Maximum likelihood estimation over directed acyclic gaussian graphs

Yiping Yuan, Xiaotong Shen, Wei Pan

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)523-530
Number of pages8
JournalStatistical Analysis and Data Mining
Issue number6
StatePublished - Dec 2012


  • Collapsed networks
  • Nonconvex constraints
  • Pairwise coordinate descent


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