  We propose a novel class of network models for temporal dyadic interaction
data. Our goal is to capture a number of important features often observed in
social interactions: sparsity, degree heterogeneity, community structure and
reciprocity. We propose a family of models based on self-exciting Hawkes point
processes in which events depend on the history of the process. The key
component is the conditional intensity function of the Hawkes Process, which
captures the fact that interactions may arise as a response to past
interactions (reciprocity), or due to shared interests between individuals
(community structure). In order to capture the sparsity and degree
heterogeneity, the base (non time dependent) part of the intensity function
builds on compound random measures following Todeschini et al. (2016). We
conduct experiments on a variety of real-world temporal interaction data and
show that the proposed model outperforms many competing approaches for link
prediction, and leads to interpretable parameters.
