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）。本文针对图上的离散事件数据提出了一种新颖的点过程模型，其中事件交互发生在潜在图结构中。该模型基于Hawkes在原始自激励点过程工作中提出的经典影响核公式，以捕捉历史事件对未来事件发生的影响。其核心思想是通过图神经网络表示影响核，在利用GNN强大表征能力的同时捕捉底层图结构。相较于先前直接使用神经网络建模条件强度函数的研究，我们的核表示方法通过结合统计模型与深度模型，更有效地捕捉了重复事件影响模式，实现了更优的模型估计/学习效率和卓越的预测性能。本研究显著扩展了现有的深度时空点过程核方法——由于观测空间本质上是欧氏空间而非图空间的根本差异，原有方法不适用于本场景。我们在合成数据与真实数据上进行了全面实验，结果表明所提方法在预测未来事件和揭示数据间关系结构方面均优于当前最优方法。