  Gaussian graphical modeling has been widely used to explore various network
structures, such as gene regulatory networks and social networks. We often use
a penalized maximum likelihood approach with the $L_1$ penalty for learning a
high-dimensional graphical model. However, the penalized maximum likelihood
procedure is sensitive to outliers. To overcome this problem, we introduce a
robust estimation procedure based on the $\gamma$-divergence. The proposed
method has a redescending property, which is known as a desirable property 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 showed
that our procedure performed much better than the existing methods, in
particular, when the contamination ratio was large. Two real data analyses were
carried out to illustrate the usefulness of our proposed procedure.
