ReTaSA: A Nonparametric Functional Estimation Approach for Addressing Continuous Target Shift

TL;DR

This paper introduces ReTaSA, a nonparametric method for estimating importance weights to address continuous target shift in regression, overcoming limitations of existing classification-focused approaches.

Contribution

The paper proposes a novel nonparametric regularized approach, ReTaSA, to solve the ill-posed integral equation for importance weight estimation under continuous target shift.

Findings

ReTaSA effectively estimates importance weights in both synthetic and real-world datasets.

Theoretical analysis justifies the accuracy of the importance weight estimation.

Extensive experiments demonstrate improved adaptation to target shift in regression tasks.

Abstract

The presence of distribution shifts poses a significant challenge for deploying modern machine learning models in real-world applications. This work focuses on the target shift problem in a regression setting (Zhang et al., 2013; Nguyen et al., 2016). More specifically, the target variable y (also known as the response variable), which is continuous, has different marginal distributions in the training source and testing domain, while the conditional distribution of features x given y remains the same. While most literature focuses on classification tasks with finite target space, the regression problem has an infinite dimensional target space, which makes many of the existing methods inapplicable. In this work, we show that the continuous target shift problem can be addressed by estimating the importance weight function from an ill-posed integral equation. We propose a nonparametric regularized approach named ReTaSA to solve the ill-posed integral equation and provide theoretical justification for the estimated importance weight function. The effectiveness of the proposed method has been demonstrated with extensive numerical studies on synthetic and real-world datasets.