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

arXiv: https://arxiv.org/abs/2307.11320 · HTML: https://mlsanity.com/paper/2307.11320/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jul 2023.

## Built on by (most cited first, 1 of 1)

- [Identification of Non-causal Graphical Models](https://mlsanity.com/paper/2410.09480/) (2024)

## Abstract (arXiv)

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.