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.
翻译:描述目标人群之间相互作用的关系数据日益普遍,这促使人们广泛研究统计网络分析的文献,在许多应用中,互动可能涉及两个以上的人口成员,而这些数据更适宜由高光谱来代表。在本文中,我们提出了一个高光学数据模型,扩展了已确立的图表潜在空间方法的模型,并通过从计算表层中绘制模型,我们开发了一种模型,其计算成本低廉的可能性。建议采用延迟接受的MCMC计划,以获取后方样本,我们依靠Bookstein坐标来消除与潜在代表有关的可识别性问题。我们理论上审查了在我们的框架下产生的高光谱的分布程度,通过模拟,我们研究了模型的灵活性,并考虑了预测分布的估计。最后,我们探索了我们的模型对两个真实世界数据集的应用。