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difficulty 3/5

Model calibration

Definition

Making a model's stated confidence mean what it says — of the predictions it makes at 90% confidence, 90% should be right. Accuracy does not measure this, and modern networks fail it badly.

Formula
P(Y^=Y∣P^=p)=p,∀p∈[0,1]\mathbb{P}\big(\hat{Y} = Y \mid \hat{P} = p\big) = p, \qquad \forall p \in [0, 1]

Intuition

A classifier that is right 74% of the time and says so is useful. One that is right 74% of the time while claiming 87% is dangerous in a specific way: every decision downstream that consumes the number — a threshold, an expected cost, a handover to a human — is being fed a lie.

The requirement has a one-sentence test: "given 100 predictions, each with confidence of 0.8, we expect that 80 should be correctly classified" [1, §2].

Accuracy does not measure this and neither does AUC, because both only care about ordering and thresholding. A model can rank every example perfectly and still state probabilities that are uniformly far too high. Calibration is a separate property, and it is the one that matters whenever the probability itself is used rather than just the argmax.

The uncomfortable finding is that progress made it worse: "modern neural networks, unlike those from a decade ago, are poorly calibrated" [1, abstract].

Formal definition

How it works

Where it's used

Why & when

Worked example

Pitfalls

Check yourself

3 questions

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On the cheat sheet: Classification metrics →

Sources

  1. Guo, Pleiss, Sun, Weinberger. On Calibration of Modern Neural Networks (2017)paperhttps://ar5iv.labs.arxiv.org/html/1706.04599
  2. scikit-learn User Guide — Probability calibrationdocs · retrieved 2026-09-06https://scikit-learn.org/stable/modules/calibration.html

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