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.

翻译：本文聚焦于带动态潜变量的图自回归模型的识别问题。潜变量的动态结构由矩阵多项式传递函数描述。综合考虑观测变量间的稀疏交互与潜变量模型的低秩特性，本文构建了一种新的稀疏加低秩优化问题，用于识别图自回归部分，并采用迹近似与重加权核范数最小化方法进行处理。随后，通过迹范数凸规划方法，从低秩谱分解中恢复潜变量的动态特性。仿真算例验证了所提方法的有效性。