Quantification of Credal Uncertainty in Machine Learning: A Critical Analysis and Empirical Comparison

Eyke Hüllermeier, Sebastien Destercke, Mohammad Shaker

Keywords: machine learning, uncertainty quantification, credal sets

TL;DR: We study the problem of uncertainty quantification for machine learning algorithms producing predictions in the form of credal sets.

Abstract: The representation and quantification of uncertainty has received increasing attention in machine learning in the recent past. The formalism of credal sets provides an interesting alternative in this regard, especially as it combines the representation of epistemic (lack of knowledge) and aleatoric (statistical) uncertainty in a rather natural way. In this paper, we elaborate on uncertainty measures for credal sets from the perspective of machine learning. More specifically, we provide an overview of proposals, discuss existing measures in a critical way, and also propose a new measure that is more tailored to the machine learning setting. Based on an experimental study, we conclude that theoretically well-justified measures also lead to better performance in practice. Besides, we corroborate the difficulty of the disaggregation problem, that is, of decomposing the amount of total uncertainty into aleatoric and epistemic uncertainty in a sound manner, thereby complementing theoretical findings with empirical evidence.