Edge detection in sparse Gaussian graphical models

In this paper, we consider the problem of detecting edges in a Gaussian graphical model. The problem is equivalent to the identification of non-zero entries of the concentration matrix of a normally distributed random vector. Following the methodology initiated in Meinshausen and Bühlmann (2006), we tackle the problem through regression models where each component of the random vector is regressed on the remaining components. We adapt a method called SLasso cum EBIC (sequential LASSO cum extended Bayesian information criterion) recently developed in Luo and Chen (2011) for feature selection in sparse regression models to suit the special nature of the concentration matrix, and propose two approaches, dubbed SR-SLasso and JR-SLasso, for the identification of non-zero entries of the concentration matrix. Comprehensive numerical studies are conducted to compare the proposed approaches with other available competing methods. The numerical studies demonstrate that the proposed approaches are more accurate than the other methods for the identification of non-zero entries of the concentration matrix.