Robust sparse Gaussian graphical modeling

Gaussian graphical modeling is popular as a means of exploring network structures, such as gene regulatory networks and social networks. An L₁ penalized maximum likelihood approach is often used to learn high-dimensional graphical models. However, the penalized maximum likelihood procedure is sensitive to outliers. To overcome this problem, we introduce a robust estimation procedure based on the γ-divergence. The proposed method has a redescending property, which is a desirable feature in robust statistics. The parameter estimation procedure is constructed using the Majorize-Minimization algorithm, which guarantees that the objective function monotonically decreases at each iteration. Extensive simulation studies show that our procedure performs much better than the existing methods, in particular, when the contamination ratio is large. Two real data analyses are used for illustration purposes.