Trans-Glasso: A Transfer Learning Approach to Precision Matrix Estimation

• 成果类型: Article; Early Access
• 署名作者: Zhao, Boxin; Ma, Cong; Kolar, Mladen
• 署名单位: University of Chicago; University of Chicago; University of Southern California; Mohamed bin Zayed University of Artificial Intelligence MBZUAI
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2025.2602856
• 发表日期: 2026-05-19
• 关键词: data integration; differential network; Graphical Models; multi-task learning; inverse covariance estimation; CONVERGENCE; selection; Lasso; rates; MODEL

摘要

Precision matrix estimation is essential in various fields, yet it is challenging when samples for the target study are limited. Transfer learning can enhance estimation accuracy by leveraging data from related source studies. We propose Trans-Glasso, a two-step transfer learning method for precision matrix estimation. First, we obtain initial estimators using a multi-task learning objective that captures both shared and unique features across studies. Then, we refine these estimators through differential network estimation to adjust for structural differences between the target and source precision matrices. Under the assumption that most entries of the target precision matrix are shared with those of the source matrices, we derive non-asymptotic error bounds and show that Trans-Glasso achieves minimax optimality under certain conditions. Extensive simulations demonstrate Trans-Glasso's superior performance compared to baseline methods, particularly in small-sample settings. We further validate Trans-Glasso in applications to gene networks across brain tissues and protein networks for various cancer subtypes, showcasing its effectiveness in biological contexts. Additionally, we derive the minimax optimal rate for differential network estimation, representing the first such guarantee in this area. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.