Massive-scale estimation of exponential-family random graph models with local dependence

A flexible approach to modeling network data is based on exponential-family random graph models. We consider here exponential-family random graph models with additional structure in the form of local dependence, which have important conceptual and statistical advantages over models without additional structure. An open problem is how to estimate such models from large random graphs. We pave the ground for massive-scale estimation of such models by exploiting model structure for the purpose of parallel computing. The main idea is that we can first decompose random graphs into subgraphs with local dependence and then perform parallel computing on subgraphs. We hence propose a two-step likelihood-based approach. The first step estimates the local structure underlying random graphs. The second step estimates parameters given the estimated local structure of random graphs. Both steps can be implemented in parallel, which enables massive-scale estimation. We demonstrate the advantages of the two-step likelihood-based approach by simulations and an application to a large Amazon product network.