Abstract: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.
| Comments: | 22 pages, 8 figures. A previous version was accepted at the EIML Workshop at NeurIPS 2025 |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2602.03331 [cs.LG] |
| (or arXiv:2602.03331v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2602.03331 arXiv-issued DOI via DataCite |
From: Fanyi Wu [view email]
[v1]
Tue, 3 Feb 2026 09:58:27 UTC (4,921 KB)
[v2]
Thu, 7 May 2026 15:27:53 UTC (6,008 KB)
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