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

TL;DR

This paper introduces a novel method for identifying graphical autoregressive models with dynamical latent variables by combining sparse and low-rank optimization techniques, improving the recovery of latent structures.

Contribution

It formulates a new sparse plus low-rank optimization framework for identifying latent-variable graphical AR models, utilizing trace approximation and nuclear norm minimization.

Findings

Effective recovery of latent variable dynamics demonstrated in simulations

Improved identification accuracy over existing methods

Robustness to noise and model complexity

Abstract

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.