Applied Mathematics Colloquium
Cascading chains of interactions are a salient feature of many real-world social networks. One particularly well-studied example is social reciprocity between two people, but more distributed series of interactions are also possible: kindnesses are "paid forward", gang violence begets retaliations, nation-state conflicts are accompanied by proxy wars, and chain emails are regularly forwarded. This talk addresses the challenge of tracking how the actions within a social network stimulate or influence future actions. We adopt an online learning framework well-suited to streaming data, using a multivariate Hawkes 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 social network, but also to track that 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. Joint work with Eric Hall.