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

Reese Pathak, Cong Ma, Martin Wainwright
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:17517-17530, 2022.

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 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{ö}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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-pathak22a, title = {A new similarity measure for covariate shift with applications to nonparametric regression}, author = {Pathak, Reese and Ma, Cong and Wainwright, Martin}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {17517--17530}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/pathak22a/pathak22a.pdf}, url = {https://proceedings.mlr.press/v162/pathak22a.html}, 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 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{ö}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.} }
Endnote
%0 Conference Paper %T A new similarity measure for covariate shift with applications to nonparametric regression %A Reese Pathak %A Cong Ma %A Martin Wainwright %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-pathak22a %I PMLR %P 17517--17530 %U https://proceedings.mlr.press/v162/pathak22a.html %V 162 %X 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 H{ö}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.
APA
Pathak, R., Ma, C. & Wainwright, M.. (2022). A new similarity measure for covariate shift with applications to nonparametric regression. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:17517-17530 Available from https://proceedings.mlr.press/v162/pathak22a.html.

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