A One-step Approach to Covariate Shift Adaptation

TL;DR

This paper introduces a novel one-step method for covariate shift adaptation that jointly learns the predictive model and importance weights, improving upon traditional two-step approaches by directly minimizing an upper bound of test risk.

Contribution

The paper proposes a unified one-step optimization approach for covariate shift adaptation, with theoretical analysis and empirical validation, advancing beyond existing two-step methods.

Findings

The method effectively reduces test risk under covariate shift.

Theoretical generalization error bounds are established.

Empirical results demonstrate improved performance over traditional methods.

Abstract

A default assumption in many machine learning scenarios is that the training and test samples are drawn from the same probability distribution. However, such an assumption is often violated in the real world due to non-stationarity of the environment or bias in sample selection. In this work, we consider a prevalent setting called covariate shift, where the input distribution differs between the training and test stages while the conditional distribution of the output given the input remains unchanged. Most of the existing methods for covariate shift adaptation are two-step approaches, which first calculate the importance weights and then conduct importance-weighted empirical risk minimization. In this paper, we propose a novel one-step approach that jointly learns the predictive model and the associated weights in one optimization by minimizing an upper bound of the test risk. We theoretically analyze the proposed method and provide a generalization error bound. We also empirically demonstrate the effectiveness of the proposed method.