Learning the hub graphical Lasso model with the structured sparsity via an efficient algorithm
This work addresses a computational bottleneck for researchers and practitioners using hub graphical models in fields like biology and recommender systems, offering an incremental improvement in efficiency.
The paper tackles the computational difficulty of fitting graphical models with hub nodes in high-dimensional data by introducing a two-phase algorithm that combines dual ADMM and SSN-based ALM, achieving over 70% execution time savings while maintaining high-quality estimation.
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.