Latent Space Modeling of Hypergraph Data

• 成果类型: Article
• 署名作者: Turnbull, Kathryn; Lunagomez, Simon; Nemeth, Christopher; Airoldi, Edoardo
• 署名单位: Lancaster University; Instituto Tecnologico Autonomo de Mexico; Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2023.2270750
• 发表日期: 2024
• 页码: 2634-2646
• 关键词: network; inference

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 article, we present a model for hypergraph data that 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. Supplementary materials for this article are available online.