# Gaussian Processes on Hypergraphs

arXiv: https://arxiv.org/abs/2106.01982 · HTML: https://mlsanity.com/paper/2106.01982/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 59 references that are in the map.
- First posted on arXiv 3 Jun 2021.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Hypergraph Convolution and Hypergraph Attention](https://mlsanity.com/paper/1901.08150/) (2019)
- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [GPflow: A Gaussian process library using TensorFlow](https://mlsanity.com/paper/1610.08733/) (2016)
- [Networks beyond pairwise interactions: structure and dynamics](https://mlsanity.com/paper/2006.01764/) (2020)
- [Gaussian Processes for Data-Efficient Learning in Robotics and Control](https://mlsanity.com/paper/1502.02860/) (2015)
- [Hilbert Space Methods for Reduced-Rank Gaussian Process Regression](https://mlsanity.com/paper/1401.5508/) (2014)
- [Mat'ern Gaussian processes on Riemannian manifolds](https://mlsanity.com/paper/2006.10160/) (2020)
- [Control functionals for Monte Carlo integration](https://mlsanity.com/paper/1410.2392/) (2014)
- [Convergence of Sparse Variational Inference in Gaussian Processes Regression](https://mlsanity.com/paper/2008.00323/) (2020)
- [A Framework for Interdomain and Multioutput Gaussian Processes](https://mlsanity.com/paper/2003.01115/) (2020)
- [Natural Gradients in Practice: Non-Conjugate Variational Inference in Gaussian Process Models](https://mlsanity.com/paper/1803.09151/) (2018)
- [A Tutorial on Sparse Gaussian Processes and Variational Inference](https://mlsanity.com/paper/2012.13962/) (2020)
- [Gaussian Processes on Graphs via Spectral Kernel Learning](https://mlsanity.com/paper/2006.07361/) (2020)
- [Doubly Sparse Variational Gaussian Processes](https://mlsanity.com/paper/2001.05363/) (2020)
- [Hypergraph p-Laplacian: A Differential Geometry View](https://mlsanity.com/paper/1711.08171/) (2017)
- [Three hypergraph eigenvector centralities](https://mlsanity.com/paper/1807.09644/) (2018)
- [Graph Convolutional Gaussian Processes For Link Prediction](https://mlsanity.com/paper/2002.04337/) (2020)
- [Latent Space Modelling of Hypergraph Data](https://mlsanity.com/paper/1909.00472/) (2019)

## Built on by (most cited first, 4 of 4)

- [Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structures](https://mlsanity.com/paper/2407.09468/) (2024)
- [Gaussian Processes on Cellular Complexes](https://mlsanity.com/paper/2311.01198/) (2023)
- [Graph and Simplicial Complex Prediction Gaussian Process via the Hodgelet Representations](https://mlsanity.com/paper/2505.10877/) (2025)
- [Hypergraph Generation via Structured Stochastic Diffusion](https://mlsanity.com/paper/2605.05024/) (2026)

## Abstract (arXiv)

We derive a Matern Gaussian process (GP) on the vertices of a hypergraph. This enables estimation of regression models of observed or latent values associated with the vertices, in which the correlation and uncertainty estimates are informed by the hypergraph structure. We further present a framework for embedding the vertices of a hypergraph into a latent space using the hypergraph GP. Finally, we provide a scheme for identifying a small number of representative inducing vertices that enables scalable inference through sparse GPs. We demonstrate the utility of our framework on three challenging real-world problems that concern multi-class classification for the political party affiliation of legislators on the basis of voting behaviour, probabilistic matrix factorisation of movie reviews, and embedding a hypergraph of animals into a low-dimensional latent space.