On Regularization Parameter Estimation under Covariate Shift

TL;DR

This paper examines the challenge of estimating regularization parameters in domain adaptation, highlighting issues with traditional methods and evaluating importance weighting techniques through empirical analysis.

Contribution

It identifies limitations of standard cross-validation in covariate shift scenarios and assesses the effectiveness of importance weighting for regularization parameter estimation.

Findings

Source validation data leads to underestimation of regularization parameters

Importance weighting correction is insufficient for accurate estimation

Empirical analysis compares various importance weight estimators' impact

Abstract

This paper identifies a problem with the usual procedure for L2-regularization parameter estimation in a domain adaptation setting. In such a setting, there are differences between the distributions generating the training data (source domain) and the test data (target domain). The usual cross-validation procedure requires validation data, which can not be obtained from the unlabeled target data. The problem is that if one decides to use source validation data, the regularization parameter is underestimated. One possible solution is to scale the source validation data through importance weighting, but we show that this correction is not sufficient. We conclude the paper with an empirical analysis of the effect of several importance weight estimators on the estimation of the regularization parameter.