Maximum Likelihood Estimation Over Directed Acyclic Gaussian Graphs

• Activity Number: 285
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Yiping Yuan*+
• Companies: University of Minnesota
• Keywords: Multiple directed acyclic graphs ; Maximum likelihood ; Non-convex constraints ; Pairwise coordinate descent

Abstract

Directed acyclic graphs(DAGs) are useful to represent causal relations among random variables. Estimation of DAGs in multiple graphical models becomes challenging in the presence of inhomogeneous data. In this article, we estimate multiple DAGs from Gaussian graphical models with a known partial ordering, where inferring causality between variables is of particular interest, through identifying the sparseness structure, with efforts focused towards detection of structural change over adjacency matrices of DAGs. For maximum likelihood estimation, we introduce non-convex constraints on the elements as well as element-wise differences of adjacency matrices. Computationally, we introduce an efficient algorithm based on the augmented Lagrange multipliers, difference convex method and a novel fast algorithm for solving a convex relaxed problem. Numerical results illustrate that the proposed method performs well against its alternatives.