Dynamic Matrix Recovery

• 成果类型: Article
• 署名作者: Chen, Ziyuan; Yang, Ying; Yao, Fang
• 署名单位: Peking University; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2023.2297468
• 发表日期: 2024
• 页码: 2996-3007
• 关键词: tensor regression; Optimal Rates; rank; algorithm

摘要

Matrix recovery from sparse observations is an extensively studied topic emerging in various applications, such as recommendation system and signal processing, which includes the matrix completion and compressed sensing models as special cases. In this article, we propose a general framework for dynamic matrix recovery of low-rank matrices that evolve smoothly over time. We start from the setting that the observations are independent across time, then extend to the setting that both the design matrix and noise possess certain temporal correlation via modified concentration inequalities. By pooling neighboring observations, we obtain sharp estimation error bounds of both settings, showing the influence of the underlying smoothness, the dependence and effective samples. We propose a dynamic fast iterative shrinkage-thresholding algorithm that is computationally efficient, and characterize the interplay between algorithmic and statistical convergence. Simulated and real data examples are provided to support such findings. Supplementary materials for this article are available online.