Learning Network of Multivariate Hawkes Processes: A Time Series Approach

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 of a class of multivariate Hawkes processes with exponential exciting functions (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.