Transfer Learning for Nonparametric Classification: Minimax Rate and Adaptive Classifier
This work addresses the problem of knowledge transfer between related tasks in classification, providing theoretical guarantees and practical methods, though it is incremental as it builds on existing transfer learning frameworks.
The paper tackles transfer learning for nonparametric classification under a posterior drift model, establishing the minimax rate of convergence and proposing a rate-optimal two-sample weighted K-NN classifier, with simulations and real data applications illustrating the results.
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.