Bayesian scalar-on-network regression with applications to brain functional connectivity.

Area of Science:

• Neuroimaging
• Statistical Modeling
• Machine Learning

Background:

• Brain functional connectivity is often represented as symmetric positive definite (SPD) matrices.
• Existing methods often ignore the geometric structure of SPD matrices by vectorization.
• This leads to a loss of information and potentially suboptimal model performance.

Purpose of the Study:

• To develop a Bayesian regression model that respects the Riemannian geometry of SPD matrices.
• To enable dimension reduction and prediction of scalar outcomes using brain connectivity data.
• To identify key brain regions predictive of specific outcomes.

Main Methods:

• Utilized tangent space modeling to handle SPD matrices.
• Implemented dimension reduction in the tangent space.
• Employed a sparsity-inducing prior on a Stiefel manifold for the dimension reduction matrix to prevent overfitting.

Main Results:

• Developed a parsimonious Bayesian regression model for brain functional connectivity.
• The model allows for uncertainty quantification of all parameters.
• Successfully predicted Picture Vocabulary scores using Human Connectome Project data.

Conclusions:

• The proposed method effectively models brain functional connectivity data by respecting its geometric properties.
• The approach allows for robust prediction and identification of important brain regions.
• This offers a valuable tool for neuroimaging research and clinical applications.