# Learning the hub graphical Lasso model with the structured sparsity via an efficient algorithm

arXiv: https://arxiv.org/abs/2308.08852 · HTML: https://mlsanity.com/paper/2308.08852/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 57 references that are in the map.
- First posted on arXiv 17 Aug 2023.

## Builds on (most cited first, 18 of 18)

- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Graph signal processing for machine learning: A review and new perspectives](https://mlsanity.com/paper/2007.16061/) (2020)
- [Structure Learning in Graphical Modeling](https://mlsanity.com/paper/1606.02359/) (2016)
- [SDPNAL+: A Majorized Semismooth Newton-CG Augmented Lagrangian Method for Semidefinite Programming with Nonnegative Constraints](https://mlsanity.com/paper/1406.0942/) (2014)
- [An efficient Hessian based algorithm for solving large-scale sparse group Lasso problems](https://mlsanity.com/paper/1712.05910/) (2017)
- [Sparse Inverse Covariance Matrix Estimation Using Quadratic Approximation](https://mlsanity.com/paper/1306.3212/) (2013)
- [Estimation of Graphical Models through Structured Norm Minimization](https://mlsanity.com/paper/1609.09010/) (2016)
- [Learning Latent Variable Gaussian Graphical Models](https://mlsanity.com/paper/1406.2721/) (2014)
- [Learning Graphical Models With Hubs](https://mlsanity.com/paper/1402.7349/) (2014)
- [QPPAL: A two-phase proximal augmented Lagrangian method for high dimensional convex quadratic programming problems](https://mlsanity.com/paper/2103.13108/) (2021)
- [A Convex Formulation for Learning Scale-Free Networks via Submodular Relaxation](https://mlsanity.com/paper/1407.2697/) (2014)
- [Estimation of sparse Gaussian graphical models with hidden clustering structure](https://mlsanity.com/paper/2004.08115/) (2020)
- [Shrinking characteristics of precision matrix estimators](https://mlsanity.com/paper/1704.04820/) (2017)
- [Learning Gaussian Graphical Models Using Discriminated Hub Graphical Lasso](https://mlsanity.com/paper/1705.06364/) (2017)
- [A dual spectral projected gradient method for log-determinant semidefinite problems](https://mlsanity.com/paper/1812.00523/) (2018)
- [A Proximal Point Dual Newton Algorithm for Solving Group Graphical Lasso Problems](https://mlsanity.com/paper/1906.04647/) (2019)
- [Learning Gaussian Graphical Models via Multiplicative Weights](https://mlsanity.com/paper/2002.08663/) (2020)
- [A dual semismooth Newton based augmented Lagrangian method for large-scale linearly constrained sparse group square-root Lasso problems](https://mlsanity.com/paper/2111.13878/) (2021)

## Abstract (arXiv)

Graphical models have exhibited their performance in numerous tasks ranging from biological analysis to recommender systems. However, graphical models with hub nodes are computationally difficult to fit, particularly when the dimension of the data is large. To efficiently estimate the hub graphical models, we introduce a two-phase algorithm. The proposed algorithm first generates a good initial point via a dual alternating direction method of multipliers (ADMM), and then warm starts a semismooth Newton (SSN) based augmented Lagrangian method (ALM) to compute a solution that is accurate enough for practical tasks. We fully excavate the sparsity structure of the generalized Jacobian arising from the hubs in the graphical models, which ensures that the algorithm can obtain a nice solution very efficiently. Comprehensive experiments on both synthetic data and real data show that it obviously outperforms the existing state-of-the-art algorithms. In particular, in some high dimensional tasks, it can save more than 70% of the execution time, meanwhile still achieves a high-quality estimation.