Tracking Dynamic Point Processes on Networks

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 the 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 the 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.