Abstract

Collections of networks are available in many research fields. In connectomic applications, inter-connections among brain regions are collected from each patient, with interest focusing on studying shared structure and the population distribution of deviations across individuals. Current methods focus on reducing network data to features prior to statistical analysis, while we propose a fully generative Bayesian nonparametric approach for modeling the population distribution of network-valued data. The joint distribution of the edges follows a multivariate Bernoulli distribution, with transformed edge probability vectors expressed as the sum of a shared similarity vector and a class-specific deviation modeled via flexible low-rank factorization exploiting the network structure. The formulation is provably flexible, leads to a simple and computationally efficient Gibbs sampler, and provides a framework for clustering graph-valued data, while inferring a cluster-specific rank. We discuss theoretical properties and illustrate the performance in simulations and application to human brain network data.