Bayesian Conformal Prediction as a Decision Risk Problem
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911658554687488 |
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| author | Wu, Fanyi Lohmanova, Veronika Kaski, Samuel Caprio, Michele |
| author_facet | Wu, Fanyi Lohmanova, Veronika Kaski, Samuel Caprio, Michele |
| contents | We propose Bayesian Conformal Prediction (BCP), a framework that combines Bayesian posterior predictive distributions with PAC-style conformal risk control to produce prediction sets with finite-sample coverage guarantees. Standard quantile-threshold conformal methods often construct prediction sets using a single fixed threshold, which typically yields connected prediction sets. While valid, such sets can be inefficient when the posterior predictive distribution is multimodal, since they may span low-density regions between separated modes. The main contribution of BCP is to formulate conformal prediction as a decision-risk optimisation problem, extending standard fixed quantile-threshold sets to optimised highest posterior density (HPD) prediction sets. These sets can be disjoint, concentrating probability mass on separated high-density regions. Validity is enforced using a PAC-style risk constraint, which provides coverage control even when the Bayesian model is misspecified. In standard nested-threshold settings, BCP recovers the smallest feasible threshold, aligning with existing PAC-based approaches. In the multimodal experiment, HPD geometry substantially improves efficiency, reducing mean prediction set size from $4.82$ to $2.07$ while satisfying the target PAC pass rate. Across regression, classification, and distribution-shift experiments, BCP maintains reliable coverage under model misspecification, whereas Bayesian credible intervals can fail to preserve nominal coverage. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_03331 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bayesian Conformal Prediction as a Decision Risk Problem Wu, Fanyi Lohmanova, Veronika Kaski, Samuel Caprio, Michele Machine Learning We propose Bayesian Conformal Prediction (BCP), a framework that combines Bayesian posterior predictive distributions with PAC-style conformal risk control to produce prediction sets with finite-sample coverage guarantees. Standard quantile-threshold conformal methods often construct prediction sets using a single fixed threshold, which typically yields connected prediction sets. While valid, such sets can be inefficient when the posterior predictive distribution is multimodal, since they may span low-density regions between separated modes. The main contribution of BCP is to formulate conformal prediction as a decision-risk optimisation problem, extending standard fixed quantile-threshold sets to optimised highest posterior density (HPD) prediction sets. These sets can be disjoint, concentrating probability mass on separated high-density regions. Validity is enforced using a PAC-style risk constraint, which provides coverage control even when the Bayesian model is misspecified. In standard nested-threshold settings, BCP recovers the smallest feasible threshold, aligning with existing PAC-based approaches. In the multimodal experiment, HPD geometry substantially improves efficiency, reducing mean prediction set size from $4.82$ to $2.07$ while satisfying the target PAC pass rate. Across regression, classification, and distribution-shift experiments, BCP maintains reliable coverage under model misspecification, whereas Bayesian credible intervals can fail to preserve nominal coverage. |
| title | Bayesian Conformal Prediction as a Decision Risk Problem |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2602.03331 |