Transfer learning for nonparametric classification: Minimax rate and adaptive classifier
研究了后验漂移模型下基于不同分布观测的非参数分类迁移学习，建立了极小化最优收敛速率，构造了速率最优的两样本加权K近邻分类器，并提出了数据驱动的自适应分类器。
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.