Nonparametric Identification in the Dynamic Stochastic Block Model

We show nonparametric identification of the parameters in the dynamic stochastic block model as recently introduced by Matias and Miele (2017) in the case of binary, finitely weighted, and general edge states. We formulate conditions on the true parameters, which guarantee actual point identification instead of mere generic identification, and which also lead to novel conclusions in the static case. In particular, our results justify in terms of the identification of the applications by Matias and Miele to finitely weighted edges with three edge states. We also give numerical illustrations via the variational EM algorithm in simulation settings covered by our identification analysis.