  We consider the problem of inferring the conditional independence graph (CIG)
of a high-dimensional stationary multivariate Gaussian time series. A
sparse-group lasso based frequency-domain formulation of the problem has been
considered in the literature where the objective is to estimate the sparse
inverse power spectral density (PSD) of the data. The CIG is then inferred from
the estimated inverse PSD. In this paper we investigate use of a sparse-group
log-sum penalty (LSP) instead of sparse-group lasso penalty. An alternating
direction method of multipliers (ADMM) approach for iterative optimization of
the non-convex problem is presented. We provide sufficient conditions for local
convergence in the Frobenius norm of the inverse PSD estimators to the true
value. This results also yields a rate of convergence. We illustrate our
approach using numerical examples utilizing both synthetic and real data.
