ReLaSH: Reconstructing Joint Latent Spaces for Efficient Generation of Synthetic Hypergraphs with Hyperlink Attributes

Hypergraph network data, which capture multi-way interactions among entities, have become increasingly prevalent in the big data era, spanning fields such as social science, medical research, and biology. Generating synthetic hyperlinks with attributes from an observed hypergraph has broad applications in data augmentation, simulation, and advancing the understanding of real-world complex systems. This task, however, poses unique challenges due to special properties of hypergraphs, including discreteness, hyperlink sparsity, and the mixed data types of hyperlinks and their attributes, rendering many existing generative models unsuitable. In this paper, we introduce ReLaSH (REconstructing joint LAtent Spaces for Hypergraphs with attributes), a general generative framework for producing realistic synthetic hypergraph data with hyperlink attributes via training a likelihoodbased joint embedding model and reconstructing the joint latent space. Given a hypergraph dataset, ReLaSH first embeds the hyperlinks and their attributes into a joint latent space by training a likelihood-based model, and then reconstructs this joint latent space using a distribution-free generator. The generation task is completed by first sampling embeddings from the distribution-free generator and then decoding them into hyperlinks and attributes through the trained likelihoodbased model. Compared with existing generative models, ReLaSH explicitly accounts for the unique structure of hypergraphs and jointly models hyperlinks and their attributes. Moreover, the likelihood-based embedding model provides efficiency and interpretability relative to deep black-box architectures, while the distribution-free generator in the joint latent space ensures flexibility. We theoretically demonstrate the consistency and generalizability of ReLaSH. Empirical results on a range of real-world datasets from diverse domains demonstrate the strong performance of ReLaSH, underscoring its broad utility and effectiveness in practical applications.