  We consider the problem of inferring the conditional independence graph (CIG)
of a sparse, high-dimensional, stationary matrix-variate Gaussian time series.
All past work on high-dimensional matrix graphical models assumes that
independent and identically distributed (i.i.d.) observations of the
matrix-variate are available. Here we allow dependent observations. We consider
a sparse-group lasso-based frequency-domain formulation of the problem with a
Kronecker-decomposable power spectral density (PSD), and solve it via an
alternating direction method of multipliers (ADMM) approach. The problem is
bi-convex which is solved via flip-flop optimization. We provide sufficient
conditions for local convergence in the Frobenius norm of the inverse PSD
estimators to the true value. This result also yields a rate of convergence. We
illustrate our approach using numerical examples utilizing both synthetic and
real data.
