  Point process is the dominant paradigm for modeling event sequences occurring
at irregular intervals. In this paper we aim at modeling latent dynamics of
event propagation in graph, where the event sequence propagates in a directed
weighted graph whose nodes represent event marks (e.g., event types). Most
existing works have only considered encoding sequential event history into
event representation and ignored the information from the latent graph
structure. Besides they also suffer from poor model explainability, i.e.,
failing to uncover causal influence across a wide variety of nodes. To address
these problems, we propose a Graph Regularized Point Process (GRPP) that can be
decomposed into: 1) a graph propagation model that characterizes the event
interactions across nodes with neighbors and inductively learns node
representations; 2) a temporal attentive intensity model, whose excitation and
time decay factors of past events on the current event are constructed via the
contextualization of the node embedding. Moreover, by applying a graph
regularization method, GRPP provides model interpretability by uncovering
influence strengths between nodes. Numerical experiments on various datasets
show that GRPP outperforms existing models on both the propagation time and
node prediction by notable margins.
