Abstract

: This talk discusses various regression frameworks with network objects and scalar variables. We first introduce a binary logistic regression framework with the network as the predictor and model the associated network coefficient using a novel class of global-local network shrinkage priors. The proposed model draws inference on the regression coefficient and network nodes influentially related to the scalar variables. Acknowledging heterogeneity in the relationship between scalar variables and network objects among subjects, we also introduce a novel nonparametric Bayesian mixture modeling framework with an undirected network response and scalar predictors. This framework clusters subjects based on the regression relationship between network objects and scalar variables, and draws inference on regression coefficients and network nodes in each cluster of subjects. Both frameworks are theoretically investigated and empirically illustrated with brain connectome datasets.