An Axiomatic Assessment of Entropy- and Variance-based Uncertainty Quantification in Regression

• URL: http://arxiv.org/abs/2504.18433v1
• Date: Fri, 25 Apr 2025 15:44:46 GMT
• Title: An Axiomatic Assessment of Entropy- and Variance-based Uncertainty Quantification in Regression
• Authors: Christopher Bülte, Yusuf Sale, Timo Löhr, Paul Hofman, Gitta Kutyniok, Eyke Hüllermeier,
• Abstract summary: We introduce a set of axioms to rigorously assess measures of aleatoric, epistemic, and total uncertainty in supervised regression.<n>We analyze the widely used entropy- and variance-based measures regarding limitations and challenges.
• Score: 26.822418248900547
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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.

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