Robust sparse Gaussian graphical modeling

TL;DR

This paper introduces a robust method for sparse Gaussian graphical modeling using gamma-divergence, improving resistance to outliers with a guaranteed convergence algorithm, and demonstrating superior performance in simulations and real data.

Contribution

It proposes a novel robust estimation approach based on gamma-divergence for sparse Gaussian graphical models, with an efficient Majorize-Minimization algorithm.

Findings

Outperforms existing methods in high contamination scenarios

Demonstrates effectiveness through simulations

Shows practical utility in real data analyses

Abstract

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.