# Identification of Non-causal Graphical Models

arXiv: https://arxiv.org/abs/2410.09480 · HTML: https://mlsanity.com/paper/2410.09480/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 41 references that are in the map.
- First posted on arXiv 12 Oct 2024.

## Builds on (most cited first, 17 of 17)

- [Oracle Inequalities for High Dimensional Vector Autoregressions](https://mlsanity.com/paper/1311.0811/) (2013)
- [AR Identification of Latent-variable Graphical Models](https://mlsanity.com/paper/1405.0027/) (2014)
- [Identification of Sparse Reciprocal Graphical Models](https://mlsanity.com/paper/1806.04423/) (2018)
- [Learning linear modules in a dynamic network using regularized kernel-based methods](https://mlsanity.com/paper/2005.06266/) (2020)
- [Topology Learning of Linear Dynamical Systems with Latent Nodes using Matrix Decomposition](https://mlsanity.com/paper/1912.07152/) (2019)
- [On the identification of ARMA graphical models](https://mlsanity.com/paper/2308.14384/) (2023)
- [Empirical Bayesian Learning in AR Graphical Models](https://mlsanity.com/paper/1907.03829/) (2019)
- [Data-driven Link Prediction over Graphical Models](https://mlsanity.com/paper/2004.14187/) (2020)
- [Autoregressive Identification of Kronecker Graphical Models](https://mlsanity.com/paper/2004.14199/) (2020)
- [Nonparametric Identification of Kronecker Networks](https://mlsanity.com/paper/2206.05156/) (2022)
- [Learning Sparse High-Dimensional Matrix-Valued Graphical Models From Dependent Data](https://mlsanity.com/paper/2404.19073/) (2024)
- [Multidimensional Rational Covariance Extension with Applications to Spectral Estimation and Image Compression](https://mlsanity.com/paper/1507.01430/) (2015)
- [A Scalable Strategy for the Identification of Latent-variable Graphical Models](https://mlsanity.com/paper/1809.01608/) (2018)
- [A Well-Posed Multidimensional Rational Covariance and Generalized Cepstral Extension Problem](https://mlsanity.com/paper/2110.06425/) (2021)
- [On the Statistical Consistency of a Generalized Cepstral Estimator](https://mlsanity.com/paper/2301.06784/) (2023)
- [Sparse plus low-rank identification for dynamical latent-variable graphical AR models](https://mlsanity.com/paper/2307.11320/) (2023)
- [ℓ0 Factor Analysis: A P-Stationary Point Theory](https://mlsanity.com/paper/2409.01888/) (2024)

## Abstract (arXiv)

The paper considers the problem to estimate non-causal graphical models whose edges encode smoothing relations among the variables. We propose a new covariance extension problem and show that the solution minimizing the transportation distance with respect to white noise process is a double-sided autoregressive non-causal graphical model. Then, we generalize the paradigm to a class of graphical autoregressive moving-average models. Finally, we test the performance of the proposed method through some numerical experiments.