  Cascading chains of events are a salient feature of many real-world social,
biological, and financial networks. In social networks, social reciprocity
accounts for retaliations in gang interactions, proxy wars in nation-state
conflicts, or Internet memes shared via social media. Neuron spikes stimulate
or inhibit spike activity in other neurons. Stock market shocks can trigger a
contagion of volatility throughout a financial network. In these and other
examples, only individual events associated with network nodes are observed,
usually without knowledge of the underlying dynamic relationships between
nodes. This paper addresses the challenge of tracking how events within such
networks stimulate or influence future events. The proposed approach is an
online learning framework well-suited to streaming data, using a multivariate
Hawkes point process model to encapsulate autoregressive features of observed
events within the social network. Recent work on online learning in dynamic
environments is leveraged not only to exploit the dynamics within the
underlying network, but also to track the network structure as it evolves.
Regret bounds and experimental results demonstrate that the proposed method
performs nearly as well as an oracle or batch algorithm.
