Junyao You

The paper considers the problem to estimate non-causal graphical models whose edges encode smoothing relations among the variables. We propose a new covariance extension problem and show that the solution minimizing the transportation distance with respect to white noise process is a double-sided autoregressive non-causal graphical model. Then, we generalize the paradigm to a class of graphical autoregressive moving-average models. Finally, we test the performance of the proposed method through some numerical experiments.

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.

This paper focuses on the joint estimation of parameters and time-delays of the multiple-input single-output output-error systems. Since the time-delays are unknown, an effective identification model with a high dimensional and sparse parameter vector is established based on overparameterization. Then, the identification problem is converted to a sparse optimization problem. Based on the basis pursuit de-noising criterion and the auxiliary model identification idea, an auxiliary model based basis pursuit de-noising iterative algorithm is presented. The parameters are estimated by solving a quadratic program, and the unavailable terms in the information vector are updated by the auxiliary model outputs iteratively. The time-delays are estimated according to the sparse structure of the parameter vector. The proposed method can obtain effective estimates of the parameters and time-delays from few sampled data. The simulation results illustrate the effectiveness of the proposed algorithm.