Large-scale estimation of random graph models with local dependence

We consider random graph models that combine features of two important classes of random graph models, exponential-family models and latent structure models, with the goal of retaining the strengths of both of them while reducing the weaknesses of each of them. An open problem is how to estimate such models from large networks. We facilitate large-scale estimation 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 large-scale estimation. We demonstrate the advantages of the two-step likelihood-based approach by simulations and an application to a large Amazon product recommendation network.