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A new similarity measure for covariate shift with applications to nonparametric regression

Reese Pathak · Cong Ma · Martin Wainwright

Hall E #1114

Keywords: [ T: Domain Adaptation and Transfer Learning ]


We study covariate shift in the context of nonparametric regression. We introduce a new measure of distribution mismatch between the source and target distributions using the integrated ratio of probabilities of balls at a given radius. We use the scaling of this measure with respect to the radius to characterize the minimax rate of estimation over a family of Hölder continuous functions under covariate shift. In comparison to the recently proposed notion of transfer exponent, this measure leads to a sharper rate of convergence and is more fine-grained. We accompany our theory with concrete instances of covariate shift that illustrate this sharp difference.

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