Provable Uncertainty Decomposition via Higher-Order Calibration

TL;DR

This paper introduces a formal method for decomposing predictive uncertainty into aleatoric and epistemic parts using higher-order calibration, providing guarantees without assumptions on data distribution.

Contribution

It proposes higher-order calibration as a new framework for uncertainty decomposition with formal guarantees and applicability to existing models.

Findings

Guarantees aleatoric uncertainty matches real-world data.

Applicable to Bayesian and ensemble models.

Effective in image classification experiments.

Abstract

We give a principled method for decomposing the predictive uncertainty of a model into aleatoric and epistemic components with explicit semantics relating them to the real-world data distribution. While many works in the literature have proposed such decompositions, they lack the type of formal guarantees we provide. Our method is based on the new notion of higher-order calibration, which generalizes ordinary calibration to the setting of higher-order predictors that predict mixtures over label distributions at every point. We show how to measure as well as achieve higher-order calibration using access to $k$-snapshots, namely examples where each point has $k$ independent conditional labels. Under higher-order calibration, the estimated aleatoric uncertainty at a point is guaranteed to match the real-world aleatoric uncertainty averaged over all points where the prediction is made. To our knowledge, this is the first formal guarantee of this type that places no assumptions whatsoever on the real-world data distribution. Importantly, higher-order calibration is also applicable to existing higher-order predictors such as Bayesian and ensemble models and provides a natural evaluation metric for such models. We demonstrate through experiments that our method produces meaningful uncertainty decompositions for image classification.