# Efficient proximal gradient algorithms for joint graphical lasso

arXiv: https://arxiv.org/abs/2107.07799 · HTML: https://mlsanity.com/paper/2107.07799/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 44 references that are in the map.
- First posted on arXiv 16 Jul 2021.

## Builds on (most cited first, 6 of 6)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Network Inference via the Time-Varying Graphical Lasso](https://mlsanity.com/paper/1703.01958/) (2017)
- [Dynamic Visualization and Fast Computation for Convex Clustering via Algorithmic Regularization](https://mlsanity.com/paper/1901.01477/) (2019)
- [Composite Self-Concordant Minimization](https://mlsanity.com/paper/1308.2867/) (2013)
- [Regularized Estimation of Piecewise Constant Gaussian Graphical Models: The Group-Fused Graphical Lasso](https://mlsanity.com/paper/1512.06171/) (2015)
- [Exact Hybrid Covariance Thresholding for Joint Graphical Lasso](https://mlsanity.com/paper/1503.02128/) (2015)

## Abstract (arXiv)

We consider learning an undirected graphical model from sparse data. While several efficient algorithms have been proposed for graphical lasso (GL), the alternating direction method of multipliers (ADMM) is the main approach taken concerning for joint graphical lasso (JGL). We propose proximal gradient procedures with and without a backtracking option for the JGL. These procedures are first-order and relatively simple, and the subproblems are solved efficiently in closed form. We further show the boundedness for the solution of the JGL problem and the iterations in the algorithms. The numerical results indicate that the proposed algorithms can achieve high accuracy and precision, and their efficiency is competitive with state-of-the-art algorithms.