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