# Bayesian Regularization for Functional Graphical Models with Applications to Neuroimaging

arXiv: https://arxiv.org/abs/2110.05575 · HTML: https://mlsanity.com/paper/2110.05575/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 54 references that are in the map.
- First posted on arXiv 11 Oct 2021.

## Builds on (most cited first, 6 of 6)

- [Can parametric statistical methods be trusted for fMRI based group studies?](https://mlsanity.com/paper/1511.01863/) (2015)
- [The Graphical Horseshoe Estimator for Inverse Covariance Matrices](https://mlsanity.com/paper/1707.06661/) (2017)
- [Bayesian Graphical Models for Multivariate Functional Data](https://mlsanity.com/paper/1411.4158/) (2014)
- [Partial Separability and Functional Graphical Models for Multivariate Gaussian Processes](https://mlsanity.com/paper/1910.03134/) (2019)
- [A Bayesian Group Sparse Multi-Task Regression Model for Imaging Genetics](https://mlsanity.com/paper/1605.02234/) (2016)
- [Bayesian functional graphical models](https://mlsanity.com/paper/2108.05034/) (2021)

## Abstract (arXiv)

Graphical models, used to express conditional dependence between random variables observed at various nodes, are used extensively in many fields such as genetics, neuroscience, and social network analysis. While most current statistical methods for estimating graphical models focus on scalar data, there is interest in estimating analogous dependence structures when the data observed at each node are functional, such as signals or images. In this paper, we propose a fully Bayesian regularization scheme for estimating functional graphical models. We first consider a direct Bayesian analog of the functional graphical lasso proposed by Qiao et al. (2019). We then propose a regularization strategy via the graphical horseshoe. We compare these approaches via simulation study and apply our proposed functional graphical horseshoe to two motivating applications, electroencephalography data for comparing brain activation between an alcoholic group and controls, as well as changes in structural connectivity in the presence of traumatic brain injury (TBI). Our results yield insight into how the brain attempts to compensate for disconnected networks after injury.