# Speeding Up Latent Variable Gaussian Graphical Model Estimation via Nonconvex Optimizations

arXiv: https://arxiv.org/abs/1702.08651 · HTML: https://mlsanity.com/paper/1702.08651/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Feb 2017.

## Built on by (most cited first, 4 of 4)

- [Fast Projected Newton-like Method for Precision Matrix Estimation under Total Positivity](https://mlsanity.com/paper/2112.01939/) (2021)
- [Variance-Aware Linear UCB with Deep Representation for Neural Contextual Bandits](https://mlsanity.com/paper/2411.05979/) (2024)
- [Compressive Recovery of Sparse Precision Matrices](https://mlsanity.com/paper/2311.04673/) (2023)
- [Gaussian Graphical Models as an Ensemble Method for Distributed Gaussian Processes](https://mlsanity.com/paper/2202.03287/) (2022)

## Abstract (arXiv)

We study the estimation of the latent variable Gaussian graphical model (LVGGM), where the precision matrix is the superposition of a sparse matrix and a low-rank matrix. In order to speed up the estimation of the sparse plus low-rank components, we propose a sparsity constrained maximum likelihood estimator based on matrix factorization, and an efficient alternating gradient descent algorithm with hard thresholding to solve it. Our algorithm is orders of magnitude faster than the convex relaxation based methods for LVGGM. In addition, we prove that our algorithm is guaranteed to linearly converge to the unknown sparse and low-rank components up to the optimal statistical precision. Experiments on both synthetic and genomic data demonstrate the superiority of our algorithm over the state-of-the-art algorithms and corroborate our theory.