Conformal Prediction Regions are Imprecise Highest Density Regions
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arXiv
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| Format: | Preprint |
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2025
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| author | Caprio, Michele Sale, Yusuf Hüllermeier, Eyke |
| author_facet | Caprio, Michele Sale, Yusuf Hüllermeier, Eyke |
| contents | Recently, Cella and Martin proved how, under an assumption called consonance, a credal set (i.e. a closed and convex set of probabilities) can be derived from the conformal transducer associated with transductive conformal prediction. We show that the Imprecise Highest Density Region (IHDR) associated with such a credal set corresponds to the classical Conformal Prediction Region. In proving this result, we establish a new relationship between Conformal Prediction and Imprecise Probability (IP) theories, via the IP concept of a cloud. A byproduct of our presentation is the discovery that consonant plausibility functions are monoid homomorphisms, a new algebraic property of an IP tool. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_06331 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conformal Prediction Regions are Imprecise Highest Density Regions Caprio, Michele Sale, Yusuf Hüllermeier, Eyke Machine Learning Probability Primary: 68T37, Secondary: 62M20, 60G25, 20M32, 15A80 Recently, Cella and Martin proved how, under an assumption called consonance, a credal set (i.e. a closed and convex set of probabilities) can be derived from the conformal transducer associated with transductive conformal prediction. We show that the Imprecise Highest Density Region (IHDR) associated with such a credal set corresponds to the classical Conformal Prediction Region. In proving this result, we establish a new relationship between Conformal Prediction and Imprecise Probability (IP) theories, via the IP concept of a cloud. A byproduct of our presentation is the discovery that consonant plausibility functions are monoid homomorphisms, a new algebraic property of an IP tool. |
| title | Conformal Prediction Regions are Imprecise Highest Density Regions |
| topic | Machine Learning Probability Primary: 68T37, Secondary: 62M20, 60G25, 20M32, 15A80 |
| url | https://arxiv.org/abs/2502.06331 |