  Hawkes processes are a popular framework to model the occurrence of
sequential events, i.e., occurrence dynamics, in several fields such as social
diffusion. In real-world scenarios, the inter-arrival time among events is
irregular. However, existing neural network-based Hawkes process models not
only i) fail to capture such complicated irregular dynamics, but also ii)
resort to heuristics to calculate the log-likelihood of events since they are
mostly based on neural networks designed for regular discrete inputs. To this
end, we present the concept of Hawkes process based on controlled differential
equations (HP-CDE), by adopting the neural controlled differential equation
(neural CDE) technology which is an analogue to continuous RNNs. Since HP-CDE
continuously reads data, i) irregular time-series datasets can be properly
treated preserving their uneven temporal spaces, and ii) the log-likelihood can
be exactly computed. Moreover, as both Hawkes processes and neural CDEs are
first developed to model complicated human behavioral dynamics, neural
CDE-based Hawkes processes are successful in modeling such occurrence dynamics.
In our experiments with 4 real-world datasets, our method outperforms existing
methods by non-trivial margins.
