Bayesian Regression With Undirected Network Predictors With an Application to Brain Connectome Data

Abstract

This article focuses on the relationship between a measure of creativity and the human brain network for subjects in a brain connectome dataset obtained using a diffusion weighted magnetic resonance imaging procedure. We identify brain regions and interconnections that have a significant effect on creativity. Brain networks are often expressed in terms of symmetric adjacency matrices, with row and column indices of the matrix representing the regions of interest (ROI), and a cell entry signifying the estimated number of fiber bundles connecting the corresponding row and column ROIs. Current statistical practices for regression analysis with the brain network as the predictor and the measure of creativity as the response typically vectorize the network predictor matrices prior to any analysis, thus failing to account for the important structural information in the network. This results in poor inferential and predictive performance in presence of small sample sizes. To answer the scientific questions discussed above, we develop a flexible Bayesian framework that avoids reshaping the network predictor matrix, draws inference on brain ROIs and interconnections significantly related to creativity, and enables accurate prediction of creativity from a brain network. A novel class of network shrinkage priors for the coefficient corresponding to the network predictor is proposed to achieve these goals simultaneously. The Bayesian framework allows characterization of uncertainty in the findings. Empirical results in simulation studies illustrate substantial inferential and predictive gains of the proposed framework in comparison with the ordinary high-dimensional Bayesian shrinkage priors and penalized optimization schemes. Our framework yields new insights into the relationship of brain regions with creativity, also providing the uncertainty associated with the scientific findings. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

KEYWORDS:

• Brain connectome
• High-dimensional regression
• Influential edges
• Influential nodes
• Network predictors
• Network shrinkage prior

Supplementary Materials

Appendix A: This section shows posterior propriety of parameters in the BNSP model.

Appendix B: This section provides details of posterior computation for all the parameters.

Appendix C: This section describes the procedure for edge selection in BNSP.

Appendix D: This section presents inference on the effective dimensionality in BNSP.

Appendix E: This section presents inference on the latent positions in the BNSP model.

Additional information

Funding

Sharmistha Guha was partially supported by funds from the Trinity College of Arts & Sciences at Duke University. Abel Rodriguez was partially supported by award NSF-DMS 1738053 and 1740850.