Quantifying Aleatoric and Epistemic Uncertainty with Proper Scoring Rules

• URL: http://arxiv.org/abs/2404.12215v2
• Date: Fri, 19 Apr 2024 09:14:28 GMT
• Title: Quantifying Aleatoric and Epistemic Uncertainty with Proper Scoring Rules
• Authors: Paul Hofman, Yusuf Sale, Eyke Hüllermeier,
• Abstract summary: Uncertainty representation and quantification are paramount in machine learning. We propose measures for the quantification of aleatoric and (epistemic) uncertainty based on proper scoring rules.
• Score: 19.221081896134567
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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