Transfer learning techniques are often used when one tries to adapt a model learned from a source domain with abundant labeled samples to the target domain with limited labeled samples. In this paper, we consider the regression problem under model shift condition, i.e., regression functions are different but related in the source and target domains. We approach this problem through the use of transformation functions which characterize the relation between the source and the target domain. These transformation functions are able to transform the original problem of learning the complicated regression function of target domain into a problem of learning a simple auxiliary function. This transformation function based technique includes some previous works as special cases, but the class we propose is significantly more general. In this work we consider two widely used non-parametric estimators, Kernel Smoothing (KS) and Kernel Ridge Regression (KRR) for this setting and show improved statistical rates for excess risk than non-transfer learning. Through an $\epsilon$-cover technique, we show that we can find the best transformation function a function class. Lastly, experiments on synthesized, robotics and neural imaging data demonstrate the effectiveness of our framework.

本文提出了用于假设转移学习（HTL）的一种基于算法的新型框架，通过变换函数对源域和目标域之间的关系进行表征及风险分析，首次证明了，如果两个域之间存在关系，则HTL对于Kernel Smoothing和Kernel Ridge Regression的超额风险收敛速度比经典的非转移学习设定更快，实验结果表明了本框架的有效性。

通过变换函数进行假设迁移学习