Bayesian scalar-on-network regression with applications to brain functional connectivity
arxiv(2024)
摘要
This study presents a Bayesian regression framework to model the relationship
between scalar outcomes and brain functional connectivity represented as
symmetric positive definite (SPD) matrices. Unlike many proposals that simply
vectorize the connectivity predictors thereby ignoring their matrix structures,
our method respects the Riemannian geometry of SPD matrices by modelling them
in a tangent space. We perform dimension reduction in the tangent space,
relating the resulting low-dimensional representations with the responses. The
dimension reduction matrix is learnt in a supervised manner with a
sparsity-inducing prior imposed on a Stiefel manifold to prevent overfitting.
Our method yields a parsimonious regression model that allows uncertainty
quantification of the estimates and identification of key brain regions that
predict the outcomes. We demonstrate the performance of our approach in
simulation settings and through a case study to predict Picture Vocabulary
scores using data from the Human Connectome Project.
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