An Axiomatic Assessment of Entropy- And Variance-Based Uncertainty Quantification in Regression
MCML Authors
Gitta Kutyniok
Prof. Dr.
Core PI
Eyke Hüllermeier
Prof. Dr.
Core PI
Abstract
Gitta Kutyniok
Prof. Dr.
Core PI
Eyke Hüllermeier
Prof. Dr.
Core PI
Abstract
Uncertainty quantification 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 provide a formal way of representing uncertainty in continuous space, using a general parametric formulation, allowing for tractable analysis and evaluation of uncertainty measures. Within this framework, we propose a set of axioms that enable rigorous assessment of total, aleatoric, and epistemic uncertainty measures. Together, this allows for a theoretical examination of uncertainty measures and their corresponding properties. As a specific example, we compare the widely used entropy- and variance-based measures with respect to established predictive models and analyze their limitations and challenges in uncertainty quantification. Our work provides a principled way to understand and develop uncertainty measures in supervised regression, offering theoretical insights and practical guidelines for reliable uncertainty assessment.
inproceedings BSL+26
UAI 2026
42nd Conference on Uncertainty in Artificial Intelligence. Amsterdam, The Netherlands, Aug 17-21, 2026.
Authors
C. Bülte • Y. Sale • T. Löhr • P. Hofman • G. Kutyniok • E. HüllermeierLinks
URLResearch Areas
BibTeXKey: BSL+26