Sparse Plus Low-Rank Identification of Latent-Variable Graphical ARMA Models

This paper deals with the identification of graphical autoregressive moving-average (ARMA) models with latent variables. Combining sparse structural characteristics of the graphical model with low-rank modeling of the latent variables, a sparse plus low-rank based iterative identification algorithm is proposed. The topological information embedded in the sparse AR dynamics is estimated from a regularized Yule-Walker optimization problem, which is then treated as prior graphical structure constraint. The latent-variable plus MA part is identified by solving a convex constrained trace norm minimization problem. Based on the MA part estimate and the structural constraint, the graphical AR estimates are updated by the sparse plus low-rank optimization framework and are then used for the update of the latent-variable plus MA part. The effectiveness of the proposed method is illustrated through a simulation study.