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This paper considers the problem of networks reconstruction fromheterogeneous data using a Gaussian Graphical Mixture Model (GGMM). It is wellknown that parameter estimation in this context is challenging due to largenumbers of variables coupled with the degeneracy of the likelihood. We proposeas a solution a penalized maximum likelihood technique by imposing an $l_{1}$penalty on the precision matrix. Our approach shrinks the parameters therebyresulting in better identifiability and variable selection. We use theExpectation Maximization (EM) algorithm which involves the graphical LASSO toestimate the mixing coefficients and the precision matrices. We show that undercertain regularity conditions the Penalized Maximum Likelihood (PML) estimatesare consistent. We demonstrate the performance of the PML estimator throughsimulations and we show the utility of our method for high dimensional dataanalysis in a genomic application.

High dimensional Sparse Gaussian Graphical Mixture Model