Conformal Bayes under Label Shift: Post-Hoc Calibration vs. In-Training Adaptation

Title:Conformal Bayes under Label Shift: Post-Hoc Calibration vs. In-Training Adaptation

Abstract:Conformal Bayes combines Bayesian posterior predictives with conformal calibration to produce prediction sets that are both statistically valid and geometrically efficient. We study conformal Bayes under label shift from a unified perspective, identifying two complementary approaches that restore nominal target-domain coverage through importance-weighted conformal calibration but operate through independent mechanisms. \emph{Post-hoc calibration} tilts the posterior predictive toward the target domain and corrects the conformal threshold via an importance-weighted quantile, leaving the parameter posterior unchanged. \emph{In-training adaptation} tilts the parameter posterior itself to the target domain, producing a corrected predictive whose highest predictive density region serves as the highest predictive density (HPD) based prediction set under the fitted target predictive; efficiency is model-dependent and does not imply finite-sample conditional optimality. Two controlled experiments show that in an unbiased training regime both strategies achieve valid coverage equally, while in a lead-optimization regime in-training adaptation acts as a debiasing operator, reducing interval width at unchanged coverage.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2606.11865 [stat.ML]

(or arXiv:2606.11865v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2606.11865 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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