Uncertainty Quantification for Regression: A Unified Framework Based on Kernel Scores
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
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.
inproceedings BSK+26
UAI 2026
42nd Conference on Uncertainty in Artificial Intelligence. Amsterdam, The Netherlands, Aug 17-21, 2026. To be published. Preprint available.
Authors
C. Bülte • Y. Sale • G. Kutyniok • E. HüllermeierLinks
arXivResearch Areas
BibTeXKey: BSK+26