Chain-Linked Multiple Matrix Integration via Embedding Alignment

• 成果类型: Article; Early Access
• 署名作者: Zheng, Runbing; Tang, Minh
• 署名单位: Johns Hopkins University; North Carolina State University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2025.2550677
• 发表日期: 2025-10-17
• 关键词: 2 ->infinity norm; data integration; matrix completion; normal approximations; Low-rank Matrix; completion; number; algorithms; RECOVERY

摘要

Motivated by the increasing demand for multi-source data integration in various scientific fields, in this article we study matrix completion in scenarios where the data exhibits certain block-wise missing structures-specifically, where only a few noisy submatrices representing (overlapping) parts of the full matrix are available. We propose the Chain-linked Multiple Matrix Integration (CMMI) procedure to efficiently combine the information that can be extracted from these individual noisy submatrices. CMMI begins by deriving entity embeddings for each observed submatrix, then aligns these embeddings using overlapping entities between pairs of submatrices, and finally aggregates them to reconstruct the entire matrix of interest. We establish, under mild regularity conditions, entrywise error bounds and normal approximations for the CMMI estimates. Simulation studies and real data applications show that CMMI is computationally efficient and effective in recovering the full matrix, even when overlaps between the observed submatrices are minimal. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.