On the identification of ARMA graphical models

TL;DR

This paper introduces a novel approach for estimating ARMA graphical models using a maximum entropy extension, connecting it with maximum likelihood, and providing a Bayesian framework for unknown topologies, validated through numerical experiments.

Contribution

It proposes a new maximum entropy covariance and cepstral extension method for ARMA graphical models, linking it with maximum likelihood and Bayesian estimation.

Findings

The method effectively estimates ARMA graphical models.

The dual problem aligns with maximum likelihood principles.

Numerical experiments demonstrate the approach's performance.

Abstract

The paper considers the problem to estimate a graphical model corresponding to an autoregressive moving-average (ARMA) Gaussian stochastic process. We propose a new maximum entropy covariance and cepstral extension problem and we show that the problem admits an approximate solution which represents an ARMA graphical model whose topology is determined by the selected entries of the covariance lags considered in the extension problem. Then, we show how the corresponding dual problem is connected with the maximum likelihood principle. Such connection allows to design a Bayesian model and characterize an approximate maximum a posteriori estimator of the ARMA graphical model in the case the graph topology is unknown. We test the performance of the proposed method through some numerical experiments.