Honest calibration assessment for binary outcome predictions

TL;DR

This paper introduces honest, adaptive confidence bands for assessing the calibration of binary outcome predictions, providing valid, narrower, and locally adaptive tools for evaluating model calibration.

Contribution

It proposes novel confidence bands for calibration curves that are valid under isotonicity, adapt to local smoothness and variance, and improve upon existing methods.

Findings

Finite sample coverage guarantee

Narrower than existing approaches

Provides informative calibration insights in real data

Abstract

Probability predictions from binary regressions or machine learning methods ought to be calibrated: If an event is predicted to occur with probability $x$, it should materialize with approximately that frequency, which means that the so-called calibration curve $p(\cdot)$ should equal the identity, $p(x) = x$ for all $x$ in the unit interval. We propose honest calibration assessment based on novel confidence bands for the calibration curve, which are valid only subject to the natural assumption of isotonicity. Besides testing the classical goodness-of-fit null hypothesis of perfect calibration, our bands facilitate inverted goodness-of-fit tests whose rejection allows for the sought-after conclusion of a sufficiently well specified model. We show that our bands have a finite sample coverage guarantee, are narrower than existing approaches, and adapt to the local smoothness of the calibration curve $p$ and the local variance of the binary observations. In an application to model predictions of an infant having a low birth weight, the bounds give informative insights on model calibration.