Uncertainty Quantification for Regression: A Unified Framework Based on Kernel Scores

MCML Authors

Christopher Bülte

→ Group Gitta Kutyniok
 Mathematical Foundations of Artificial Intelligence

Yusuf Sale

→ Group Eyke Hüllermeier
 Artificial Intelligence and Machine Learning

Gitta Kutyniok

Prof. Dr.

Principal Investigator

Mathematical Foundations of Artificial Intelligence

Eyke Hüllermeier

Prof. Dr.

Principal Investigator

Artificial Intelligence and Machine Learning

Abstract

Regression tasks, notably in safety-critical domains, require proper uncertainty quantification, yet the literature remains largely classification-focused. In this light, we introduce a family of measures for total, aleatoric, and epistemic uncertainty based on proper scoring rules, with a particular emphasis on kernel scores. The framework unifies several well-known measures and provides a principled recipe for designing new ones whose behavior, such as tail sensitivity, robustness, and out-of-distribution responsiveness, is governed by the choice of kernel. We prove explicit correspondences between kernel-score characteristics and downstream behavior, yielding concrete design guidelines for task-specific measures. Extensive experiments demonstrate that these measures are effective in downstream tasks and reveal clear trade-offs among instantiations, including robustness and out-of-distribution detection performance.

misc BSK+25

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Preprint

Oct. 2025

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Authors

C. Bülte • Y. Sale • G. Kutyniok • E. Hüllermeier

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Links

arXiv

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Research Areas

 A2 | Mathematical Foundations

 A3 | Computational Models