Transfer learning for nonparametric classification: Minimax rate and adaptive classifier

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