Human learners have the natural ability to use knowledge gained in one setting for learning in a different but related setting. This ability to transfer knowledge from one task to another is essential for effective learning. In this paper, we study transfer learning in the context of nonparametric classification based on observations from different distributions under the posterior drift model, which is a general framework and arises in many practical problems. We first establish the minimax rate of convergence and construct a rate-optimal two-sample weighted $K$-NN classifier. The results characterize precisely the contribution of the observations from the source distribution to the classification task under the target distribution. A data-driven adaptive classifier is then proposed and is shown to simultaneously attain within a logarithmic factor of the optimal rate over a large collection of parameter spaces. Simulation studies and real data applications are carried out where the numerical results further illustrate the theoretical analysis. Extensions to the case of multiple source distributions are also considered.

本文研究了在后验漂移模型下，基于不同分布的观测数据的非参数分类问题中的迁移学习，首先构建了一个速率最优的两样本加权 K-NN 分类器并证明了收敛速率下限，接着提出了一种数据驱动的自适应分类器，证明了其能够同时在大量参数空间上实现接近最优速率，并给出了仿真研究和实际数据应用。同时，本文还考虑了多个源分布的情况。

非参数分类的迁移学习：极小极大风险和自适应分类器