Calibration (Machine Learning)

In machine learning, a probabilistic classifier is calibrated when the probabilities it outputs correspond to the empirical frequency of the predicted event. Formally, for predictions binned by stated probability p, a perfectly calibrated model has an in-bin accuracy equal to p — so among predictions tagged "70% positive," about 70% are actually positive. Calibration is distinct from accuracy: a model can be highly accurate but overconfident (predicting 0.99 on questions it gets right 90% of the time) or under-accurate but well-calibrated (predicting 0.55 and being right 55% of the time). The standard diagnostic is the reliability diagram, which plots binned predicted probability against empirical accuracy; a calibrated model sits on the diagonal. The single-number summary most commonly reported is Expected Calibration Error (ECE), a weighted average of the gap between confidence and accuracy across bins. ECE is intuitive but binning-sensitive; proper scoring rules such as the Brier Score and log loss are alternatives that reward both calibration and sharpness without requiring a binning choice. Modern deep networks, including LLMs trained with Reinforcement Learning from Human Feedback, tend to be overconfident: their stated probabilities cluster near 1 even when accuracy is lower. Standard remedies include Platt scaling, isotonic regression, and temperature scaling — the last of which divides the pre-softmax logits by a single learned temperature parameter, leaving the argmax unchanged while spreading the probability mass. Calibration matters whenever a downstream system thresholds on probability — medical triage, fraud detection, selective prediction, or routing low-confidence LLM outputs to a human reviewer.