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.

翻译：本文研究非参数回归中的迁移学习问题。首先针对该问题分析了非渐近极小风险，并提出一种名为置信阈值估计器的新型估计方法，该方法被证明能在对数因子范围内达到极小最优风险。研究结果揭示了迁移学习中区别于传统非参数回归的两个独特现象：自动平滑与超加速效应。随后提出一种数据驱动算法，该算法能在广泛参数空间内自适应地在对数因子范围内达到极小风险。通过仿真实验评估了该自适应迁移学习算法的数值表现，并基于实际案例展示了所提方法的优越性。