Quantifying Aleatoric and Epistemic Uncertainty with Proper Scoring Rules
This work addresses uncertainty quantification for safety-critical applications in ML, representing an incremental advancement in methodology.
The paper tackles the problem of quantifying aleatoric and epistemic uncertainty in machine learning by proposing novel measures based on proper scoring rules, bridging representations through credal sets and second-order distributions, with formal justification provided.
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.