标题： 迁移学习用于矩阵补全 显示英文标题

标题： Transfer Learning for Matrix Completion

摘要： 在本文中，我们探讨了矩阵补全设置下的知识迁移，其目的是利用可用的辅助数据来提高低秩目标矩阵的估计。 我们提出了一种在已知哪些源数据集有利的先验信息下的迁移学习过程。 我们研究了其收敛速率并证明了其最小最大最优性。 我们的分析表明，当源矩阵足够接近目标矩阵时，我们的方法优于仅使用单个目标数据的传统方法。 特别是，我们利用在\cite{brailovskaya2024universality}中引入的先进的尖锐集中不等式来消除收敛速率中的对数因子，这对于证明最小最大最优性至关重要。 当源数据集的相关性未知时，我们开发了一个高效的检测过程来识别有信息量的源，并建立了其选择一致性。 通过模拟和实际数据分析来支持我们方法的有效性。 显示英文摘要

摘要： In this paper, we explore the knowledge transfer under the setting of matrix completion, which aims to enhance the estimation of a low-rank target matrix with auxiliary data available. We propose a transfer learning procedure given prior information on which source datasets are favorable. We study its convergence rates and prove its minimax optimality. Our analysis reveals that with the source matrices close enough to the target matrix, out method outperforms the traditional method using the single target data. In particular, we leverage the advanced sharp concentration inequalities introduced in \cite{brailovskaya2024universality} to eliminate a logarithmic factor in the convergence rate, which is crucial for proving the minimax optimality. When the relevance of source datasets is unknown, we develop an efficient detection procedure to identify informative sources and establish its selection consistency. Simulations and real data analysis are conducted to support the validity of our methodology.