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

• URL: http://arxiv.org/abs/2202.02837v1
• Date: Sun, 6 Feb 2022 19:14:50 GMT
• Title: A new similarity measure for covariate shift with applications to nonparametric regression
• Authors: Reese Pathak and Cong Ma and Martin J. Wainwright
• Abstract summary: We introduce a new measure of distribution mismatch based on the integrated ratio of probabilities of balls at a given radius. In comparison to the recently proposed notion of transfer exponent, this measure leads to a sharper rate of convergence.
• Score: 43.457497490211985
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We study covariate shift in the context of nonparametric regression. We introduce a new measure of distribution mismatch between the source and target distributions that is based on 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\"older 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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