Statistical Inference for Subgraph Frequencies of Exchangeable Hyperedge Models

TL;DR

This paper develops new statistical inference methods for subgraph frequencies in exchangeable hyperedge models, addressing limitations of traditional binary adjacency matrix models, with applications to real-world hypergraph data.

Contribution

Introduces novel subgraph statistics and inferential tools for hypergraphs that account for edge multiplicity and node deletion robustness, advancing network analysis methods.

Findings

Methods outperform traditional binary adjacency matrix approaches in simulations

Subgraph statistics show robustness to low-degree node deletion

Empirical analysis on collaboration hypergraphs demonstrates practical effectiveness

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.