Bayesian Regularization for Functional Graphical Models
- URL: http://arxiv.org/abs/2110.05575v1
- Date: Mon, 11 Oct 2021 19:33:07 GMT
- Title: Bayesian Regularization for Functional Graphical Models
- Authors: Jiajing Niu, Boyoung Hur, John Absher, and D. Andrew Brown
- Abstract summary: We propose a fully Bayesian regularization scheme for estimating graphical models.
Our results yield insight into how the brain attempts to compensate for disconnected networks after injury.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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