%APathak, Reese%AMa, Cong%AWainwright, Martin%BJournal Name: Proceedings of the International Conference on Machine Learning
%D2022%I
%JJournal Name: Proceedings of the International Conference on Machine Learning
%K
%MOSTI ID: 10343723
%PMedium: X
%TA new similarity measure for covariate shift with applications to nonparametric regression
%XWe 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 H{รถ}lder 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.
%0Journal Article
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