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A new similarity measure for covariate shift with applications to nonparametric regression
Reese Pathak · Cong Ma · Martin Wainwright

Wed Jul 20 03:30 PM -- 05:30 PM (PDT) @ Hall E #1114

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.

Author Information

Reese Pathak (University of California, Berkeley)
Cong Ma (Princeton University)
Martin Wainwright (UC Berkeley / Voleon)

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