Point process models are widely used for continuous-time discrete-event data, where each data point includes time and additional information called "marks," such as locations, nodes, or event types. We present a new point process model for discrete-event data over networks, built upon Hawkes' classic influence-kernel formulation to capture the effects of historical events on the occurrence of future events. The key idea is to represent the influence kernel using graph neural networks (GNNs), thereby capturing the underlying graph structure while using the strong representation power of GNNs. Compared with prior work that directly models the conditional intensity function using neural networks, our kernel representation captures repeated patterns of event influence more effectively by combining statistical and deep learning models, leading to more efficient model estimation and better predictive performance. Our work significantly extends existing deep spatio-temporal kernels for point process data, which are inapplicable to our setting because their observation spaces are Euclidean rather than graph structured. We present comprehensive experiments on synthetic and real-world data to demonstrate the superior performance of the proposed approach over state-of-the-art methods in predicting future events and uncovering graph structure from the data.

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