Stochastic Gradient Descent-based Inference for Dynamic Network Models with Attractors

In Coevolving Latent Space Networks with Attractors (CLSNA) models, nodes in a latent space represent social actors, and edges indicate their dynamic interactions. Attractors are added at the latent level to capture the notion of attractive and repulsive forces between nodes, borrowing from dynamical systems theory. However, CLSNA reliance on MCMC estimation makes scaling difficult, and the requirement for nodes to be present throughout the study period limit practical applications. We address these issues by (i) introducing a Stochastic gradient descent (SGD) parameter estimation method, (ii) developing a novel approach for uncertainty quantification using SGD, and (iii) extending the model to allow nodes to join and leave over time. Simulation results show that our extensions result in little loss of accuracy compared to MCMC, but can scale to much larger networks. We apply our approach to the longitudinal social networks of members of US Congress on the social media platform X. Accounting for node dynamics overcomes selection bias in the network and uncovers uniquely and increasingly repulsive forces within the Republican Party. Supplemental materials for the article are available online.

在带吸引子的协同演化潜空间网络（Coevolving Latent Space Networks with Attractors, CLSNA）模型中，潜空间内的节点代表社会行动者，边则表示二者间的动态互动关系。该模型在潜空间层面引入吸引子，以捕捉节点间的吸引力与排斥力概念，其设计借鉴了动力系统理论。然而，CLSNA模型依赖马尔可夫链蒙特卡洛（Markov Chain Monte Carlo, MCMC）估计，这导致其难以扩展，且要求节点在整个研究周期内始终存在，限制了实际应用场景。针对上述问题，我们从三方面进行改进：(i) 引入随机梯度下降（Stochastic gradient descent, SGD）参数估计方法；(ii) 提出一种基于SGD的不确定性量化新方法；(iii) 对模型进行扩展，允许节点随时间加入或退出网络。仿真结果表明，相较于MCMC方法，我们的扩展模型仅存在微小的精度损失，却可适配规模大得多的网络。我们将所提方法应用于美国国会议员在社交媒体平台X上的纵向社会网络数据。考虑节点动态变化这一要素，可克服网络中的选择偏差，并揭示出共和党内部独有的、且不断增强的排斥力特征。本文的补充材料可在线获取。