Reweighting for Transfer Classification: Exact Risk Conversion and Minimax Adaptation

Aoran Chen, Yang Feng

A source can make a training mixture easier to learn while making its accuracy less valuable for the target. We study how the training problem a source creates and the finite-sample error of learning it jointly determine target-risk guarantees under reweighting. For binary classification, for each pair of laws and each positive target weight, we derive the sharpest target excess hinge-risk bound implied by mixture excess alone, uniformly over clipped predictors. This exact conversion curve is determined by density-weighted local votes. A two-sample oracle inequality for weighted support vector machines supplies the mixture excess, and the composition becomes explicit for Gaussian kernels. On a tilted-boundary class, we establish the all-procedure minimax classification rate $[n+s_+^2/(m^{-1}+τ^2)]^{-1}$ in the transferable strength $s_+$ and the tilt $τ$, separating source sampling uncertainty ($m^{-1}$) from relation uncertainty ($τ^2$). A target-checked Gaussian-SVM selector adapts to unknown $s_+$ and $τ$ up to a logarithmic factor for fixed dimension, and retains the target-only rate up to the same factor against arbitrary independent sources under the stated target model. On…