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.

arXiv comment35 pages, 15 figures

References in corpus (15)

• Rejoinder to "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Least Angle Regression
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• High-dimensional graphs and variable selection with the Lasso
• Pathwise coordinate optimization
• Coordinate descent algorithms for lasso penalized regression
• Uncovering latent structure in valued graphs: A variational approach
• Multiple Testing and Error Control in Gaussian Graphical Model Selection

Cited by in corpus (3)

• Automated calibration for stability selection in penalised regression and graphical models
• Learning block structured graphs in Gaussian graphical models
• Bayesian Learning of Graph Substructures