Estimation and inference for stochastic blockmodels

Abstract: This paper is concerned with nonparametric estimation of the weighted stochastic block model. We first show that the model implies a set of multilinear restrictions on the joint distribution of edge weights of certain subgraphs involving (in its simplest form) triplets and quadruples of nodes. From this system of equations the unknown components of the model can be recovered nonparametrically, up to the usual labeling ambiguity. We introduce a simple and computationally-attractive manner to do this. Estimators then follow from the analogy principle. Limit theory is provided. We find that component distributions and their functionals, as well as their density functions (for the case where edge weights are continuous) are all estimable at the parametric rate. Numerical experiments are reported on.