Multivariate Gaussian Network Structure Learning

• Activity Number: 81 - Graphical Models
• Type: Contributed
• Date/Time: Sunday, July 30, 2017 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Xingqi Du* and Subhashis Ghoshal
• Companies: North Carolina State University and North Carolina State University
• Keywords: network ; group penalty ; multivariate

Abstract

We consider a graphical model where a multivariate normal vector is associated with each node of the underlying graph and estimate the graphical structure. We minimize a loss function obtained by regressing the vector at each node on those at the remaining ones under a group penalty. We show that the proposed estimator can computed by a fast convex optimization algorithm. We show that as the sample size increases, the estimated regression coefficients and the 15 correct graphical structure are correctly estimated with probability tending to one. By extensive simulations, we show the superiority of the proposed method over others. We apply the technique on a real dataset to identify gene and protein networks showing up in cancer cell lines.