# Exploration of the search space of Gaussian graphical models for paired data

arXiv: https://arxiv.org/abs/2303.05561 · HTML: https://mlsanity.com/paper/2303.05561/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 35 references that are in the map.
- First posted on arXiv 9 Mar 2023.

## Builds on (most cited first, 8 of 8)

- [Joint Gaussian Graphical Model Estimation: A Survey](https://mlsanity.com/paper/2110.10281/) (2021)
- [The Gaussian Graphical Model in Cross-sectional and Time-series Data](https://mlsanity.com/paper/1609.04156/) (2016)
- [Partial Correlation Graphical LASSO](https://mlsanity.com/paper/2104.10099/) (2021)
- [Fused graphical lasso for brain networks with symmetries](https://mlsanity.com/paper/2005.11785/) (2020)
- [Approximate Bayesian estimation in large coloured graphical Gaussian models](https://mlsanity.com/paper/1605.08441/) (2016)
- [Joint Estimation of Multiple Dependent Gaussian Graphical Models with Applications to Mouse Genomics](https://mlsanity.com/paper/1608.08659/) (2016)
- [Bayesian model selection approach for colored graphical Gaussian models](https://mlsanity.com/paper/2004.00764/) (2020)
- [Penalized composite likelihood for colored graphical Gaussian models](https://mlsanity.com/paper/2004.01328/) (2020)

## Abstract (arXiv)

We consider the problem of learning a Gaussian graphical model in the case where the observations come from two dependent groups sharing the same variables. We focus on a family of coloured Gaussian graphical models specifically suited for the paired data problem. Commonly, graphical models are ordered by the submodel relationship so that the search space is a lattice, called the model inclusion lattice. We introduce a novel order between models, named the twin order. We show that, embedded with this order, the model space is a lattice that, unlike the model inclusion lattice, is distributive. Furthermore, we provide the relevant rules for the computation of the neighbours of a model. The latter are more efficient than the same operations in the model inclusion lattice, and are then exploited to achieve a more efficient exploration of the search space. These results can be applied to improve the efficiency of both greedy and Bayesian model search procedures. Here we implement a stepwise backward elimination procedure and evaluate its performance by means of simulations. Finally, the procedure is applied to learn a brain network from fMRI data where the two groups correspond to the left and right hemispheres, respectively.