# A Markov Random Field model for Hypergraph-based Machine Learning

arXiv: https://arxiv.org/abs/2308.14172 · HTML: https://mlsanity.com/paper/2308.14172/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 51 references that are in the map.
- First posted on arXiv 27 Aug 2023.

## Builds on (most cited first, 29 of 29)

- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Inductive Biases for Deep Learning of Higher-Level Cognition](https://mlsanity.com/paper/2011.15091/) (2020)
- [Hypergraph Convolution and Hypergraph Attention](https://mlsanity.com/paper/1901.08150/) (2019)
- [Cross-Entropy Loss Functions: Theoretical Analysis and Applications](https://mlsanity.com/paper/2304.07288/) (2023)
- [Adversarial Attack and Defense on Graph Data: A Survey](https://mlsanity.com/paper/1812.10528/) (2018)
- [Graph-less Neural Networks: Teaching Old MLPs New Tricks via Distillation](https://mlsanity.com/paper/2110.08727/) (2021)
- [How to learn a graph from smooth signals](https://mlsanity.com/paper/1601.02513/) (2016)
- [Contextual Stochastic Block Models](https://mlsanity.com/paper/1807.09596/) (2018)
- [UniGNN: a Unified Framework for Graph and Hypergraph Neural Networks](https://mlsanity.com/paper/2105.00956/) (2021)
- [GroupNet: Multiscale Hypergraph Neural Networks for Trajectory Prediction with Relational Reasoning](https://mlsanity.com/paper/2204.08770/) (2022)
- [You are AllSet: A Multiset Function Framework for Hypergraph Neural Networks](https://mlsanity.com/paper/2106.13264/) (2021)
- [Graph-MLP: Node Classification without Message Passing in Graph](https://mlsanity.com/paper/2106.04051/) (2021)
- [What are higher-order networks?](https://mlsanity.com/paper/2104.11329/) (2021)
- [Modeling the Data-Generating Process is Necessary for Out-of-Distribution Generalization](https://mlsanity.com/paper/2206.07837/) (2022)
- [Structural Patterns and Generative Models of Real-world Hypergraphs](https://mlsanity.com/paper/2006.07060/) (2020)
- [Dynamic-Group-Aware Networks for Multi-Agent Trajectory Prediction with Relational Reasoning](https://mlsanity.com/paper/2206.13114/) (2022)
- [Large Scale Graph Learning from Smooth Signals](https://mlsanity.com/paper/1710.05654/) (2017)
- [Learning to Learn Graph Topologies](https://mlsanity.com/paper/2110.09807/) (2021)
- [Learning Sparse Graphs Under Smoothness Prior](https://mlsanity.com/paper/1609.03448/) (2016)
- [Improving Inductive Link Prediction Using Hyper-Relational Facts](https://mlsanity.com/paper/2107.04894/) (2021)
- [Understanding Non-linearity in Graph Neural Networks from the Bayesian-Inference Perspective](https://mlsanity.com/paper/2207.11311/) (2022)
- [Hypergraph reconstruction from network data](https://mlsanity.com/paper/2008.04948/) (2020)
- [A Unifying Generative Model for Graph Learning Algorithms: Label Propagation, Graph Convolutions, and Combinations](https://mlsanity.com/paper/2101.07730/) (2021)
- [Set2Graph: Learning Graphs From Sets](https://mlsanity.com/paper/2002.08772/) (2020)
- [Kernel-based Graph Learning from Smooth Signals: A Functional Viewpoint](https://mlsanity.com/paper/2008.10065/) (2020)
- [Learning Hypergraphs From Signals With Dual Smoothness Prior](https://mlsanity.com/paper/2211.01717/) (2022)
- [HyperAttack: Multi-Gradient-Guided White-box Adversarial Structure Attack of Hypergraph Neural Networks](https://mlsanity.com/paper/2302.12407/) (2023)
- [Pruning Edges and Gradients to Learn Hypergraphs from Larger Sets](https://mlsanity.com/paper/2106.13919/) (2021)

## Built on by (most cited first, 5 of 5)

- [Position: Topological Deep Learning is the New Frontier for Relational Learning](https://mlsanity.com/paper/2402.08871/) (2024)
- [Hypergraph Transformer for Semi-Supervised Classification](https://mlsanity.com/paper/2312.11385/) (2023)
- [Training-Free Message Passing for Learning on Hypergraphs](https://mlsanity.com/paper/2402.05569/) (2024)
- [Hypergraph-MLP: Learning on Hypergraphs without Message Passing](https://mlsanity.com/paper/2312.09778/) (2023)
- [From topology learning to graph generation: A unifying perspective](https://mlsanity.com/paper/2609.02286/) (2026)

## Abstract (arXiv)

Understanding the data-generating process is essential for building machine learning models that generalise well while ensuring robustness and interpretability. This paper addresses the fundamental challenge of modelling the data generation processes on hypergraphs and explores how such models can inform the design of machine learning algorithms for hypergraph data. The key to our approach is the development of a hypergraph Markov random field that models the joint distribution of the node features and hyperedge features in a hypergraph through a multivariate Gaussian distribution whose covariance matrix is uniquely determined by the hypergraph structure. The proposed data-generating process provides a valuable inductive bias for various hypergraph machine learning tasks, thus enhancing the algorithm design. In this paper, we focus on two representative downstream tasks: structure inference and node classification. Accordingly, we introduce two novel frameworks: 1) an original hypergraph structure inference framework named HGSI, and 2) a novel learning framework entitled Hypergraph-MLP for node classification on hypergraphs. Empirical evaluation of the proposed frameworks demonstrates that: 1) HGSI outperforms existing hypergraph structure inference methods on both synthetic and real-world data; and 2) Hypergraph-MLP outperforms baselines in six hypergraph node classification benchmarks, at the same time promoting runtime efficiency and robustness against structural perturbations during inference.