标题： 超图数据的潜在空间建模 显示英文标题

标题： Latent Space Modelling of Hypergraph Data

摘要： 目标群体交互关系数据的日益普及激发了关于统计网络分析的大量文献。 在许多应用中，交互可能涉及群体中的两个以上成员，这种数据更适合用超图来表示。 本文提出了一种用于超图数据的模型，该模型扩展了图的已建立的潜在空间方法，并通过与计算拓扑学中的结构建立联系，我们开发出一种似然计算成本低廉的模型。 提出了一个延迟接受的MCMC方案以获取后验样本，并依赖Bookstein坐标解决潜在表示相关的可识别性问题。 我们从理论上研究了在本框架下生成的超图的度分布，并通过模拟探讨了模型的灵活性以及预测分布的估计。 最后，我们探索了将模型应用于两个真实世界数据集的可能性。 显示英文摘要

摘要： The increasing prevalence of relational data describing interactions among a target population has motivated a wide literature on statistical network analysis. In many applications, interactions may involve more than two members of the population and this data is more appropriately represented by a hypergraph. In this paper, we present a model for hypergraph data which extends the well established latent space approach for graphs and, by drawing a connection to constructs from computational topology, we develop a model whose likelihood is inexpensive to compute. A delayed-acceptance MCMC scheme is proposed to obtain posterior samples and we rely on Bookstein coordinates to remove the identifiability issues associated with the latent representation. We theoretically examine the degree distribution of hypergraphs generated under our framework and, through simulation, we investigate the flexibility of our model and consider estimation of predictive distributions. Finally, we explore the application of our model to two real-world datasets.