Hypergraph learning captures diverse multiway interactions effectively
Hypergraph Representation Learning with Hyperlink Random Effects
Machine Learning
Summary
Many complex systems involve connections among groups of things, not just pairs. This study developed a way to better understand these group connections by considering that different groups form in diverse ways and sizes. The authors designed a model that can find simpler patterns and handle different kinds of groups simultaneously. They proved their method works in theory and tested it on both simulations and real-world data. This approach helps reveal hidden structures in complicated networks with many-to-many relationships.
What this means in practice
- •For health data scientists: Identify heterogeneous patterns in patient symptom co-occurrences to improve disease understanding beyond uniform assumptions.
- •For social network analysts: Analyze varied group interactions among users with non-uniform membership sizes and mixed latent causes for link formation.
Authors
Zimeng Li, Shihao Wu, Gongjun Xu, Ji Zhu
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.