Understanding dramatic changes in the evolution of networks is central to statistical network inference, as underscored by recent challenges of predicting and distinguishing pandemic-induced transformations in organizational and communication networks. We consider a joint network model in which each node has an associated time-varying low-dimensional latent vector of feature data, and connection probabilities are functions of these vectors. Under mild assumptions, the time-varying evolution of the constellation of latent vectors exhibits low-dimensional manifold structure under a suitable notion of distance. This distance can be approximated by a measure of separation between the observed networks themselves, and there exist consistent Euclidean representations for underlying network structure, as characterized by this distance, at any given time. These Euclidean representations permit the visualization of network evolution and transform network inference questions such as change-point and anomaly detection into a classical setting. We illustrate our methodology with real and synthetic data, and identify change points corresponding to massive shifts in pandemic policies in a communication network of a large organization.

翻译：理解网络演化中的剧烈变化是统计网络推断的核心，这由近期预测和区分组织及通信网络中疫情引发的转型所带来的挑战所凸显。我们提出一种联合网络模型，其中每个节点具有一个随时间变化的低维潜在特征数据向量，而连接概率是这些向量的函数。在温和假设下，潜在向量星座的时间演化在合适的距离概念下表现出低维流形结构。该距离可通过观测网络之间的分离度量近似，并且存在一致的欧几里得表示来刻画任意时刻的基础网络结构（由该距离表征）。这些欧几里得表示实现了网络演化的可视化，并将网络推断问题（如变点检测和异常检测）转化为经典统计框架。我们通过真实与合成数据验证了该方法，并在一个大型组织的通信网络中识别出与疫情政策大规模转变相对应的变点。