Is the Volume of a Credal Set a Good Measure for Epistemic Uncertainty?
This work addresses the problem of uncertainty quantification in machine learning, highlighting pitfalls in using geometric measures, and is incremental in refining existing methods.
The paper investigates whether the volume of a credal set serves as a good measure for epistemic uncertainty, finding it meaningful for binary classification but less effective for multi-class classification.
Adequate uncertainty representation and quantification have become imperative in various scientific disciplines, especially in machine learning and artificial intelligence. As an alternative to representing uncertainty via one single probability measure, we consider credal sets (convex sets of probability measures). The geometric representation of credal sets as $d$-dimensional polytopes implies a geometric intuition about (epistemic) uncertainty. In this paper, we show that the volume of the geometric representation of a credal set is a meaningful measure of epistemic uncertainty in the case of binary classification, but less so for multi-class classification. Our theoretical findings highlight the crucial role of specifying and employing uncertainty measures in machine learning in an appropriate way, and for being aware of possible pitfalls.