Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 3 (2009), 205-238.
Inferring sparse Gaussian graphical models with latent structure
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 ℓ1 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.
Electron. J. Statist. Volume 3 (2009), 205-238.
First available in Project Euclid: 26 March 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62H20: Measures of association (correlation, canonical correlation, etc.) 62J07: Ridge regression; shrinkage estimators
Secondary: 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20]
Ambroise, Christophe; Chiquet, Julien; Matias, Catherine. Inferring sparse Gaussian graphical models with latent structure. Electron. J. Statist. 3 (2009), 205--238. doi:10.1214/08-EJS314. http://projecteuclid.org/euclid.ejs/1238078905.