Inferring sparse Gaussian graphical models with latent structure

Christophe Ambroise (1) , Julien Chiquet (1) , Catherine Matias (1)

1 LSG - Laboratoire Statistique et Génome

Our concern is selecting the concentration matrix's nonzero coefficients for a sparse Gaussian graphical model in a high-dimensional setting. This corresponds to estimating the graph of conditional dependencies between the variables. We describe a novel framework taking into account a latent structure on the concentration matrix. This latent structure is used to drive a penalty matrix and thus to recover a graphical model with a constrained topology. Our method uses an $\ell_1$ penalized likelihood criterion. Inference of the graph of conditional dependencies between the variates and of the hidden variables is performed simultaneously in an iterative EM-like algorithm named SIMoNe (Statistical Inference for Modular Networks). Performances are illustrated on synthetic as well as real data, the latter concerning breast cancer. For gene regulation networks, our method can provide a useful insight both on the mutual influence existing between genes, and on the modules existing in the network.

Mots clés: Gaussian graphical model; Mixture model; $\ell_1$-penalization; Model selection; Variational inference; EM algorithm

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Christophe Ambroise, Julien Chiquet, Catherine Matias. Inferring sparse Gaussian graphical models with latent structure. Electronic Journal of Statistics , 2009, 3, pp.205-238. ⟨10.1214/08-EJS314⟩. ⟨hal-00592201⟩