Quantification of Credal Uncertainty: A Distance-Based Approach

2026-03-28

AI Summary

This work addresses the challenge of quantifying aleatoric and epistemic uncertainties in multi-class classification, where uncertainty is characterized via predictive sets. Building upon the integral probability metric (IPM) framework, the authors propose a novel uncertainty quantification method based on total variation distance. This approach provides, for the first time, a semantically clear, theoretically rigorous, and computationally efficient mechanism to decompose total uncertainty into its aleatoric and epistemic components in multi-class settings. The method naturally generalizes existing uncertainty measures designed for binary classification. Empirical evaluations demonstrate that the proposed technique achieves superior practical performance while maintaining low computational overhead.

Abstract

Credal sets, i.e., closed convex sets of probability measures, provide a natural framework to represent aleatoric and epistemic uncertainty in machine learning. Yet how to quantify these two types of uncertainty for a given credal set, particularly in multiclass classification, remains underexplored. In this paper, we propose a distance-based approach to quantify total, aleatoric, and epistemic uncertainty for credal sets. Concretely, we introduce a family of such measures within the framework of Integral Probability Metrics (IPMs). The resulting quantities admit clear semantic interpretations, satisfy natural theoretical desiderata, and remain computationally tractable for common choices of IPMs. We instantiate the framework with the total variation distance and obtain simple, efficient uncertainty measures for multiclass classification. In the binary case, this choice recovers established uncertainty measures, for which a principled multiclass generalization has so far been missing. Empirical results confirm practical usefulness, with favorable performance at low computational cost.

Problem

• credal sets
• aleatoric uncertainty
• epistemic uncertainty
• uncertainty quantification
• multiclass classification

Innovation

• credal sets
• uncertainty quantification
• Integral Probability Metrics
• total variation distance
• multiclass classification