Open Access
Translator Disclaimer
2017 Graphical model selection with latent variables
Changjing Wu, Hongyu Zhao, Huaying Fang, Minghua Deng
Electron. J. Statist. 11(2): 3485-3521 (2017). DOI: 10.1214/17-EJS1331


Gaussian graphical models are commonly used to characterize the conditional dependence among variables. However, ignorance of the effect of latent variables may blur the structure of a graph and corrupt statistical inference. In this paper, we propose a method for learning $\underline{\mathrm{L}}$atent $\underline{\mathrm{V}}$ariables graphical models via $\ell_{1}$ and trace penalized $\underline{\mathrm{D}}$-trace loss (LVD), which achieves parameter estimation and model selection consistency under certain identifiability conditions. We also present an efficient ADMM algorithm to obtain the penalized estimation of the sparse precision matrix. Using simulation studies, we validate the theoretical properties of our estimator and show its superior performance over other methods. The usefulness of the proposed method is also demonstrated through its application to a yeast genetical genomic data.


Download Citation

Changjing Wu. Hongyu Zhao. Huaying Fang. Minghua Deng. "Graphical model selection with latent variables." Electron. J. Statist. 11 (2) 3485 - 3521, 2017.


Received: 1 October 2016; Published: 2017
First available in Project Euclid: 6 October 2017

zbMATH: 1384.62210
MathSciNet: MR3709861
Digital Object Identifier: 10.1214/17-EJS1331

Keywords: ADMM , Gaussian graphical models , latent variable , low rank , model selection consistency , Sparsity


Vol.11 • No. 2 • 2017
Back to Top