Nonparametric Bayes Modeling of Populations of Networks

• Activity Number: 148 - JASA Theory and Methods Invited Session
• Type: Invited
• Date/Time: Monday, July 31, 2017 : 10:30 AM to 12:20 PM
• Sponsor: JASA, Theory and Methods
• Author(s): David Dunson*
• Companies: Duke University
• Keywords: Bayesian Nonparametrics ; Brain Networks ; Latent Space ; Matrix Factorization ; Network-Valued Random Variable

Abstract

Replicated network data are increasingly available in many research fields. In connectomic applications, inter-connections among brain regions are collected for each patient under study, motivating statistical models which can exibly characterize the probabilistic generative mechanism underlying these network-valued data. We propose a exible Bayesian nonparametric approach for modeling the population distribution of network-valued data. The joint distribution of the edges is defined via a mixture model which reduces dimensionality and efficiently incorporates network information within each mixture component by leveraging latent space representations. The formulation leads to an efficient Gibbs sampler and provides simple and coherent strategies for inference and goodness-of-fit assessments. We provide theoretical results on the exibility of our model and illustrate improved performance | compared to state-of-the-art models---in simulations and application to human brain networks.