UCSC-SOE-21-03: Bayesian Supervised Clustering of Undirected Networks with Cluster Speci fic Inference on Signi ficant Nodes and Edges

S. Guha and R. Guhaniyogi
05/12/2021 01:35 PM
Motivated by the connectome datasets acquired from various imaging modalities, this article focuses on model based clustering of subjects according to the shared relationship of subject-speci fic networks and covariates. Additionally, it is of interest to identify network nodes signifi cantly associated with each covariate in each cluster of subjects. To address these methodological questions, we propose a novel nonparametric Bayesian mixture modeling framework with an undirected network response and scalar predictors. The symmetric matrix coeffecients corresponding to the scalar predictors of interest in each mixture component are embedded with low-rankness and group
sparsity within the low-rank structure. While the low-rank structure on the network coeffecients adds parsimony and computational efficiency, the group sparsity within the low-rank structure enables drawing inference on network nodes and cells signifi cantly associated with each scalar predictor. Being a principled Bayesian framework allows precise characterization of uncertainty in identifying signifi cant network nodes in each cluster. Theoretically, we establish convergence of the posterior predictive density from the proposed model to the true data generating density at a rate very close to the finite dimensional optimal rate. Empirical results in various simulation scenarios
illustrate substantial inferential gains of the proposed framework in comparison with competitors. Analysis of a brain connectome data with the proposed model reveals interesting insights into the brain regions of interest (ROIs) signifi cantly related to creative achievement in each cluster of subjects.