A common goal in network modeling is to uncover the latent community structure present among nodes. For many real-world networks, the true connections consist of events arriving as streams, which are then aggregated to form edges, ignoring the dynamic temporal component. A natural way to take account of these temporal dynamics of interactions is to use point processes as the foundation of network models for community detection. Computational complexity hampers the scalability of such approaches to large sparse networks. To circumvent this challenge, we propose a fast online variational inference algorithm for estimating the latent structure underlying dynamic event arrivals on a network, using continuous-time point process latent network models. We describe this procedure for networks models capturing community structure. This structure can be learned as new events are observed on the network, updating the inferred community assignments. We investigate the theoretical properties of such an inference scheme, and provide regret bounds on the loss function of this procedure. The proposed inference procedure is then thoroughly compared, using both simulation studies and real data, to non-online variants. We demonstrate that online inference can obtain comparable performance, in terms of community recovery, to non-online variants, while realising computational gains. Our proposed inference framework can also be readily modified to incorporate other popular network structures.

翻译：网络建模的常见目标是揭示节点间的潜在社区结构。对于许多现实网络而言，真实连接由到达的事件流构成，这些事件被聚合形成边，从而忽略了动态时间组分。考虑交互时间动态的自然方法是使用点过程作为社区检测网络模型的基础。计算复杂性阻碍了此类方法在大规模稀疏网络中的可扩展性。为应对这一挑战，我们提出一种快速在线变分推理算法，利用连续时间点过程潜在网络模型估计网络上动态事件到达的潜在结构。我们针对捕捉社区结构的网络模型描述了这一过程。当网络上新事件被观测时，该结构可得以学习，并更新推断的社区分配。我们研究了此类推理方案的理论性质，并提供了该过程损失函数的遗憾界。随后，通过模拟研究与真实数据，将所提出的推理过程与非在线变体进行全面比较。我们证明，在线推理在社区恢复方面可获得与非在线变体相当的性能，同时实现计算增益。我们提出的推理框架也可轻松修改以融入其他流行的网络结构。