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

TL;DR

This paper introduces an efficient two-phase algorithm for estimating hub graphical models with structured sparsity, significantly reducing computation time while maintaining high accuracy in high-dimensional data scenarios.

Contribution

The authors develop a novel two-phase algorithm combining dual ADMM and semismooth Newton methods, exploiting sparsity for efficient hub graphical model estimation.

Findings

Outperforms existing algorithms in synthetic and real data experiments.

Reduces execution time by over 70% in high-dimensional tasks.

Achieves high-quality estimation with efficient computation.

Abstract

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.