Analysis of Semi-Supervised Learning on Hypergraphs
Machine Learning
2025-11-25 v2 Statistics Theory
Statistics Theory
Abstract
Hypergraphs provide a natural framework for modeling higher-order interactions, yet their theoretical underpinnings in semi-supervised learning remain limited. We provide an asymptotic consistency analysis of variational learning on random geometric hypergraphs, precisely characterizing the conditions ensuring the well-posedness of hypergraph learning as well as showing convergence to a weighted -Laplacian equation. Motivated by this, we propose Higher-Order Hypergraph Learning (HOHL), which regularizes via powers of Laplacians from skeleton graphs for multiscale smoothness. HOHL converges to a higher-order Sobolev seminorm. Empirically, it performs strongly on standard baselines.
Cite
@article{arxiv.2510.25354,
title = {Analysis of Semi-Supervised Learning on Hypergraphs},
author = {Adrien Weihs and Andrea L. Bertozzi and Matthew Thorpe},
journal= {arXiv preprint arXiv:2510.25354},
year = {2025}
}