Empirical Bayes Estimation for the Stochastic Blockmodel
This provides a practical estimation method for network analysis in fields like social networks and connectomics, but it is incremental as it builds on existing spectral embedding theory.
The paper tackles the problem of estimating block memberships in stochastic blockmodels for network data by developing an empirical Bayes methodology, demonstrating its utility through simulations and a Wikipedia dataset.
Inference for the stochastic blockmodel is currently of burgeoning interest in the statistical community, as well as in various application domains as diverse as social networks, citation networks, brain connectivity networks (connectomics), etc. Recent theoretical developments have shown that spectral embedding of graphs yields tractable distributional results; in particular, a random dot product latent position graph formulation of the stochastic blockmodel informs a mixture of normal distributions for the adjacency spectral embedding. We employ this new theory to provide an empirical Bayes methodology for estimation of block memberships of vertices in a random graph drawn from the stochastic blockmodel, and demonstrate its practical utility. The posterior inference is conducted using a Metropolis-within-Gibbs algorithm. The theory and methods are illustrated through Monte Carlo simulation studies, both within the stochastic blockmodel and beyond, and experimental results on a Wikipedia data set are presented.