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

@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.}
}