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

Fuente: arXiv
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Main Authors: Bülte, Christopher, Sale, Yusuf, Löhr, Timo, Hofman, Paul, Kutyniok, Gitta, Hüllermeier, Eyke
Format: Preprint
Published: 2025
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author Bülte, Christopher
Sale, Yusuf
Löhr, Timo
Hofman, Paul
Kutyniok, Gitta
Hüllermeier, Eyke
author_facet Bülte, Christopher
Sale, Yusuf
Löhr, Timo
Hofman, Paul
Kutyniok, Gitta
Hüllermeier, Eyke
contents 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 uncertainty quantification in regression, offering theoretical insights and practical guidelines for reliable uncertainty assessment.
format Preprint
id arxiv_https___arxiv_org_abs_2504_18433
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle An Axiomatic Assessment of Entropy- and Variance-based Uncertainty Quantification in Regression
Bülte, Christopher
Sale, Yusuf
Löhr, Timo
Hofman, Paul
Kutyniok, Gitta
Hüllermeier, Eyke
Machine Learning
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 uncertainty quantification in regression, offering theoretical insights and practical guidelines for reliable uncertainty assessment.
title An Axiomatic Assessment of Entropy- and Variance-based Uncertainty Quantification in Regression
topic Machine Learning
url https://arxiv.org/abs/2504.18433