Modeling the dynamics of interacting entities using an evolving graph is an
essential problem in fields such as financial networks and e-commerce.
Traditional approaches focus primarily on pairwise interactions, limiting their
ability to capture the complexity of real-world interactions involving multiple
entities and their intricate relationship structures. This work addresses the
problem of forecasting higher-order interaction events in multi-relational
recursive hypergraphs. This is done using a dynamic graph representation
learning framework 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 event's occurrence. 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 use noise contrastive estimation 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.

使用动态图表示学习框架预测多关系递归超图中的高阶交互事件，通过学习动态节点表示和超边链接预测的编码器和解码器来捕捉涉及多个实体的复杂关系，从而优于以前的交互预测方法。

多关系递归超图中的交互事件预测：一种时间点过程方法

Interaction Event Forecasting in Multi-Relational Recursive HyperGraphs:  A Temporal Point Process Approach

Real-world systems are made of interacting entities that evolve with time.
Creating models that can forecast interactions by learning the dynamics of
entities is an important problem in numerous fields. Earlier works used dynamic
graph models to achieve this. However, real-world interactions are more complex
than pairwise, as they involve more than two entities, and many of these
higher-order interactions have directional components. Examples of these can be
seen in communication networks such as email exchanges that involve a sender,
and multiple recipients, citation networks, where authors draw upon the work of
others, and so on. In this paper, we solve the problem of higher-order directed
interaction forecasting by proposing a deep neural network-based model
\textit{Directed HyperNode Temporal Point Process} for directed hyperedge event
forecasting, as hyperedge provides native framework for modeling relationships
among the variable number of nodes. Our proposed technique reduces the search
space of possible candidate hyperedges by first forecasting the nodes at which
events will be observed, based on which it generates candidate hyperedges. To
demonstrate the efficiency of our model, we curated four datasets and conducted
an extensive empirical study. We believe that this is the first work that
solves the problem of forecasting higher-order directional interactions.

本论文提出了一种基于深度神经网络的模型，名为 “有向超节点时间点过程 (Directed HyperNode Temporal Point Process)”，用于预测高阶有向交互作用，具有很高的效率并经过了大量实证研究。