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To model recurrent interaction events in continuous time, an extension of thestochastic block model is proposed where every individual belongs to a latentgroup and interactions between two individuals follow a conditionalinhomogeneous Poisson process with intensity driven by the individuals' latentgroups. The model is shown to be identifiable and its estimation is based on asemiparametric variational expectation-maximization algorithm. Two versions ofthe method are developed, using either a nonparametric histogram approach (withan adaptive choice of the partition size) or kernel intensity estimators. Thenumber of latent groups can be selected by an integrated classificationlikelihood criterion. Finally, we demonstrate the performance of our procedureon synthetic experiments, analyse two datasets to illustrate the utility of ourapproach and comment on competing methods.

A semiparametric extension of the stochastic block model for longitudinal networks