Maximum Likelihood Estimation Over Directed Acyclic Gaussian Graphs

Authors:
Yiping Yuan;Xiaotong Shen;Wei Pan
Affiliations:
School of Statistics, University of Minnesota, Minneapolis, MN 55455, USA;School of Statistics, University of Minnesota, Minneapolis, MN 55455, USA;Division of Biostatistics, University of Minnesota, Minneapolis, MN 55455, USA
Venue:
Statistical Analysis and Data Mining
Year:
2012

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Abstract

Estimation of multiple directed graphs becomes challenging in the presence of inhomogeneous data, where directed acyclic graphs (DAGs) are used to represent causal relations among random variables. To infer causal relations among variables, we estimate multiple DAGs given a known ordering in Gaussian graphical models. In particular, we propose a constrained maximum likelihood method with nonconvex constraints over elements and element-wise differences of adjacency matrices, for identifying the sparseness structure as well as detecting structural changes over adjacency matrices of the graphs. Computationally, we develop an efficient algorithm based on augmented Lagrange multipliers, the difference convex method, and a novel fast algorithm for solving convex relaxation subproblems. Numerical results suggest that the proposed method performs well against its alternatives for simulated and real data. Statistical Analysis and Data Mining 2011 DOI: 10.1002/sam.11168 © 2012 Wiley Periodicals, Inc.