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

• URL: http://arxiv.org/abs/2401.12272v1
• Date: Mon, 22 Jan 2024 16:24:04 GMT
• Title: Transfer Learning for Nonparametric Regression: Non-asymptotic Minimax Analysis and Adaptive Procedure
• Authors: T. Tony Cai and Hongming Pu
• Abstract summary: We develop a novel estimator called the confidence thresholding estimator, which is shown to achieve the minimax optimal risk up to a logarithmic factor. 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.
• Score: 5.303044915173525
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 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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