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Title: Latent space representations of hypergraphs Authors:  Simon Lunagomez - Lancaster University (United Kingdom) [presenting]
Christopher Nemeth - Lancaster University (United Kingdom)
Edoardo Airoldi - Harvard University (United States)
Kathryn Turnbull - Lancaster University (United Kingdom)
Abstract: 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. We present a model for hypergraph data which extends a previous latent space distance model and, by drawing a connection to constructs from computational topology, we develop a model whose likelihood is inexpensive to compute. We obtain posterior samples via an MCMC scheme and we rely on Bookstein coordinates to remove the identifiability issues associated with the latent representation. We demonstrate that the latent space construction imposes desirable properties on the hypergraphs generated in our framework and provides a convenient visualisation of the data. Furthermore, through simulation, we investigate the flexibility of our model and consider estimating predictive distributions. Finally, we explore the application of our model to a real world co-occurrence dataset.