Multiple matrix Gaussian graphs estimation

• 成果类型: Article
• 署名作者: Zhu, Yunzhang; Li, Lexin
• 署名单位: University System of Ohio; Ohio State University; University of California System; University of California Berkeley
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12278
• 发表日期: 2018
• 页码: 927-950
• 关键词: attention-deficit/hyperactivity disorder; inverse covariance estimation; variable selection; functional connectivity; brain connectivity; joint estimation; network; MODEL; Lasso; CONVERGENCE

摘要

Matrix-valued data, where the sampling unit is a matrix consisting of rows and columns of measurements, are emerging in numerous scientific and business applications. Matrix Gaussian graphical models are a useful tool to characterize the conditional dependence structure of rows and columns. We employ non-convex penalization to tackle the estimation of multiple graphs from matrix-valued data under a matrix normal distribution. We propose a highly efficient non-convex optimization algorithm that can scale up for graphs with hundreds of nodes. We establish the asymptotic properties of the estimator, which requires less stringent conditions and has a sharper probability error bound than existing results. We demonstrate the efficacy of our proposed method through both simulations and real functional magnetic resonance imaging analyses.