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.

翻译：点过程模型广泛应用于连续异步事件数据，其中每个数据点包含时间信息以及称为"标记"的附加信息（如位置、节点或事件类型）。针对图结构上的离散事件数据，本文提出一种新型点过程模型，其事件交互发生在潜在图结构内部。该模型基于霍克斯经典自激发点过程中基于影响核的原始公式，旨在捕捉历史事件对未来事件发生的驱动作用。核心思想在于：利用图神经网络（GNN）表征影响核，在保留GNN强大表征能力的同时捕捉底层图结构。相较于聚焦于使用神经网络直接建模条件强度函数的现有研究，本方法通过融合统计模型与深度模型，更高效地归纳重复事件的影响模式，从而在模型估计/学习效率与预测性能上实现显著提升。本文研究大幅拓展了现有适用于点过程数据的深度时空核方法——由于观测空间本质为欧几里得空间而非图结构，原方法无法直接应用于本文场景。我们在合成数据与真实数据上开展全面实验，验证了所提方法在事件预测精度与数据关联结构挖掘方面相对于现有最优方法的优越性。