  This paper focuses on the identification of graphical autoregressive models
with dynamical latent variables. The dynamical structure of latent variables is
described by a matrix polynomial transfer function. Taking account of the
sparse interactions between the observed variables and the low-rank property of
the latent-variable model, a new sparse plus low-rank optimization problem is
formulated to identify the graphical auto-regressive part, which is then
handled using the trace approximation and reweighted nuclear norm minimization.
Afterwards, the dynamics of latent variables are recovered from low-rank
spectral decomposition using the trace norm convex programming method.
Simulation examples are used to illustrate the effectiveness of the proposed
approach.
