Covariate Shift by Kernel Mean Matching
Arthur Gretton, AJ Smola, Jiayuan Huang, Marcel Schmittfull, Karsten Borgwardt, Bernhard Schölkopf · The MIT Press eBooks · 2008
This chapter addresses the problem of distribution matching between training and test stages. It proposes a method called kernel mean matching, which allows direct estimation of the importance weight without going through density estimation. The chapter then relates the re-weighted estimation approaches to local learning, where labels on test data are estimated given a subset of training data in a neighborhood of the test point. Examples are nearest-neighbor estimators and Watson–Nadaraya-type estimators. The chapter also provides detailed proofs concerning the statistical properties of the kernel mean matching estimator, and detailed experimental analyses for both covariate shift and local learning.