An Axiomatic Assessment of Entropy- And Variance-Based Uncertainty Quantification in Regression

MCML Authors

Christopher Bülte

→ Group Gitta Kutyniok
 Mathematical Foundations of Artificial Intelligence

Yusuf Sale

→ Group Eyke Hüllermeier
 Artificial Intelligence and Machine Learning

Timo Löhr

→ Group Eyke Hüllermeier
 Artificial Intelligence and Machine Learning

Paul Hofman

→ Group Eyke Hüllermeier
 Artificial Intelligence and Machine Learning

Gitta Kutyniok

Prof. Dr.

Core PI

Mathematical Foundations of Artificial Intelligence

Eyke Hüllermeier

Prof. Dr.

Core PI

Artificial Intelligence and Machine Learning

Abstract

Uncertainty quantification (UQ) is crucial in machine learning, yet most (axiomatic) studies of uncertainty measures focus on classification, leaving a gap in regression settings with limited formal justification and evaluations. In this work, we introduce a set of axioms to rigorously assess measures of aleatoric, epistemic, and total uncertainty in supervised regression. By utilizing a predictive exponential family, we can generalize commonly used approaches for uncertainty representation and corresponding uncertainty measures. More specifically, we analyze the widely used entropy- and variance-based measures regarding limitations and challenges. Our findings provide a principled foundation for UQ in regression, offering theoretical insights and practical guidelines for reliable uncertainty assessment.

inproceedings BSL+26

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UAI 2026

42nd Conference on Uncertainty in Artificial Intelligence. Amsterdam, The Netherlands, Aug 17-21, 2026. To be published. Preprint available.

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Authors

C. Bülte • Y. Sale • T. Löhr • P. Hofman • G. Kutyniok • E. Hüllermeier

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Links

arXiv

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Research Areas

 A2 | Mathematical Foundations

 A3 | Computational Models