Multiple Gaussian graphical estimation with jointly sparse penalty

• A jointly sparse penalty is designed to make graphs share similar sparsity structure.
• We derive a new re-weighed algorithm to solve the proposed model.
• The proposed algorithm maintains advantages than FMGL and GGL with the general cases.

In this paper, we consider estimating multiple Gaussian graphs with a similar sparsity structure. Most related solving methods, such as GGL (Group graphical lasso) and FMGL (Fused multiple graphical lasso), focus on the information of the edge values, and pay few attention to the estimation based on structure information. We construct a jointly sparse penalty to encourage graphs to share a similar sparsity structure by utilizing information of the common structure across the graphs. The new objective function is neither convex nor differentiable. Combining block coordinate descent and majorization–minimization strategies, we derive a new re-weighed algorithm to solve the problem by transforming the subproblems in every iteration into convex ones. Experimental results show that the proposed algorithm outperforms FMGL and GGL when the sparsity structure is similar but the edge values are not.