# 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.

## 64 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.

### Identification of Low Rank Vector Processes

- Computer ScienceArXiv
- 2021

This work considers processes having an innovation of reduced dimension for which Prediction Error Methods (PEM) algorithms are not directly applicable and shows that these processes admit a special feedback structure with a deterministic feedback channel which can be used to split the identiﬁcation in two steps.

### 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.

## References

SHOWING 1-10 OF 32 REFERENCES

### ARMA Identification of Graphical Models

- Computer Science, MathematicsIEEE Transactions on Automatic Control
- 2013

This paper develops a theoretical framework and an optimization procedure which is applied to the identification problem of estimating the ARMA parameters as well as the topology of the graph from statistical data.

### Latent variable graphical model selection via convex optimization

- Computer Science2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
- 2010

The modeling framework can be viewed as a combination of dimensionality reduction and graphical modeling (to capture remaining statistical structure not attributable to the latent variables) and it consistently estimates both the number of hidden components and the conditional graphical model structure among the observed variables.

### Graphical interaction models for multivariate time series1

- Mathematics, Computer Science
- 2000

A partial correlation graph for time series is defined and the partial spectral coherence between two components given the remaining components to identify the edges of the graph is used.

### Modelling High-Dimensional Time Series by Generalized Linear Dynamic Factor Models: an Introductory Survey

- Computer Science, EconomicsCommun. Inf. Syst.
- 2007

This work presents an introductory survey to factor models for time series, where the factors represent the comovement between the single time series.

### Topology Selection in Graphical Models of Autoregressive Processes

- Computer Science, MathematicsJ. Mach. Learn. Res.
- 2010

An algorithm is presented for topology selection in graphical models of autoregressive Gaussian time series that reduces to a convex optimization problem and is described as a large-scale algorithm that solves the dual problem via the gradient projection method.

### Tree-structured statistical modeling via convex optimization

- Mathematics, Computer ScienceIEEE Conference on Decision and Control and European Control Conference
- 2011

A semidefinite-programming-based approach to stochastic modeling with multiscale autoregressive (MAR) processes—a class of Stochastic processes indexed by the vertices of a tree that can recover a parametrization that matches the leaf-covariance and has the correct state dimensions.

### Remarks Concerning Graphical Models for Time Series and Point Processes

- Computer Science, Mathematics
- 1996

In this paper the nodal random variables will be time series or point processes and the cases of undirected and directed graphs are focussed on.

### Linear Stochastic Systems: A Geometric Approach to Modeling, Estimation and Identification

- Mathematics, Computer Science
- 2016

This chapter discusses the development of linear Finite-Dimensional Stochastic Systems with Inputs, and some Topics in Linear Algebra and Hilbert Space Theory.

### Gaussian Multiresolution Models: Exploiting Sparse Markov and Covariance Structure

- Computer ScienceIEEE Transactions on Signal Processing
- 2010

This paper proposes a new class of Gaussian MR models in which variables at each scale have sparse conditional covariance structure conditioned on other scales, and shows the modeling and inference advantages of this approach over methods that use MR tree models and single-scale approximation methods that do not use hidden variables.

### Modeling Complex Systems by Generalized Factor Analysis

- Computer ScienceIEEE Transactions on Automatic Control
- 2015

A new modeling paradigm for large dimensional aggregates of stochastic systems by Generalized Factor Analysis models that describes the data as the sum of a flocking plus an uncorrelated idiosyncratic component is proposed.