Effective Sample Size, Dimensionality, and Generalization in Covariate Shift Adaptation

TL;DR

This paper develops a unified theory linking effective sample size, data dimensionality, and generalization in covariate shift adaptation, highlighting the benefits of dimensionality reduction for improved domain adaptation performance.

Contribution

It provides a formal framework connecting ESS, dimensionality, and generalization, and advocates for dimensionality reduction prior to covariate shift adaptation.

Findings

Dimensionality reduction increases effective sample size.

Theoretical connection between ESS, dimensionality, and generalization.

Dimensionality reduction improves covariate shift adaptation effectiveness.

Abstract

In supervised learning, training and test datasets are often sampled from distinct distributions. Domain adaptation techniques are thus required. Covariate shift adaptation yields good generalization performance when domains differ only by the marginal distribution of features. Covariate shift adaptation is usually implemented using importance weighting, which may fail, according to common wisdom, due to small effective sample sizes (ESS). Previous research argues this scenario is more common in high-dimensional settings. However, how effective sample size, dimensionality, and model performance/generalization are formally related in supervised learning, considering the context of covariate shift adaptation, is still somewhat obscure in the literature. Thus, a main challenge is presenting a unified theory connecting those points. Hence, in this paper, we focus on building a unified view connecting the ESS, data dimensionality, and generalization in the context of covariate shift adaptation. Moreover, we also demonstrate how dimensionality reduction or feature selection can increase the ESS, and argue that our results support dimensionality reduction before covariate shift adaptation as a good practice.