Prediction Sets Adaptive to Unknown Covariate Shift

Hongxiang Qiu; Edgar Dobriban; Eric Tchetgen Tchetgen

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arXiv · 2203.06126

Prediction Sets Adaptive to Unknown Covariate Shift

Hongxiang Qiu·Edgar Dobriban·Eric Tchetgen Tchetgen

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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 paper, 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 \textit{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.

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Hongxiang Qiu, Edgar Dobriban, Eric Tchetgen Tchetgen. 2022-03-11. Prediction Sets Adaptive to Unknown Covariate Shift. https://arxiv.org/abs/2203.06126

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