Finite Mixtures of ERGMs for Modeling Ensembles of Networks

• Activity Number: 56 - Bayesian Analysis of Functional and Structured Data
• Type: Contributed
• Date/Time: Monday, August 3, 2020 : 10:00 AM to 2:00 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Fan Yin* and Carter Tribley Butts and Weining Shen
• Companies: University of California, Irvine and University of California, Irvine and University of California, Irvine
• Keywords: Mixture model; Exponential-family random graph models (ERGMs); MCMC; Deviance information criterion (DIC); Political co-voting networks

Abstract

Ensembles of networks arise in many scientific fields, but there are few statistical tools for inferring their generative processes, particularly in the presence of both dyadic dependence and cross-graph heterogeneity. To fill in this gap, we propose characterizing network ensembles via finite mixtures of exponential family random graph models, a framework for parametric modeling of graphs that has been successful in modeling the complex stochastic processes that govern the structure of edges in a network. Our proposed modeling framework can also be used for applications such as model-based clustering of ensembles of networks and density estimation for complex graph distributions. We develop a Metropolis-within-Gibbs algorithm to conduct fully Bayesian inference and adapt a version of deviance information criterion for missing data models to choose the number of latent heterogeneous generative mechanisms. Simulation studies show that the proposed procedure can recover the true number of latent heterogeneous generative processes and corresponding parameters. We demonstrate the utility of the proposed approach using an ensemble of political co-voting networks among US Senators.