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