{Reference Type}: Journal Article
{Title}: Prediction sets adaptive to unknown covariate shift.
{Author}: Qiu H;Dobriban E;Tchetgen Tchetgen E;
{Journal}: J R Stat Soc Series B Stat Methodol
{Volume}: 85
{Issue}: 5
{Year}: 2023 Nov
{Factor}: 4.933
{DOI}: 10.1093/jrsssb/qkad069
{Abstract}: 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 asymptotically probably approximately correct, having well-calibrated coverage error with high confidence for large samples. We illustrate that it achieves nominal coverage in a number of experiments and a data set concerning HIV risk prediction in a South African cohort study. Our theory hinges on a new bound for the convergence rate of the coverage of Wald confidence intervals based on general asymptotically linear estimators.