  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.
