  We present a new CUSUM procedure for sequentially detecting change-point in
the self and mutual exciting processes, a.k.a. Hawkes networks using discrete
events data. Hawkes networks have become a popular model for statistics and
machine learning due to their capability in modeling irregularly observed data
where the timing between events carries a lot of information. The problem of
detecting abrupt changes in Hawkes networks arises from various applications,
including neuronal imaging, sensor network, and social network monitoring.
Despite this, there has not been a computationally and memory-efficient online
algorithm for detecting such changes from sequential data. We present an
efficient online recursive implementation of the CUSUM statistic for Hawkes
processes, both decentralized and memory-efficient, and establish the
theoretical properties of this new CUSUM procedure. We then show that the
proposed CUSUM method achieves better performance than existing methods,
including the Shewhart procedure based on count data, the generalized
likelihood ratio (GLR) in the existing literature, and the standard score
statistic. We demonstrate this via a simulated example and an application to
population code change-detection in neuronal networks.
