# AR Identification of Latent-Variable Graphical Models

@article{Zorzi2016ARIO, title={AR Identification of Latent-Variable Graphical Models}, author={Mattia Zorzi and Rodolphe Sepulchre}, journal={IEEE Transactions on Automatic Control}, year={2016}, volume={61}, pages={2327-2340} }

The paper proposes an identification procedure for autoregressive Gaussian stationary stochastic processes under the assumption that the manifest (or observed) variables are nearly independent when conditioned on a limited number of latent (or hidden) variables. The method exploits the sparse plus low-rank decomposition of the inverse of the manifest spectral density and the efficient convex relaxations recently proposed for such decompositions.

## 62 Citations

### A Scalable Strategy for the Identification of Latent-Variable Graphical Models

- Computer Science, MathematicsIEEE Transactions on Automatic Control
- 2022

An identification method for latent-variable graphical models associated with autoregressive (AR) Gaussian stationary processes exploiting the approximation of AR processes through stationary reciprocal processes thus benefiting of the numerical advantages of dealing with block-circulant matrices.

### On the Identification of Sparse plus Low-rank Graphical Models

- Mathematics
- 2017

This thesis proposes an identification procedure for periodic, Gaussian, stationary reciprocal processes, under the assumption that the conditional dependence relations among the observed variables…

### Identification of Sparse Reciprocal Graphical Models

- Mathematics, Computer ScienceIEEE Control Systems Letters
- 2018

It is shown that the proposed paradigm leads to a regularized, circulant matrix completion problem whose solution only requires computations of the eigenvalues of matrices of dimension equal to the dimension of the process.

### Learning AR factor models

- Mathematics2020 59th IEEE Conference on Decision and Control (CDC)
- 2020

An approximate moment matching approach is proposed to estimate the number of factors as well as the parameters of the model to solve the factor analysis problem using a particular class of auto-regressive processes.

### Maximum Entropy Expectation-Maximization Algorithm for Fitting Latent-Variable Graphical Models to Multivariate Time Series

- Computer ScienceEntropy
- 2018

It is shown how an algorithm which was originally used for finding zeros in the inverse of the covariance matrix can be generalized such that to identify the sparsity pattern of theverse of spectral density matrix.

### Learning Latent Variable Dynamic Graphical Models by Confidence Sets Selection

- Computer Science, MathematicsIEEE Transactions on Automatic Control
- 2020

A new method is proposed, which accounts for the uncertainty in the estimation by computing a “confidence neighborhood” containing the true model with a prescribed probability, which allows for the presence of a small number of latent variables in order to enforce sparsity of the identified graph.

### Sparse plus low-rank autoregressive identification in neuroimaging time series

- Computer Science2015 54th IEEE Conference on Decision and Control (CDC)
- 2015

This paper uses the alternating direction method of multipliers (ADMM) to solve the problem of identifying multivariate autoregressive (AR) sparse plus low-rank graphical models efficiently as a convex program for sizes encountered in neuroimaging applications.

### A Bayesian approach to sparse plus low rank network identification

- Computer Science2015 54th IEEE Conference on Decision and Control (CDC)
- 2015

A Bayesian approach is proposed to identify multivariate stochastic processes with parsimonious dynamical models which can be represented with a sparse dynamic network with few latent nodes which translates into a sparse plus low rank model.

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