Alternating direction methods for latent variable gaussian graphical model selection

Shiqian Ma, Lingzhou Xue, Hui Zou

Research output: Contribution to journalLetterpeer-review

64 Scopus citations


Chandrasekaran, Parrilo, and Willsky (2012) proposed a convex optimization problem for graphicalmodel selection in the presence of unobserved variables. This convex optimization problem aims to estimate an inverse covariance matrix that can be decomposed into a sparse matrix minus a low-rank matrix from sample data. Solving this convex optimization problem is very challenging, especially for large problems. In this letter, we propose two alternating direction methods for solving this problem. The first method is to apply the classic alternating direction method of multipliers to solve the problem as a consensus problem. The second method is a proximal gradient-based alternating-direction method of multipliers. Our methods take advantage of the special structure of the problem and thus can solve large problems very efficiently. A global convergence result is established for the proposed methods. Numerical results on both synthetic data and gene expression data show that our methods usually solve problems with 1 million variables in 1 to 2 minutes and are usually 5 to 35 times faster than a state-of-the-artNewton-CG proximal point algorithm.

Original languageEnglish (US)
Pages (from-to)2172-2198
Number of pages27
JournalNeural computation
Issue number8
StatePublished - 2013


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