Relational events are a type of social interactions, that sometimes are referred to as dynamic networks. Its dynamics typically depends on emerging patterns, so-called endogenous variables, or external forces, referred to as exogenous variables. Comprehensive information on the actors in the network, especially for huge networks, is rare, however. A latent space approach in network analysis has been a popular way to account for unmeasured covariates that are driving network configurations. Bayesian and EM-type algorithms have been proposed for inferring the latent space, but both the sheer size many social network applications as well as the dynamic nature of the process, and therefore the latent space, make computations prohibitively expensive. In this work we propose a likelihood-based algorithm that can deal with huge relational event networks. We propose a hierarchical strategy for inferring network community dynamics embedded into an interpretable latent space. Node dynamics are described by smooth spline processes. To make the framework feasible for large 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 a model-based approach for separating macro-microstructures and perform a hierarchical analysis within successive hierarchies. The method can fit millions of nodes on a public Colab GPU in a few minutes. The code and a tutorial are available in a Github repository.

翻译：关系事件是一种社会互动形式，有时被称为动态网络。其动力学通常依赖于涌现模式（即内生变量）或外力作用（即外生变量）。然而，对于大型网络而言，关于行为者的全面信息往往难以获取。潜在空间方法作为网络分析中处理未观测协变量（驱动网络构型）的主流技术，虽然已有贝叶斯和EM类算法被提出用于推断潜在空间，但许多社交网络应用的大规模特征、过程的动态性以及随之而来的潜在空间变化，使得计算代价极其高昂。本文提出了一种基于似然的算法，能够处理大规模关系事件网络。我们引入了一种分层策略，用于在可解释的潜在空间中推断网络社区动力学。节点动力学通过平滑样条过程进行建模。为使该框架适用于大型网络，我们借鉴了机器学习优化方法。通过凸聚类惩罚实现基于模型的聚类，鼓励共享轨迹以增强可解释性。我们提出了基于模型的宏微观结构分离方法，并在连续层级中进行分层分析。该算法可在公共Colab GPU上数分钟内处理数百万节点。相关代码与教程已发布于GitHub仓库。