  Multivariate Hawkes processes are commonly used to model streaming networked
event data in a wide variety of applications. However, it remains a challenge
to extract reliable inference from complex datasets with uncertainty
quantification. Aiming towards this, we develop a statistical inference
framework to learn causal relationships between nodes from networked data,
where the underlying directed graph implies Granger causality. We provide
uncertainty quantification for the maximum likelihood estimate of the network
multivariate Hawkes process by providing a non-asymptotic confidence set. The
main technique is based on the concentration inequalities of continuous-time
martingales. We compare our method to the previously-derived asymptotic Hawkes
process confidence interval, and demonstrate the strengths of our method in an
application to neuronal connectivity reconstruction.
