Most existing temporal point process models are characterized by conditional intensity function. These models often require numerical approximation methods for likelihood evaluation, which potentially hurts their performance. By directly modelling the integral of the intensity function, i.e., the cumulative hazard function (CHF), the likelihood can be evaluated accurately, making it a promising approach. However, existing CHF-based methods are not well-defined, i.e., the mathematical constraints of CHF are not completely satisfied, leading to untrustworthy results. For multivariate temporal point process, most existing methods model intensity (or density, etc.) functions for each variate, limiting the scalability. In this paper, we explore using neural networks to model a flexible but well-defined CHF and learning the multivariate temporal point process with low parameter complexity. Experimental results on six datasets show that the proposed model achieves the state-of-the-art performance on data fitting and event prediction tasks while having significantly fewer parameters and memory usage than the strong competitors. The source code and data can be obtained from https://github.com/lbq8942/NPP.

翻译：现有大多数时空点过程模型以条件强度函数为特征。这类模型通常需要数值近似方法进行似然估计，这可能会损害其性能。通过直接建模强度函数的积分形式，即累积风险函数（CHF），可以实现似然的精确计算，因此这是一种有前景的方法。然而，现有基于CHF的方法定义不完善，即未完全满足CHF的数学约束条件，导致结果不可靠。针对多元时空点过程，现有方法多为每个变量单独建模强度函数（或密度函数等），限制了可扩展性。本文探索利用神经网络构建灵活且数学定义完善的CHF模型，以较低参数复杂度实现多元时空点过程学习。在六个数据集上的实验结果表明，所提模型在数据拟合与事件预测任务中均达到最优性能，同时参数数量与内存占用显著低于强基线模型。源代码与数据可从https://github.com/lbq8942/NPP获取。