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arxiv: 2401.12272 · v1 · pith:C6MWKGM4new · submitted 2024-01-22 · 📊 stat.ML · cs.LG

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

T. Tony Cai , Hongming Pu This is my paper
classification 📊 stat.ML cs.LG
keywords learningminimaxtransfernonparametricregressionriskadaptivealgorithm
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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 two unique phenomena in transfer learning: auto-smoothing and super-acceleration, which differentiate 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.

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