In this work, we study the event occurrences of individuals interacting in a
network. To characterize the dynamic interactions among the individuals, we
propose a group network Hawkes process (GNHP) model whose network structure is
observed and fixed. In particular, we introduce a latent group structure among
individuals to account for the heterogeneous user-specific characteristics. A
maximum likelihood approach is proposed to simultaneously cluster individuals
in the network and estimate model parameters. A fast EM algorithm is
subsequently developed by utilizing the branching representation of the
proposed GNHP model. Theoretical properties of the resulting estimators of
group memberships and model parameters are investigated under both settings
when the number of latent groups G is over-specified or correctly specified.
A data-driven criterion that can consistently identify the true G under mild
conditions is derived. Extensive simulation studies and an application to a
data set collected from Sina Weibo are used to illustrate the effectiveness of
the proposed methodology.Comment: 35 page
