Hypergraph Representation Learning with Hyperlink Random Effects

2026-10-03

AI Summary

This study addresses the limitations of existing hypergraph methods that overlook low-rank structures and struggle with non-uniform hyperedges and heterogeneous interaction mechanisms. We propose a general framework integrating hyperedge random effects with low-rank structure. By transcending tensor decomposition constraints, this approach accommodates non-uniform hyperedges and characterizes heterogeneous generative mechanisms through categorical, Gaussian mixture, and score-based random effect models, while establishing parameter identifiability and theoretical guarantees. Simulation and empirical studies demonstrate that the proposed framework effectively recovers latent structures and accurately captures heterogeneous interaction patterns, significantly enhancing both the theoretical completeness and practical utility of hypergraph modeling.

Abstract

Hypergraphs record multi-way interactions among entities. Extracting information from the combinatorial structure underlying observed multi-way interactions is a central task in many real-world problems. Existing methods face several limitations. First, many deep architectures for hypergraphs do not explicitly exploit the potential low-rank structure, which can sacrifice parsimony and interpretability in the learned representations. Second, many low-rank-based methods operate on tensor representations, which typically require hyperlinks to have uniform sizes and thus limit their applicability to general hypergraphs with non-uniform hyperlink sizes. Third, many methods ignore the fact that hyperlinks often arise from heterogeneous mechanisms. For example, medical symptoms may co-occur in the profiles of patients with very different conditions, and such heterogeneity should be incorporated into the learning process. In this work, we develop a general framework for hypergraph representation learning using hyperlink random effects while exploiting the low-rank structure in hypergraphs. The proposed framework accommodates latent heterogeneity in hyperlink formation while preserving entity interaction patterns. We establish identifiability of the model parameters and theoretical guarantees of representation-level recovery under this framework. The framework allows flexible specifications for the hyperlink random effects; in this paper, we study three choices: categorical, Gaussian mixture, and score-based effects, and develop corresponding estimation algorithms. Through simulation studies, we demonstrate the effectiveness of the proposed method in recovering latent structure and capturing heterogeneous interaction patterns. Empirical studies on real-world hypergraph datasets further illustrate the practical utility of our approach.

Problem

• Hypergraph Representation Learning
• Low-rank Structure
• Non-uniform Hyperlinks
• Heterogeneous Mechanisms
• Multi-way Interactions

Innovation

• Hypergraph Representation Learning
• Hyperlink Random Effects
• Low-rank Structure
• Latent Heterogeneity
• Identifiability