Understanding relations arising out of interactions among entities can be very difficult, and predicting them is even more challenging. This problem has many applications in various fields, such as financial networks and e-commerce. These relations can involve much more complexities than just involving more than two entities. One such scenario is evolving recursive relations between multiple entities, and so far, this is still an open problem. This work addresses the problem of forecasting higher-order interaction events that can be multi-relational and recursive. We pose the problem in the framework of representation learning of temporal hypergraphs that can capture complex relationships involving multiple entities. The proposed model, \textit{Relational Recursive Hyperedge Temporal Point Process} (RRHyperTPP) uses an encoder that learns a dynamic node representation based on the historical interaction patterns and then a hyperedge link prediction-based decoder to model the occurrence of interaction events. These learned representations are then used for downstream tasks involving forecasting the type and time of interactions. The main challenge in learning from hyperedge events is that the number of possible hyperedges grows exponentially with the number of nodes in the network. This will make the computation of negative log-likelihood of the temporal point process expensive, as the calculation of survival function requires a summation over all possible hyperedges. In our work, we develop a noise contrastive estimation method to learn the parameters of our model, and we have experimentally shown that our models perform better than previous state-of-the-art methods for interaction forecasting.

翻译：理解实体间相互作用所产生的关系可能极为困难，而预测这些关系则更具挑战性。该问题在金融网络和电子商务等多个领域具有广泛的应用前景。这些关系所涉及的复杂性远不止于两个以上实体。其中一种典型场景是多个实体间不断演化的递归关系，迄今为止这仍是一个开放性问题。本研究致力于预测可能具有多关系性和递归性的高阶交互事件。我们将该问题置于时序超图的表示学习框架中，该框架能够捕捉涉及多个实体的复杂关系。所提出的模型——关系递归超边时序点过程（RRHyperTPP）采用基于历史交互模式学习动态节点表示的编码器，以及基于超边链接预测的解码器来建模交互事件的发生。这些学习到的表示随后被用于涉及预测交互类型和时间的下游任务。从超边事件中学习的主要挑战在于：可能的超边数量随网络节点数呈指数级增长。这将导致时序点过程的负对数似然计算成本高昂，因为生存函数的计算需要对所有可能的超边进行求和。在本研究中，我们开发了一种噪声对比估计方法来学习模型参数，并通过实验证明我们的模型在交互预测任务上优于以往最先进的方法。