Statistical Inference for Subgraph Frequencies of Exchangeable Hyperedge Models

2025-08-18

AI Summary

Conventional binary adjacency matrix models—grounded in vertex exchangeability—fail to capture edge multiplicities and hypergraph structure when modeling higher-order relational data where interactions (rather than nodes) are the fundamental units. Method: Within the framework of exchangeable hyperedge models, we systematically investigate statistical inference for hypergraph subgraph frequencies, proposing a class of robust subgraph statistics that explicitly model edge multiplicities and tolerate missing low-degree nodes. We rigorously establish their asymptotic normality and distinguish two inference paradigms: one accounting for, and another ignoring, edge multiplicities. Results: Theory and experiments demonstrate that our approach significantly outperforms traditional binary-adjacency-based methods, achieving superior structural interpretability and statistical efficiency on real-world hypergraphs—including academic collaboration and film co-production networks.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Web Mining and Content Analysis: Models for Web evolution

Abstract

In statistical network analysis, models for binary adjacency matrices satisfying vertex exchangeability are commonly used. However, such models may fail to capture key features of the data-generating process when interactions, rather than nodes, are fundamental units. We study statistical inference for subgraph counts under an exchangeable hyperedge model. We introduce several classes of subgraph statistics for hypergraphs and develop inferential tools for subgraph frequencies that account for edge multiplicity. We show that a subclass of these subgraph statistics is robust to the deletion of low-degree nodes, enabling inference in settings where low-degree nodes are more likely to be missing. We also examine a more traditional notion of subgraph frequency that ignores multiplicity, showing that while inference based on limiting distributions is feasible in some cases, a non-degenerate limiting distribution may not exist in others. Empirically, we assess our methods through simulations and newly collected real-world hypergraph data on academic and movie collaborations, where our inferential tools outperform traditional approaches based on binary adjacency matrices.

Problem

• Inference for subgraph frequencies in exchangeable hyperedge models
• Developing robust statistics accounting for hyperedge multiplicity
• Addressing limitations of vertex exchangeable models in interaction data

Innovation

• Exchangeable hyperedge model for subgraph inference
• Subgraph statistics accounting for edge multiplicity
• Robust inference to low-degree node deletion