Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibration

TL;DR

This paper introduces Dirichlet calibration, a new multiclass calibration method that improves probability estimates across various models and datasets by generalizing binary beta calibration to the multiclass setting.

Contribution

It presents a natively multiclass calibration technique based on Dirichlet distributions, extending beta calibration, and demonstrates its effectiveness over existing methods.

Findings

Improved calibration metrics across multiple datasets and classifiers.

Easy implementation with neural networks via log-transform and linear layer.

Provides insights into model biases through Dirichlet parameters.

Abstract

Class probabilities predicted by most multiclass classifiers are uncalibrated, often tending towards over-confidence. With neural networks, calibration can be improved by temperature scaling, a method to learn a single corrective multiplicative factor for inputs to the last softmax layer. On non-neural models the existing methods apply binary calibration in a pairwise or one-vs-rest fashion. We propose a natively multiclass calibration method applicable to classifiers from any model class, derived from Dirichlet distributions and generalising the beta calibration method from binary classification. It is easily implemented with neural nets since it is equivalent to log-transforming the uncalibrated probabilities, followed by one linear layer and softmax. Experiments demonstrate improved probabilistic predictions according to multiple measures (confidence-ECE, classwise-ECE, log-loss, Brier score) across a wide range of datasets and classifiers. Parameters of the learned Dirichlet calibration map provide insights to the biases in the uncalibrated model.