Uncertainty Quantification for Regression: A Unified Framework based on kernel scores
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866915585514799104 |
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| author | Bülte, Christopher Sale, Yusuf Kutyniok, Gitta Hüllermeier, Eyke |
| author_facet | Bülte, Christopher Sale, Yusuf Kutyniok, Gitta Hüllermeier, Eyke |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25599 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uncertainty Quantification for Regression: A Unified Framework based on kernel scores Bülte, Christopher Sale, Yusuf Kutyniok, Gitta Hüllermeier, Eyke Machine Learning 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. |
| title | Uncertainty Quantification for Regression: A Unified Framework based on kernel scores |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2510.25599 |