# On the identification of ARMA graphical models

arXiv: https://arxiv.org/abs/2308.14384 · HTML: https://mlsanity.com/paper/2308.14384/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Aug 2023.

## Built on by (most cited first, 3 of 3)

- [Identification of Non-causal Graphical Models](https://mlsanity.com/paper/2410.09480/) (2024)
- [Learning Networks from Wide-Sense Stationary Stochastic Processes](https://mlsanity.com/paper/2412.03768/) (2024)
- [Modeling and Topology Estimation of Low Rank Dynamical Networks](https://mlsanity.com/paper/2511.06674/) (2025)

## Abstract (arXiv)

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.