This paper considers the problem of networks reconstruction from

heterogeneous data using a Gaussian Graphical Mixture Model (GGMM). It is well

known that parameter estimation in this context is challenging due to large

numbers of variables coupled with the degeneracy of the likelihood. We propose

as a solution a penalized maximum likelihood technique by imposing an $l_{1}$

penalty on the precision matrix. Our approach shrinks the parameters thereby

resulting in better identifiability and variable selection. We use the

Expectation Maximization (EM) algorithm which involves the graphical LASSO to

estimate the mixing coefficients and the precision matrices. We show that under

certain regularity conditions the Penalized Maximum Likelihood (PML) estimates

are consistent. We demonstrate the performance of the PML estimator through

simulations and we show the utility of our method for high dimensional data

analysis in a genomic application.

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