 for the true class contributes -log(eps), about 36.04. Two samples of [0.0, 0.5] against labels [1, 0] score 18.36840028483855.
• Anything below the clip scores the same. 1e-20 and 0.0 are one number; 1e-15 is above it and scores 17.6159… instead.
• A perfect prediction is not 0 but 2.2204460492503136e-16, because the upper end is clipped too.

A row that does not sum to one is scored, not fixed

The reference warns and computes with the values as given. C# has no warning channel, so this is silent — and the number is what carries the behaviour. Measured, halving every row of a four-sample matrix takes the loss from 0.5017… to 1.1948… rather than leaving it alone. If rows may not be normalised, normalise them.

Members

Member	What it does
LogLoss.Score	The binary case, from one probability per sample.
LogLoss.MultiClass	The same over a probability matrix.