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Joint estimation of multiple undirected graphical models

Gaussian graphical models are of great interest in statistical learning. Since the conditional independence between the variables corresponds to zero entries in the inverse covariance matrix, one can learn the structure of the graph by estimating a sparse inverse covariance matrix from sample data. This is usually done by solving a convex maximum likelihood problem with a l1-regularization term applied on the inverse covariance matrix. In this study, we develop an estimator for such models appropriate for data coming from several datasets that share the same set of variables and a common network substructure. We assume that there exist a few different edges among the networks while the others (edges) are common. To this end, we form an optimization problem that exploits the problem's special structure and we propose an alternating direction method for its solution. We confirm the performance improvement of our method over existing methods in finding the dependence structure on a real dataset.