Graphical Lasso for High-dimensional Complex Gaussian Graphical Model Selection

We consider the problem of infemng the conditional independence graph (CIG) of both proper and improper, complex-valued, high- dimensional multivariate Gaussian vectors. A p-variate complex Gaussian graphical model (CGGM) associated with an undirected graph with p vemces is defined as the family of complex Gaussian distributions that obey the conditional independence restrictions im- plied by the edge set of the graph. For real random vectors, consider- able body of work exists, whereas that on proper complex Gaussian graphical models (PCGGMs) is sparse, while that on ICGGMs is non-existent. In this paper, we present a graphical lasso based penal- ized log-likelihood approach for both PCGGMs and ICGGMs. An alternating minimization algorithm is used to optimize the objective functions. Numerical examples illustrate the proposed algorithms.