Incorporating Actor Heterogeneity into Large Network Models through Variational Approximations

The analysis of network data has gained considerable interest in the recent years. This also includes the analysis of large, high dimensional networks with hundreds and thousands of nodes. While Exponential Random Graph Models (ERGMs) serve as workhorse for network data analyses, their applicability to very large networks is problematic via classical inference such as maximum likelihood or fully Bayesian estimation due to scaling and instability issues. The latter trace from the fact, that classical network statistics consider nodes as exchangeable, i.e. actors in the network are assumed to be homogeneous. This is often questionable and one way to circumvent the restrictive assumption is to include actor specific random effects which account for unobservable heterogeneity. This in turn however increases the number of unknowns considerably making the model highly-parameterized. As a solution even for very large networks we propose a scalable approach based on variational approximations, which not only leads to numerically stable estimation but is also applicable to high-dimensional directed as well as undirected networks. We furthermore show that including node specific covariates can reduce node heterogeneity which we facilitate through versatile prior formulations. We demonstrate the procedure in two complex examples, namely Facebook data and data from an international arms trading network.