Evaluating probabilistic classifiers: Reliability diagrams and score decompositions revisited

TL;DR

This paper introduces the CORP approach for creating reliable, stable, and reproducible reliability diagrams for probabilistic classifiers, enhancing calibration assessment with statistical guarantees and uncertainty quantification.

Contribution

The paper presents the CORP method, based on isotonic regression and PAV algorithm, for automated, statistically consistent reliability diagrams with uncertainty measures and generalized score decompositions.

Findings

CORP provides stable, reproducible reliability diagrams.

It enables uncertainty quantification via resampling or asymptotic theory.

Offers a generalized Brier score decomposition for proper scoring rules.

Abstract

A probability forecast or probabilistic classifier is reliable or calibrated if the predicted probabilities are matched by ex post observed frequencies, as examined visually in reliability diagrams. The classical binning and counting approach to plotting reliability diagrams has been hampered by a lack of stability under unavoidable, ad hoc implementation decisions. Here we introduce the CORP approach, which generates provably statistically Consistent, Optimally binned, and Reproducible reliability diagrams in an automated way. CORP is based on non-parametric isotonic regression and implemented via the Pool-adjacent-violators (PAV) algorithm - essentially, the CORP reliability diagram shows the graph of the PAV- (re)calibrated forecast probabilities. The CORP approach allows for uncertainty quantification via either resampling techniques or asymptotic theory, furnishes a new numerical measure of miscalibration, and provides a CORP based Brier score decomposition that generalizes to any proper scoring rule. We anticipate that judicious uses of the PAV algorithm yield improved tools for diagnostics and inference for a very wide range of statistical and machine learning methods.