Inferring sparse Gaussian graphical models with latent structure

Abstract

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 \textsc{em}-like algorithm. The performances of our method is illustrated on synthetic as well as real data, the latter concerning breast cancer.