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Relational events are a type of social interactions, that sometimes arereferred to as dynamic networks. Its dynamics typically depends on emergingpatterns, so-called endogenous variables, or external forces, referred to asexogenous variables. Comprehensive information on the actors in the network,especially for huge networks, is rare, however. A latent space approach innetwork analysis has been a popular way to account for unmeasured covariatesthat are driving network configurations. Bayesian and EM-type algorithms havebeen proposed for inferring the latent space, but both the sheer size manysocial network applications as well as the dynamic nature of the process, andtherefore the latent space, make computations prohibitively expensive. In thiswork we propose a likelihood-based algorithm that can deal with huge relationalevent networks. We propose a hierarchical strategy for inferring networkcommunity dynamics embedded into an interpretable latent space. Node dynamicsare described by smooth spline processes. To make the framework feasible forlarge networks we borrow from machine learning optimization methodology.Model-based clustering is carried out via a convex clustering penalization,encouraging shared trajectories for ease of interpretation. We propose amodel-based approach for separating macro-microstructures and perform ahierarchical analysis within successive hierarchies. The method can fitmillions of nodes on a public Colab GPU in a few minutes. The code and atutorial are available in a Github repository.

Fast inference of latent space dynamics in huge relational event networks