  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.
