In recent years, transfer learning has garnered significant attention in the machine learning community. Its ability to leverage knowledge from related studies to improve generalization performance in a target study has made it highly appealing. This paper focuses on investigating the transfer learning problem within the context of nonparametric regression over a reproducing kernel Hilbert space. The aim is to bridge the gap between practical effectiveness and theoretical guarantees. We specifically consider two scenarios: one where the transferable sources are known and another where they are unknown. For the known transferable source case, we propose a two-step kernel-based estimator by solely using kernel ridge regression. For the unknown case, we develop a novel method based on an efficient aggregation algorithm, which can automatically detect and alleviate the effects of negative sources. This paper provides the statistical properties of the desired estimators and establishes the minimax optimal rate. Through extensive numerical experiments on synthetic data and real examples, we validate our theoretical findings and demonstrate the effectiveness of our proposed method.

翻译：近年来，迁移学习在机器学习领域引起了广泛关注。其利用相关研究中的知识来提升目标研究泛化性能的能力使其极具吸引力。本文聚焦于在再生核希尔伯特空间中的非参数回归背景下研究迁移学习问题，旨在弥合实际效果与理论保证之间的差距。我们特别考虑了两种场景：迁移源已知的情况和迁移源未知的情况。对于迁移源已知的情况，我们仅通过核岭回归提出了一种两步核估计方法。对于迁移源未知的情况，我们开发了一种基于高效聚合算法的新方法，该方法能够自动检测并缓解负迁移源的影响。本文给出了所需估计量的统计性质，并建立了极小极大最优速率。通过在合成数据和真实案例上的大量数值实验，我们验证了理论发现并展示了所提方法的有效性。