[Paper Review] REM beyond dyads: relational hyperevent models for multi-actor interaction networks

Jürgen Lerner, Mark Tranmer+2 more|arXiv (Cornell University)|Dec 16, 2019

Complex Network Analysis Techniques20 references4 citations

TL;DR

This paper introduces Relational Hyperevent Models (RHEM), a generalization of relational event models to multi-actor interactions on hyperedges, enabling the modeling of time-varying event rates for any number of actors. By applying case-control sampling to overcome computational intractability, RHEM successfully estimates parameters in large networks with hundreds of thousands of nodes and hyperevents, revealing higher-order dependencies beyond dyadic interactions.

ABSTRACT

We introduce relational hyperevent models (RHEM) as a generalization of relational event models to events occurring on hyperedges involving any number of actors. RHEM can specify time-varying event rates for the full space of directed or undirected hyperedges and can be applied to model, among others, meetings, team assembly, team performance, or multi-actor communication. We illustrate the newly proposed model on two empirical hyperevent networks about meetings of government ministers and co-authoring of scientific papers.

Motivation & Objective

• To develop a general framework for modeling multi-actor interaction events that extends beyond dyadic relationships in relational event models.
• To address the computational infeasibility of full likelihood evaluation in large hypergraph networks by applying sampling techniques.
• To propose hyperedge statistics that capture higher-order network structures and shape event rate dynamics.
• To distinguish between models that condition on hyperedge size and those that control for it, improving model validity in sparse networks.
• To introduce relational outcome models (ROM) to analyze the success or impact of hyperevents, such as team performance in co-authoring.

Proposed method

• RHEM generalizes relational event models (REM) to hyperedges, allowing event rates to be specified over all possible directed or undirected hyperedges involving any number of actors.
• The model uses a log-linear formulation for event rate intensity, parameterized by hyperedge statistics that reflect network structure and history.
• To manage computational complexity, the paper applies case-control sampling, comparing observed hyperevents ('cases') with plausible non-events ('controls') from the risk set.
• The risk set is defined as all hyperedges of a given size that could have experienced an event but did not, with size conditioning used to improve model plausibility.
• Separate models are proposed for new events and repeated events to handle extreme inhomogeneity in the risk set and avoid masking of meaningful effects.
• Relational outcome models (ROM) are introduced to explain outcomes such as team performance, extending RHEM beyond event occurrence to event impact.

Experimental results

Research questions

• RQ1 How can relational event models be generalized to handle multi-actor interactions involving more than two actors through hyperedges?
• RQ2 What statistical techniques can reliably estimate RHEM parameters in large-scale hypergraph networks with exponential likelihood complexity?
• RQ3 How can plausible alternative hyperedges be defined to ensure meaningful comparison between events and non-events in case-control sampling?
• RQ4 What hyperedge statistics effectively capture higher-order network dependencies such as repetition, reciprocity, and triadic closure in multi-actor settings?
• RQ5 How can models distinguish between effects driven by hyperedge size and those driven by structural or behavioral network properties?

Key findings

• RHEM successfully models time-varying event rates across all possible hyperedges in multi-actor interaction networks, capturing dependencies that dyadic models cannot express.
• Case-control sampling enables reliable parameter estimation in a co-authorship network with over 100,000 authors and hundreds of thousands of hyperevents, overcoming exponential likelihood computation.
• The model reveals that repeated events—especially sub-repetitions of recent subsets—have significantly higher event rates, indicating strong temporal and structural dependencies.
• Conditioning on hyperedge size improves model stability and plausibility, reducing the risk of overfitting to extreme or inhomogeneous risk sets.
• Separate modeling of new and repeated events is necessary in sparse networks to prevent dominant effects from masking other meaningful structural patterns.
• Relational outcome models (ROM) successfully explain team performance in co-authoring networks, demonstrating that RHEM can be extended to analyze event outcomes beyond mere occurrence.