What is the Brier score and how does it compare to log loss?
mediumAnswer
- Brier = 1/n * sum — mean squared error between predicted probability and true label.
- Range [0, 1] for binary.
- Like log loss, it's a proper scoring rule that penalizes miscalibration.
- Differences: Brier is bounded and quadratic (less punishing on confident mistakes than log loss), decomposable into calibration + refinement + uncertainty terms (Murphy decomposition), and interpretable in probability units.
- Prefer Brier when confident misprediction shouldn't dominate the metric.
Check yourself — multiple choice
- Brier is the same as accuracy
- MSE between predicted probability and true label; bounded, decomposable, less harsh than log loss on outliers
- Brier is only for regression
- Brier score can be greater than 1
Brier = MSE(p, y). Proper scoring rule, decomposable, more forgiving than log loss.
#metrics#classification#calibration
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