An Edge Exclusion Test for Complex Gaussian Graphical Model Selection

We consider the problem of inferring the conditional independence graph (CIG) of complex-valued multivariate Gaussian vectors. A p-variate complex Gaussian graphical model (CGGM) associated with an undirected graph with p vertices is defined as the family of complex Gaussian distributions that obey the conditional independence restrictions implied by the edge set of the graph. For real random vectors, considerable body of work exists where one first tests for exclusion of each edge from the saturated model, and then infers the CIG. Much less attention has been paid to CGGMs. In this paper, we propose and analyze a generalized likelihood ratio test based edge exclusion test statistic for CGGMs. The test statistic is expressed in an alternative form compared to an existing result, where the alternative expression is in a form usually given and exploited for real GGMs. The computational complexity of the proposed statistic is $\mathcal {O}(p^{3})$ compared to $\mathcal {O}(p^{5})$ for the existing result.