Hawkes Process Based on Controlled Differential Equations
This addresses the limitation of existing neural network-based Hawkes process models in capturing irregular dynamics for fields like social diffusion, though it appears incremental as it adapts an existing technology.
The paper tackled the problem of modeling irregular event sequences in Hawkes processes by proposing HP-CDE, which uses neural controlled differential equations to handle uneven temporal spaces and compute exact log-likelihoods, resulting in outperforming existing methods on 4 real-world datasets.
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.