An Axiomatic Assessment of Entropy- and Variance-based Uncertainty Quantification in Regression
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909611790958592 |
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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 |