Nonparametric identification in the dynamic stochastic block model

Abstract: We show nonparametric identification of the parameters in the dynamic stochastic block model as recently introduced in Matias and Miele (2017) in 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 identification the applications in Matias and Miele (2017) 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.