Graphical model selection with latent variables (Q2408245)

The paper considers a factor model where the unobserved and observed variables follow a linear relationship. The interest lies in the detection of conditional dependence between the observed variables after adjusting for the effect of latent factors. The loss function is analogous to the least squares loss. An alternating direction method of multipliers (ADMM) algorithm is used in order to obtain the penalized estimation of the sparse precision matrix. Simulation studies and a real data analysis (of a yeast gene expression data set) validate the theoretical results concerning the identifiability issue, rates of convergence, estimation and model selection consistency. Comparisons to other models (the penalized likelihood approach, the classical factor analysis model) are provided.