High-Dimensional Gaussian Graphical Model for Network-Linked Data

• Activity Number: 23 - Recents Advances in Statistical Learning and Network Data Analysis
• Type: Topic Contributed
• Date/Time: Sunday, July 29, 2018 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Ji Zhu* and Boang Liu and Tianxi Li and Cheng Qian and Elizaveta Levina
• Companies: University of Michigan and University of Michigan and University of Michigan and University of Michigan and University of Michigan
• Keywords: Covariance estimation; Graphical models; High-dimensional data; Network analysis; Node covariates; Sparse estimation

Abstract

Graphical models are commonly used in representing conditional independence between random variables, and learning the conditionalindependence structure from data has attracted much attention inrecent years. However, almost all commonly used graph learning methods rely on the assumption that the observations share the same mean vector. In this paper, we extend the Gaussian graphical model to the setting where the observations are connected by a network and propose a model that allows the mean vectors for different observations to be different. We have developed an efficient estimation method for the model and demonstrated the effectiveness of the proposed method using simulation studies. Further, we prove that under the assumption of "network cohesion", the proposed method can estimate both the inverse covariance matrix and the corresponding graph structure accurately. We have also applied the proposed method to a dataset consisting of statisticians' coauthorship network to learn the statistical term dependency based on the authors' publications and obtained meaningful results.