Poisson Inverse Problems with Physical Constraints
Cascading chains of interactions 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 jumps throughout a financial network. In these and other examples, we only observe individual events associated with network nodes, usually without knowledge of the underlying network structure. This talk addresses the challenge of tracking how events within such networks stimulate or influence future events. We propose an online learning framework well-suited to streaming data, using a multivariate Hawkes model to encapsulate autoregressive features of observed events within the network. Recent work on online learning in dynamic environments is leveraged not only to exploit the dynamics within the network, but also to track the network structure as it evolves. Regret bounds and experimental results demonstrate that the proposed method (with no prior knowledge of the network) performs nearly as well as would be possible with full knowledge of the network. This is joint work with Eric Hall.