PAC Prediction Sets Under Covariate Shift

TL;DR

This paper introduces a new method for constructing PAC prediction sets that remain valid under covariate shift, effectively quantifying uncertainty even when the data distribution changes, with practical validation on large datasets.

Contribution

It develops a novel PAC prediction set construction method that accounts for covariate shift using importance weights, including when these weights are estimated with confidence intervals.

Findings

Algorithm satisfies PAC constraints under covariate shift.

Prediction sets have the smallest average normalized size among valid methods.

Effective on large-scale datasets like DomainNet and ImageNet.

Abstract

An important challenge facing modern machine learning is how to rigorously quantify the uncertainty of model predictions. Conveying uncertainty is especially important when there are changes to the underlying data distribution that might invalidate the predictive model. Yet, most existing uncertainty quantification algorithms break down in the presence of such shifts. We propose a novel approach that addresses this challenge by constructing \emph{probably approximately correct (PAC)} prediction sets in the presence of covariate shift. Our approach focuses on the setting where there is a covariate shift from the source distribution (where we have labeled training examples) to the target distribution (for which we want to quantify uncertainty). Our algorithm assumes given importance weights that encode how the probabilities of the training examples change under the covariate shift. In practice, importance weights typically need to be estimated; thus, we extend our algorithm to the setting where we are given confidence intervals for the importance weights. We demonstrate the effectiveness of our approach on covariate shifts based on DomainNet and ImageNet. Our algorithm satisfies the PAC constraint, and gives prediction sets with the smallest average normalized size among approaches that always satisfy the PAC constraint.