Inferring sparse Gaussian graphical models with latent structure

TL;DR

This paper introduces a new method for estimating sparse Gaussian graphical models that incorporates latent structures, using an EM-like algorithm with an $ ext{l}_1$ penalty to improve graph recovery in high-dimensional data.

Contribution

The authors propose a novel framework that integrates latent structures into the penalty design for sparse Gaussian graphical models, enhancing topology recovery.

Findings

Effective in synthetic data experiments

Successfully applied to breast cancer data

Improves graph structure estimation accuracy

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.