Deep graph kernel point processes

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. In this paper, we present 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 the classic influence kernel-based formulation by Hawkes 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 GNN. Compared with prior works that focus 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.