Edge correlations and link prediction in growing hypergraphs.

Area of Science:

• Network Science
• Complex Systems
• Data Science

Background:

• Empirical hypergraphs exhibit complex structures and temporal dynamics.
• Existing models often struggle to capture these emergent properties and temporal evolution.
• Understanding hypergraph formation is crucial for various fields, including social networks and biology.

Purpose of the Study:

• To propose a generative, mechanistic model for temporally evolving hypergraphs.
• To analyze the model's ability to reproduce empirical hypergraph characteristics.
• To develop a scalable algorithm for fitting the model to large datasets and assess its predictive power.

Main Methods:

• Developed a generative model based on noisy copying of hyperedges over time.
• Derived analytical descriptions of node degree, edge size, and intersection size distributions.
• Implemented a scalable stochastic expectation-maximization algorithm for model fitting.
• Evaluated the model on a hypergraph link prediction task.

Main Results:

• The model successfully reproduces several stylized facts observed in empirical hypergraphs.
• Analytical derivations provide insights into the model's parameter-dependent distributions.
• The stochastic expectation-maximization algorithm efficiently fits the model to large-scale hypergraph data.
• A simplified instantiation of the model achieved competitive performance in link prediction against complex neural networks.

Conclusions:

• The proposed generative model offers a parsimonious yet powerful framework for understanding temporally evolving hypergraphs.
• The model's ability to capture empirical features and its predictive performance highlight its utility.
• This work provides a scalable and effective approach for analyzing and predicting behavior in complex hypergraph systems.