# Latent Space Modelling of Hypergraph Data

arXiv: https://arxiv.org/abs/1909.00472 · HTML: https://mlsanity.com/paper/1909.00472/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Sep 2019.

## Built on by (most cited first, 6 of 6)

- [Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structures](https://mlsanity.com/paper/2407.09468/) (2024)
- [Tuning-Free Maximum Likelihood Training of Latent Variable Models via Coin Betting](https://mlsanity.com/paper/2305.14916/) (2023)
- [Gaussian Processes on Hypergraphs](https://mlsanity.com/paper/2106.01982/) (2021)
- [Tools Are Not Islands: Set-Level Tool Retrieval for LLM Agents via Query-Conditioned Hyperedge Prediction](https://mlsanity.com/paper/2607.25718/) (2026)
- [Higher-Order Relations Skew Link Prediction in Graphs](https://mlsanity.com/paper/2111.00271/) (2021)
- [Hypergraph Generation via Structured Stochastic Diffusion](https://mlsanity.com/paper/2605.05024/) (2026)

## Abstract (arXiv)

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.