Bayesian Regularization for Functional Graphical Models with Applications to Neuroimaging
This work addresses the need for statistical methods to model conditional dependence in functional data, particularly in neuroimaging, but it is incremental as it builds on existing functional graphical lasso approaches.
The authors tackled the problem of estimating graphical models for functional data, such as signals or images, by proposing a fully Bayesian regularization scheme, including a functional graphical horseshoe method. They applied this to neuroimaging data, showing insights into brain compensation after injury, with results from simulation studies and applications to EEG and TBI data.
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.