Abstract: The mixed membership stochastic blockmodel (MMSB) is a popular Bayesian network model for community detection. Fitting such large Bayesian network models quickly becomes computationally infeasible when the number of nodes grows into hundreds of thousands and millions. In this paper we propose a novel mini-batch strategy based on aggregated relational data that leverages nodal information to fit MMSB to massive networks. We describe a scalable inference method that can utilise nodal information that often accompanies real-world networks. Conditioning on this extra information leads to a model that admits a parallel stochastic variational inference algorithm, utilising stochastic gradients of bipartite graphs formed from aggregated network ties between node subpopulations. We apply our method to a citation network with over two million nodes and 25 million edges, capturing explainable structure in this network. Our method recovers parameters and achieves better convergence on simulated networks generated according to the MMSB.

Key words and phrases: Aggregated relational data, community detection, mixed-membership, network data.