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.

翻译：霍克斯过程是一种流行的框架，用于建模多个领域（如社交扩散）中序贯事件的发生动态。在现实场景中，事件间的到达时间间隔是不规则的。然而，现有的基于神经网络的霍克斯过程模型不仅（i）无法捕获这种复杂的非规则动态，而且（ii）由于它们主要基于为规则离散输入设计的神经网络，因此需要借助启发式方法计算事件的对数似然。为此，我们提出了基于受控微分方程的霍克斯过程（HP-CDE）概念，采用神经受控微分方程（神经CDE）技术，该技术类似于连续递归神经网络。由于HP-CDE连续读取数据，（i）可以恰当处理不规则时间序列数据集，保留其不均匀的时间间隔，（ii）并且可以精确计算对数似然。此外，由于霍克斯过程和神经CDE最初都是为了建模复杂的人类行为动态而开发的，基于神经CDE的霍克斯过程在建模这种发生动态方面非常成功。在4个真实数据集的实验中，我们的方法以显著优势超越了现有方法。