Uncertainty Estimates of Predictions via a General Bias-Variance Decomposition

TL;DR

This paper introduces a general bias-variance decomposition for proper scores, enabling more reliable uncertainty estimation in predictive models, especially under domain drift and across various tasks.

Contribution

It presents a novel bias-variance decomposition framework based on Bregman Information, applicable to multiple predictive tasks and capable of improving out-of-distribution detection.

Findings

The decomposition applies to exponential families and classification log-likelihood.

It allows expressing classification in logit space.

Enables reliable out-of-distribution detection under domain drift.

Abstract

Reliably estimating the uncertainty of a prediction throughout the model lifecycle is crucial in many safety-critical applications. The most common way to measure this uncertainty is via the predicted confidence. While this tends to work well for in-domain samples, these estimates are unreliable under domain drift and restricted to classification. Alternatively, proper scores can be used for most predictive tasks but a bias-variance decomposition for model uncertainty does not exist in the current literature. In this work we introduce a general bias-variance decomposition for proper scores, giving rise to the Bregman Information as the variance term. We discover how exponential families and the classification log-likelihood are special cases and provide novel formulations. Surprisingly, we can express the classification case purely in the logit space. We showcase the practical relevance of this decomposition on several downstream tasks, including model ensembles and confidence regions. Further, we demonstrate how different approximations of the instance-level Bregman Information allow reliable out-of-distribution detection for all degrees of domain drift.