A new similarity measure for covariate shift with applications to nonparametric regression
This work addresses covariate shift for researchers in statistical learning, offering a more fine-grained theoretical framework, though it appears incremental as it builds on prior concepts like the transfer exponent.
The authors tackled the problem of covariate shift in nonparametric regression by introducing a new distribution mismatch measure based on integrated probability ratios, which characterizes minimax estimation rates for Hölder continuous functions and yields sharper convergence rates compared to existing methods like the transfer exponent.
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 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.