ON SPARSE COMPLEX GAUSSIAN GRAPHICAL MODEL SELECTION

We consider the problem of estimating the conditional independence graph (CIG) of a sparse, high-dimensional proper complex-valued Gaussian graphical model (CGGM). A p-variate 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. The focus of this paper is on theoretical analysis of a recently proposed graphical lasso approach based on an l(1)-penalized log-likelihood objective function to estimate the sparse inverse covariance matrix. Sufficient conditions for consistency and sparsistency of the inverse covariance estimator are provided.