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Bayesian Nonparametric Mixtures of Exponential Random Graph Models for Ensembles of Networks

Ensembles of networks arise in various fields where multiple independent networks are observed on the same set of nodes, for example, a collection of brain networks constructed on the same brain regions for different individuals. However, there are few models that describe both the variations and characteristics of networks in an ensemble at the same time. In this paper, we propose to model the ensemble of networks using a Dirichlet Process Mixture of Exponential Random Graph Models (DPM-ERGMs), which divides the ensemble into different clusters and models each cluster of networks using a separate Exponential Random Graph Model (ERGM). By employing a Dirichlet process mixture, the number of clusters can be determined automatically and changed adaptively with the data provided. Moreover, in order to perform full Bayesian inference for DPM-ERGMs, we employ the intermediate importance sampling technique inside the Metropolis-within-slice sampling scheme, which addressed the problem of sampling from the intractable ERGMs on an infinite sample space. We also demonstrate the performance of DPM-ERGMs with both simulated and real datasets.