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Covariate Shift by Kernel Mean Matching

MPS-Authors
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Gretton,  A
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Smola,  AJ
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Huang,  J
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Schmittfull,  M
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Borgwardt,  KM
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Schölkopf,  B
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Gretton, A., Smola, A., Huang, J., Schmittfull, M., Borgwardt, K., & Schölkopf, B. (2009). Covariate Shift by Kernel Mean Matching. In J. Quiñonero-Candela, M. Sugiyama, A. Schwaighofer, & N. Lawrence (Eds.), Dataset Shift in Machine Learning (pp. 131-160). Cambridge, MA, USA: MIT Press.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-C5D5-1
Abstract
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.