Distributed Tensor Principal Component Analysis with Data Heterogeneity

• 成果类型: Article; Early Access
• 署名作者: Chen, Elynn; Chen, Xi; Jing, Wenbo; Zhang, Yichen
• 署名单位: New York University; Purdue University System; Purdue University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2025.2483481
• 发表日期: 2025
• 关键词: Quantile regression; rank

摘要

As tensors become widespread in modern data analysis, Tucker low-rank Principal Component Analysis (PCA) has become essential for dimensionality reduction and structural discovery in tensor datasets. Motivated by the common scenario where large-scale tensors are distributed across diverse geographic locations, this article investigates tensor PCA within a distributed framework where direct data pooling is theoretically suboptimal or practically infeasible. We offer a comprehensive analysis of three specific scenarios in distributed Tensor PCA: a homogeneous setting in which tensors at various locations are generated from a single noise-affected model; a heterogeneous setting where tensors at different locations come from distinct models but share some principal components, aiming to improve estimation across all locations; and a targeted heterogeneous setting, designed to boost estimation accuracy at a specific location with limited samples by utilizing transferred knowledge from other sites with ample data. We introduce novel estimation methods tailored to each scenario, establish statistical guarantees, and develop distributed inference techniques to construct confidence regions. Our theoretical findings demonstrate that these distributed methods achieve sharp rates of accuracy by efficiently aggregating shared information across different tensors, while maintaining reasonable communication costs. Empirical validation through simulations and real-world data applications highlights the advantages of our approaches, particularly in managing heterogeneous tensor data. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.