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Sale, Yusuf; Caprio, Michele and Hüllermeier, Eyke ORCID logoORCID: https://orcid.org/0000-0002-9944-4108 (August 2023): Is the volume of a credal set a good measure for epistemic uncertainty? Thirty-Ninth Conference on Uncertainty in Artificial Intelligence (UAI 2023), Pittsburgh, PA, USA, 1-3 August, 2023. Evans, Robin J. and Shpitser, Ilya (eds.) : In: Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, Vol. 216 PMLR. pp. 1795-1804

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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.

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