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.

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及称为"标记"的附加信息（如位置、节点或事件类型）。本文针对图结构上的离散事件数据提出新型点过程模型，其中事件交互发生在潜在图结构框架中。本模型基于霍克斯在经典自激点过程研究中提出的影响核函数框架，以捕捉历史事件对未来事件发生的影响。核心思想是通过图神经网络表示影响核函数，在利用图神经网络强大表征能力的同时捕捉底层图结构。相较于现有直接使用神经网络建模条件强度函数的方法，本模型通过统计模型与深度模型的结合，更有效地编码重复事件的影响模式，显著提升模型估计/学习效率与预测性能。本工作显著拓展了现有深度时空点过程核方法——由于观测空间本质差异（欧几里得空间与图空间），现有方法无法适用于本研究场景。通过在合成数据与真实数据上的全面实验，验证了所提方法在预测未来事件与揭示数据间关系结构方面相较于现有最优方法的卓越性能。