# Learning Latent Variable Gaussian Graphical Models

arXiv: https://arxiv.org/abs/1406.2721 · HTML: https://mlsanity.com/paper/1406.2721/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jun 2014.

## Built on by (most cited first, 8 of 8)

- [A Computationally Efficient Method for Learning Exponential Family Distributions](https://mlsanity.com/paper/2110.15397/) (2021)
- [Learning Graphical Factor Models with Riemannian Optimization](https://mlsanity.com/paper/2210.11950/) (2022)
- [Comparing the Value of Labeled and Unlabeled Data in Method-of-Moments Latent Variable Estimation](https://mlsanity.com/paper/2103.02761/) (2021)
- [Enhancing Graphical Lasso: A Robust Scheme for Non-Stationary Mean Data](https://mlsanity.com/paper/2503.19651/) (2025)
- [Learning Gaussian Graphical Models with Latent Confounders](https://mlsanity.com/paper/2105.06600/) (2021)
- [Convex Latent Effect Logit Model via Sparse and Low-rank Decomposition](https://mlsanity.com/paper/2108.09859/) (2021)
- [Learning the hub graphical Lasso model with the structured sparsity via an efficient algorithm](https://mlsanity.com/paper/2308.08852/) (2023)
- [Provable Guarantees and Efficient Learning of Structural Equation Models with Latent Confounders](https://mlsanity.com/paper/2609.18535/) (2026)

## Abstract (arXiv)

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.