非参数回归的迁移学习：非渐近极小极大分析与自适应过程
Transfer Learning for Nonparametric Regression: Non-asymptotic Minimax Analysis and Adaptive Procedure
- University of Pennsylvania（宾夕法尼亚大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究非参数回归迁移学习的非渐近极小极大风险，提出置信度阈值估计量与数据驱动自适应算法，揭示自动平滑和超加速现象，并通过模拟与真实案例验证其性能。
AI中文摘要：
本文研究非参数回归的迁移学习。我们首先研究该问题的非渐近极小极大风险，并开发了一种称为置信度阈值估计量的新型估计量，证明其能够达到至多相差一个对数因子的极小极大最优风险。我们的结果展示了迁移学习中的两个独特现象：自动平滑和超加速，这使其区别于传统设置下的非参数回归。随后，我们提出了一种数据驱动算法，该算法能够在广泛的参数空间范围内自适应地达到至多相差一个对数因子的极小极大风险。我们开展了模拟研究以评估该自适应迁移学习算法的数值性能，并提供了一个真实世界示例来证明所提方法的优势。
英文摘要：
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.
