Bayesian Regularization for Functional Graphical Models with Applications to Neuroimaging

TL;DR

This paper introduces a Bayesian regularization approach for estimating functional graphical models, enabling analysis of complex neuroimaging data to understand brain connectivity and compensation mechanisms after injury.

Contribution

It develops a novel Bayesian regularization method using the graphical horseshoe for functional graphical models, extending existing scalar data methods to functional data.

Findings

The proposed method effectively captures brain connectivity patterns.

Application to EEG data reveals insights into brain compensation post-injury.

Simulation studies demonstrate improved estimation accuracy.

Abstract

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.