Gaussian graphical models (GGM) have been widely used in many highdimensional 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.
REF also studied regularized maximum likelihood estimation and derive Frobenius norm error bounds in the highdimensional setting based on the restricted strong convexity.
Learning Latent Variable Gaussian Graphical Models
ArXiv
ArXiv
Computer Science Mathematics