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Learning the influence structure of multiple time series data is of greatinterest to many disciplines. This paper studies the problem of recovering thecausal structure in network of multivariate linear Hawkes processes. In suchprocesses, the occurrence of an event in one process affects the probability ofoccurrence of new events in some other processes. Thus, a natural notion ofcausality exists between such processes captured by the support of theexcitation matrix. We show that the resulting causal influence network isequivalent to the Directed Information graph (DIG) of the processes, whichencodes the causal factorization of the joint distribution of the processes.Furthermore, we present an algorithm for learning the support of excitationmatrix (or equivalently the DIG). The performance of the algorithm is evaluatedon synthesized multivariate Hawkes networks as well as a stock market andMemeTracker real-world dataset.

Learning Network of Multivariate Hawkes Processes: A Time Series Approach