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The exponential family random graph modeling (ERGM) framework provides aflexible approach for the statistical analysis of networks. As ERGMs typicallyinvolve normalizing factors that are costly to compute, practical inferencerelies on a variety of approximations or other workarounds. Markov Chain MonteCarlo maximum likelihood (MCMC MLE) provides a powerful tool to approximate theMLE of ERGM parameters, and is feasible for typical models on single networkswith as many as a few thousand nodes. MCMC-based algorithms for Bayesiananalysis are more expensive, and high-quality answers are challenging to obtainon large graphs. For both strategies, extension to the pooled case - in whichwe observe multiple networks from a common generative process - adds furthercomputational cost, with both time and memory scaling linearly in the number ofgraphs. This becomes prohibitive for large networks, or where large numbers ofgraph observations are available. Here, we exploit some basic properties of thediscrete exponential families to develop an approach for ERGM inference in thepooled case that (where applicable) allows an arbitrarily large number of graphobservations to be fit at no additional computational cost beyond preprocessingthe data itself. Moreover, a variant of our approach can also be used toperform Bayesian inference under conjugate priors, again with no additionalcomputational cost in the estimation phase. As we show, the conjugate prior iseasily specified, and is well-suited to applications such as regularization.Simulation studies show that the pooled method leads to estimates with goodfrequentist properties, and posterior estimates under the conjugate prior arewell-behaved. We demonstrate our approach with applications to pooled analysisof brain functional connectivity networks and to replicated x-ray crystalstructures of hen egg-white lysozyme.

Highly Scalable Maximum Likelihood and Conjugate Bayesian Inference for ERGMs on Graph Sets with Equivalent Vertices