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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