ELSA: Efficient Label Shift Adaptation through the Lens of Semiparametric Models

TL;DR

This paper introduces ELSA, a novel method for label shift adaptation in domain adaptation tasks, which is both theoretically sound and empirically effective, avoiding calibration steps and improving computational efficiency.

Contribution

The paper proposes ELSA, a moment-matching framework for label shift adaptation that estimates weights via linear systems, with proven statistical properties and superior empirical performance.

Findings

ELSA achieves state-of-the-art estimation accuracy.

ELSA does not require post-prediction calibration.

ELSA is computationally efficient and theoretically justified.

Abstract

We study the domain adaptation problem with label shift in this work. Under the label shift context, the marginal distribution of the label varies across the training and testing datasets, while the conditional distribution of features given the label is the same. Traditional label shift adaptation methods either suffer from large estimation errors or require cumbersome post-prediction calibrations. To address these issues, we first propose a moment-matching framework for adapting the label shift based on the geometry of the influence function. Under such a framework, we propose a novel method named \underline{E}fficient \underline{L}abel \underline{S}hift \underline{A}daptation (ELSA), in which the adaptation weights can be estimated by solving linear systems. Theoretically, the ELSA estimator is $\sqrt{n}$-consistent ($n$ is the sample size of the source data) and asymptotically normal. Empirically, we show that ELSA can achieve state-of-the-art estimation performances without post-prediction calibrations, thus, gaining computational efficiency.