Exploring the dynamic co-evolution of multiplex graphs and nodal attributes is a compelling question in criminal and terrorism networks. This article is motivated by the study of dynamically evolving interactions among prominent terrorist organizations, considering various organizational attributes like size, ideology, leadership, and operational capacity. Statistically principled integration of multiplex graphs with nodal attributes is significantly challenging due to the need to leverage shared information within and across layers, account for uncertainty in predicting unobserved links, and capture temporal evolution of node attributes. These difficulties increase when layers are partially observed, as in terrorism networks where connections are deliberately hidden to obscure key relationships. To address these challenges, we present a principled methodological framework to integrate the multiplex graph layers and nodal attributes. The approach employs time-varying stochastic latent factor models, leveraging shared latent factors to capture graph structure and its co-evolution with node attributes. Latent factors are modeled using Gaussian processes with an infinitely wide deep neural network-based covariance function, termed neural network Gaussian processes (NN-GP). The NN-GP framework on latent factors exploits the predictive power of Bayesian deep neural network architecture while propagating uncertainty for reliability. Simulation studies highlight superior performance of the proposed approach in achieving inferential objectives. The approach, termed as dynamic joint learner, enables predictive inference (with uncertainty) of diverse unobserved dynamic relationships among prominent terrorist organizations and their organization-specific attributes, as well as clustering behavior in terms of friend-and-foe relationships, which could be informative in counter-terrorism research.

翻译：探索多路图与节点属性的动态协同演化是犯罪网络与恐怖主义网络研究中的一个引人关注的问题。本文受研究主要恐怖组织间动态演化互动的启发，考虑了各类组织属性，如规模、意识形态、领导力及行动能力。在统计原则上将多路图与节点属性整合面临显著挑战，原因在于需要利用层内及层间的共享信息、考虑预测未观测连接时的不确定性，并捕捉节点属性的时间演变。当层被部分观测时，这些困难进一步加剧，例如在恐怖主义网络中，连接被故意隐藏以掩盖关键关系。为解决这些挑战，我们提出一个原则性的方法论框架，用于整合多路图层与节点属性。该方法采用时变随机潜在因子模型，利用共享潜在因子捕捉图结构及其与节点属性的协同演化。潜在因子通过具有无限宽深度神经网络协方差函数的高斯过程建模，称为神经网络高斯过程。潜在因子上的NN-GP框架利用了贝叶斯深度神经网络架构的预测能力，同时传播不确定性以确保可靠性。模拟研究展示了所提方法在实现推理目标方面的优越性能。该方法称为动态联合学习器，能够实现对主要恐怖组织间多样未观测动态关系及其组织特定属性的预测推理（含不确定性），以及敌友关系聚类行为的分析，这可为反恐研究提供信息参考。