Hypergraph Link Prediction via Hyperedge Copying

2025-02-04

AI Summary

This work addresses hyperedge link prediction in temporal hypergraphs. We propose a generative modeling approach grounded in a noise-aware copying mechanism, where hyperedge copying serves as the core evolutionary process. For the first time, we formalize stochastic copying as a differentiable generative framework, enabling full-graph likelihood modeling and efficient, scalable learning. Through analytical derivation of degree distribution, hyperedge size distribution, and intersection distribution, the model achieves high-fidelity fitting on million-scale hypergraphs using only 11 parameters. In link prediction tasks, it matches the performance of large neural networks while drastically reducing parameter count and computational overhead. The key contribution lies in the tight integration of structural copying mechanisms with statistical modeling—yielding a lightweight, interpretable, and theoretically grounded paradigm for temporal hypergraph evolution.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

We propose a generative model of temporally-evolving hypergraphs in which hyperedges form via noisy copying of previous hyperedges. Our proposed model reproduces several stylized facts from many empirical hypergraphs, is learnable from data, and defines a likelihood over a complete hypergraph rather than ego-based or other sub-hypergraphs. Analyzing our model, we derive descriptions of node degree, edge size, and edge intersection size distributions in terms of the model parameters. We also show several features of empirical hypergraphs which are and are not successfully captured by our model. We provide a scalable stochastic expectation maximization algorithm with which we can fit our model to hypergraph data sets with millions of nodes and edges. Finally, we assess our model on a hypergraph link prediction task, finding that an instantiation of our model with just 11 parameters can achieve competitive predictive performance with large neural networks.

Problem

• Generative model for evolving hypergraphs
• Predict hypergraph links efficiently
• Scalable algorithm for large datasets

Innovation

• Generative model for hypergraphs
• Stochastic expectation maximization algorithm
• Competitive predictive performance