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Machine Learning in Non-Stationary EnvironmentsIntroduction to Covariate Shift Adaptation$
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Masashi Sugiyama and Motoaki Kawanabe

Print publication date: 2012

Print ISBN-13: 9780262017091

Published to MIT Press Scholarship Online: September 2013

DOI: 10.7551/mitpress/9780262017091.001.0001

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Function Approximation

Function Approximation

Chapter:
(p.20) (p.21) 2 Function Approximation
Source:
Machine Learning in Non-Stationary Environments
Author(s):

Masashi Sugiyama

Motoaki Kawanabe

Publisher:
The MIT Press
DOI:10.7551/mitpress/9780262017091.003.0002

This chapter discusses function learning methods under covariate shift. Ordinary empirical risk minimization learning is not consistent under covariate shift for misspecified models, and this inconsistency issue can be resolved by considering importance-weighted loss functions. Here, various importance-weighted empirical risk minimization methods are introduced, including least squares and Huber’s method for regression, and Fisher discriminant analysis, logistic regression, support vector machines, and boosting for classification. Their adaptive and regularized variants are also described. The numerical behavior of these importance-weighted learning methods is illustrated through experiments.

Keywords:   covariate shift adaptation, misspecified models, importance-weighted empirical risk minimization methods, least squares regression, Huber regression, Fisher discriminant analysis, logistic regression, support vector machines, boosting

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