论文标题
与非参数回归应用的协变速器转移的新相似性衡量标准
A new similarity measure for covariate shift with applications to nonparametric regression
论文作者
论文摘要
我们研究非参数回归背景下的协变量转移。我们介绍了基于给定半径下球概率的集成比率的源和目标分布之间的分布不匹配的新量度。我们使用此度量相对于半径的缩放来表征在协变量转移下Hölder连续功能的最小值估计速率。与最近提出的转移指数概念相比，此措施会导致收敛速度更高，并且更细粒度。我们伴随着我们的理论，以协变量转移的具体实例说明了这种巨大的差异。
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.
