Hub Detection in Gaussian Graphical Models

• 成果类型: Article; Early Access
• 署名作者: Gomez, Jose A. Sanchez; Mo, Weibin; Zhao, Junlong; Liu, Yufeng
• 署名单位: University of California System; University of California Riverside; Purdue University System; Purdue University; Beijing Normal University; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2025.2453250
• 发表日期: 2025
• 关键词: inverse covariance estimation; Optimal Rates; selection; eigenstructure; CONVERGENCE; eigenvalues; asymptotics; expression; networks; matrices

摘要

Graphical models are popular tools for exploring relationships among a set of variables. The Gaussian graphical model (GGM) is an important class of graphical models, where the conditional dependence among variables is represented by nodes and edges in a graph. In many real applications, we are interested in detecting hubs in graphical models, which refer to nodes with a significant higher degree of connectivity compared to non-hub nodes. A typical strategy for hub detection consists of estimating the graphical model, and then using the estimated graph to identify hubs. Despite its simplicity, the success of this strategy relies on the accuracy of the estimated graph. In this article, we directly target on the estimation of hubs, without the need of estimating the graph. We establish a novel connection between the presence of hubs in a graphical model, and the spectral decomposition of the underlying covariance matrix. Based on this connection, we propose the method of inverse principal components for hub detection (IPC-HD). Both consistency and convergence rates are established for IPC-HD. Our simulation study demonstrates the superior performance and fast computation of the proposed method compared to existing methods in the literature in terms of hub detection. Our application to a prostate cancer gene expression dataset detects several hub genes with close connections to tumor development. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.