The modelling of temporal patterns in dynamic graphs is an important current research issue in the development of time-aware GNNs. Whether or not a specific sequence of events in a temporal graph constitutes a temporal pattern not only depends on the frequency of its occurrence. We consider whether it deviates from what is expected in a temporal graph where timestamps are randomly shuffled. While accounting for such a random baseline is important to model temporal patterns, it has mostly been ignored by current temporal graph neural networks. To address this issue we propose HYPA-DBGNN, a novel two-step approach that combines (i) the inference of anomalous sequential patterns in time series data on graphs based on a statistically principled null model, with (ii) a neural message passing approach that utilizes a higher-order De Bruijn graph whose edges capture overrepresented sequential patterns. Our method leverages hypergeometric graph ensembles to identify anomalous edges within both first- and higher-order De Bruijn graphs, which encode the temporal ordering of events. The model introduces an inductive bias that enhances model interpretability. We evaluate our approach for static node classification using benchmark datasets and a synthetic dataset that showcases its ability to incorporate the observed inductive bias regarding over- and under-represented temporal edges. We demonstrate the framework's effectiveness in detecting similar patterns within empirical datasets, resulting in superior performance compared to baseline methods in node classification tasks. To the best of our knowledge, our work is the first to introduce statistically informed GNNs that leverage temporal and causal sequence anomalies. HYPA-DBGNN represents a path for bridging the gap between statistical graph inference and neural graph representation learning, with potential applications to static GNNs.

翻译：动态图中时序模式的建模是开发时间感知图神经网络（GNNs）当前的重要研究课题。时序图中特定事件序列是否构成时序模式，不仅取决于其发生频率。我们考虑该序列是否偏离了在时间戳随机重排的时序图中所预期的结果。尽管考虑此类随机基线对建模时序模式至关重要，但当前的时序图神经网络大多忽略了这一点。为解决此问题，我们提出HYPA-DBGNN——一种新颖的两步方法，该方法结合了：（i）基于统计原理零模型的图上时序数据异常序列模式推断，与（ii）利用高阶德布鲁因图（其边捕获了过度表征的序列模式）的神经消息传递方法。我们的方法利用超几何图集合来识别一阶及高阶德布鲁因图中的异常边，这些边编码了事件的时间顺序。该模型引入了增强模型可解释性的归纳偏置。我们使用基准数据集和合成数据集评估了所提方法在静态节点分类任务中的表现，合成数据集展示了该方法整合关于过度表征与低度表征时序边的观测归纳偏置的能力。我们证明了该框架在经验数据集中检测相似模式的有效性，从而在节点分类任务中取得了优于基线方法的性能。据我们所知，本研究首次提出了利用时序与因果序列异常的统计信息增强型GNNs。HYPA-DBGNN为弥合统计图推断与神经图表征学习之间的差距开辟了道路，并具有应用于静态GNNs的潜力。