Quantifying Aleatoric and Epistemic Uncertainty with Proper Scoring Rules

TL;DR

This paper introduces new measures for quantifying aleatoric and epistemic uncertainty in machine learning using proper scoring rules, providing a formal framework and bridging different uncertainty representations.

Contribution

It proposes novel uncertainty measures based on proper scoring rules and establishes a formal connection between credal sets and second-order distributions.

Findings

New measures for epistemic and aleatoric uncertainty

Formal justification of the proposed measures

Bridging credal sets and second-order distributions

Abstract

Uncertainty representation and quantification are paramount in machine learning and constitute an important prerequisite for safety-critical applications. In this paper, we propose novel measures for the quantification of aleatoric and epistemic uncertainty based on proper scoring rules, which are loss functions with the meaningful property that they incentivize the learner to predict ground-truth (conditional) probabilities. We assume two common representations of (epistemic) uncertainty, namely, in terms of a credal set, i.e. a set of probability distributions, or a second-order distribution, i.e., a distribution over probability distributions. Our framework establishes a natural bridge between these representations. We provide a formal justification of our approach and introduce new measures of epistemic and aleatoric uncertainty as concrete instantiations.