Abstract

We present a novel approach for Bayesian nonlinear regression with symmetric matrix predictors, often used to represent the connectivity between different nodes. Our method results in a projection-pursuit-type estimator that effectively leverages the structure of symmetric matrices. We establish the model identifiability conditions and impose a sparsity-inducing prior on the projection directions for sparse sampling to prevent overfitting and enhance interpretability of the parameter estimates. Posterior inference is conducted through Bayesian backfitting. The performance of the proposed method is evaluated through simulation studies and a case study investigating the relationship between brain connectivity features and cognitive scores.