Learning Interaction Network of Multivariate Hawkes Processes

Learning the influence structure of multiple time series data is of great interest to many disciplines. We discuss approaches for learning causal interaction network of mutually exciting Hawkes processes. In such processes, the arrival of an event in one process increases the probability of occurrence of new events in some of the other processes. Thus, a natural notion of causality exists between the processes. In this talk, we first show that the causal interaction network learned from the above natural definition is equivalent to the Directed Information (DI) graph of the processes. DI graphs are a class of graphical models, which are well suited to capture causal interactions in times series data.  We discuss some interesting use cases of the algorithm for analyzing stock market datasets as well as clustering websites based on hyperlink information from news media articles and blog posts.