Phase Transition in Nonparametric Minimax Rates for Covariate Shifts on Approximate Manifolds
近似流形上协变量偏移的非参数极小极大速率相变
We study nonparametric regression under covariate shift with structured data, where a small amount of labeled target data is supplemented by a large labeled source dataset. In many real-world settings, the covariates in the target domain lie near a low-dimensional manifold within the support of the source, e.g., personalized handwritten digits (target) within a large, high-dimensional image repository (source). Since density ratios may not exist in these settings, standard…