biostudies-literatureQiu HNIA NIH HHSNCI NIH HHSDMSNIHNIGMS NIH HHS1680-1705https://www.ebi.ac.uk/biostudies/studies/S-EPMC10837005biostudies-literatureUnknown85(5)Predicting sets of outcomes-instead of unique outcomes-is a promising solution to uncertainty quantification in statistical learning. Despite a rich literature on constructing prediction sets with statistical guarantees, adapting to unknown covariate shift-a prevalent issue in practice-poses a serious unsolved challenge. In this article, we show that prediction sets with finite-sample coverage guarantee are uninformative and propose a novel flexible distribution-free method, PredSet-1Step, to efficiently construct prediction sets with an asymptotic coverage guarantee under unknown covariate shift. We formally show that our method is <i>asymptotically probably approximately correct</i>, having well-calibrated coverage error with high confidence for large samples. We illustrate that it achieJournal of the Royal Statistical Society. Series B, Statistical methodologyPrediction sets adaptive to unknown covariate shift.PMC108370052046874R01 AG065276R01 GM139926grants R01AI27271, R01CA222147, R01AG065276, R01GM139926R01 CA222147Dobriban EQiu HTchetgen Tchetgen EfalsePrediction sets adaptive to unknown covariate shift.Predicting sets of outcomes-instead of unique outcomes-is a promising solution to uncertainty quantification in statistical learning. Despite a rich literature on constructing prediction sets with statistical guarantees, adapting to unknown covariate shift-a prevalent issue in practice-poses a serious unsolved challenge. In this article, we show that prediction sets with finite-sample coverage guarantee are uninformative and propose a novel flexible distribution-free method, PredSet-1Step, to efficiently construct prediction sets with an asymptotic coverage guarantee under unknown covariate shift. We formally show that our method is <i>asymptotically probably approximately correct</i>, having well-calibrated coverage error with high confidence for large samples. We illustrate that it achie2023-01-01T00:00:00Z2023 Nov2025-04-25T19:13:51.575Z2025-04-06T07:54:01.561ZS-EPMC108370053831252710.1093/jrsssb/qkad069