Learning the hub graphical Lasso model with the structured sparsity via
  an efficient algorithm
Chengjing Wang Peipei Tang Wenling He Meixia Lin
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.
The sparsity structure of the generalized Jacobian 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.