Tony Cai's Papers

Transfer Learning for Nonparametric Regression: Non-asymptotic Minimax Analysis and Adaptive Procedure

Tony Cai and Hongming Pu

Abstract: Transfer learning for nonparametric regression is considered. We first study the non-asymptotic minimax risk for this problem and develop a novel estimator called the confidence thresholding estimator, which is shown to achieve the minimax optimal risk up to a logarithmic factor. Our results demonstrate a unique phenomenon in transfer learning: transferable smoothness, which differentiates it from nonparametric regression in a traditional setting. We then propose a data-driven algorithm that adaptively achieves the minimax risk up to a logarithmic factor across a wide range of parameter spaces. Simulation studies are conducted to evaluate the numerical performance of the adaptive transfer learning algorithm, and a real-world example is provided to demonstrate the benefits of the proposed method.
Paper: pdf file.