  Point process models are widely used for continuous asynchronous event data,
where each data point includes time and additional information called "marks",
which can be locations, nodes, or event types. This paper presents a novel
point process model for discrete event data over graphs, where the event
interaction occurs within a latent graph structure. Our model builds upon
Hawkes's classic influence kernel-based formulation in the original
self-exciting point processes work to capture the influence of historical
events on future events' occurrence. The key idea is to represent the influence
kernel by Graph Neural Networks (GNN) to capture the underlying graph structure
while harvesting the strong representation power of GNNs. Compared with prior
works focusing on directly modeling the conditional intensity function using
neural networks, our kernel presentation herds the repeated event influence
patterns more effectively by combining statistical and deep models, achieving
better model estimation/learning efficiency and superior predictive
performance. Our work significantly extends the existing deep spatio-temporal
kernel for point process data, which is inapplicable to our setting due to the
fundamental difference in the nature of the observation space being Euclidean
rather than a graph. We present comprehensive experiments on synthetic and
real-world data to show the superior performance of the proposed approach
against the state-of-the-art in predicting future events and uncovering the
relational structure among data.
