Learning Latent Variable Gaussian Graphical Models

By Zhaoshi Meng, Brian Eriksson, A. Hero. 2014

41 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Statistics and Probability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Lawrence Carin
2. Changyou Chen
3. Qinliang Su
4. Xuejun Liao
5. Lise Getoor
6. Ben London
7. Bert Huang
8. Chunyuan Li

In Statistics and Probability

1. Changyou Chen
2. Lawrence Carin
3. Qinliang Su
4. Xuejun Liao
5. Lise Getoor
6. Ben London
7. Bert Huang
8. Chunyuan Li

Citations in the corpus

• Nonlinear Statistical Learning with Truncated Gaussian Graphical Models (2016, background): “Gaussian graphical models (GGM) constitute a subset of graphical models that have found successful application in a diverse range of areas (Honorio et al., 2009; Liu & Will-sky, 2013; Oh & Deasy, 2014; Meng et al., 2014; Su & Wu, 2015a;b).”
• The Benefits of Learning with Strongly Convex Approximate Inference (2015, background): “Many of these works (e.g., Bickel et al., 2009; Kakade et al., 2010; Ravikumar et al., 2011; Negahban et al., 2012; Bradley & Guestrin, 2012; Meng et al., 2014) rely on a restricted eigenvalue (RE) assumption.”