High dimensional Sparse Gaussian Graphical Mixture Model
This work addresses network reconstruction for high-dimensional data, such as genomics, but is incremental as it builds on existing penalized likelihood and EM techniques.
The paper tackles the challenge of network reconstruction from heterogeneous data using a Gaussian Graphical Mixture Model, proposing a penalized maximum likelihood method with an l1 penalty that improves identifiability and variable selection, and demonstrates its performance through simulations and a genomic application.
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.