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This paper focuses on the identification of graphical autoregressive modelswith dynamical latent variables. The dynamical structure of latent variables isdescribed by a matrix polynomial transfer function. Taking account of thesparse interactions between the observed variables and the low-rank property ofthe latent-variable model, a new sparse plus low-rank optimization problem isformulated to identify the graphical auto-regressive part, which is thenhandled using the trace approximation and reweighted nuclear norm minimization.Afterwards, the dynamics of latent variables are recovered from low-rankspectral decomposition using the trace norm convex programming method.Simulation examples are used to illustrate the effectiveness of the proposedapproach.

Sparse plus low-rank identification for dynamical latent-variable graphical AR models