  Gaussian graphical models (GGM) have been widely used in many
high-dimensional applications ranging from biological and financial data to
recommender systems. Sparsity in GGM plays a central role both statistically
and computationally. Unfortunately, real-world data often does not fit well to
sparse graphical models. In this paper, we focus on a family of latent variable
Gaussian graphical models (LVGGM), where the model is conditionally sparse
given latent variables, but marginally non-sparse. In LVGGM, the inverse
covariance matrix has a low-rank plus sparse structure, and can be learned in a
regularized maximum likelihood framework. We derive novel parameter estimation
error bounds for LVGGM under mild conditions in the high-dimensional setting.
These results complement the existing theory on the structural learning, and
open up new possibilities of using LVGGM for statistical inference.
