Graphical model selection with latent variables

Abstract

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.