Inferring sparse Gaussian graphical models with latent structure

Abstract

Our concern is selecting the concentration matrix's nonzero coefficients for\na sparse Gaussian graphical model in a high-dimensional setting. This\ncorresponds to estimating the graph of conditional dependencies between the\nvariables. We describe a novel framework taking into account a latent structure\non the concentration matrix. This latent structure is used to drive a penalty\nmatrix and thus to recover a graphical model with a constrained topology. Our\nmethod uses an $\\ell_1$ penalized likelihood criterion. Inference of the graph\nof conditional dependencies between the variates and of the hidden variables is\nperformed simultaneously in an iterative \\textsc{em}-like algorithm. The\nperformances of our method is illustrated on synthetic as well as real data,\nthe latter concerning breast cancer.\n