  Learning the influence structure of multiple time series data is of great
interest to many disciplines. This paper studies the problem of recovering the
causal structure in network of multivariate linear Hawkes processes. In such
processes, the occurrence of an event in one process affects the probability of
occurrence of new events in some other processes. Thus, a natural notion of
causality exists between such processes captured by the support of the
excitation matrix. We show that the resulting causal influence network is
equivalent to the Directed Information graph (DIG) of the processes, which
encodes the causal factorization of the joint distribution of the processes.
Furthermore, we present an algorithm for learning the support of excitation
matrix (or equivalently the DIG). The performance of the algorithm is evaluated
on synthesized multivariate Hawkes networks as well as a stock market and
MemeTracker real-world dataset.
