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 this https URL

本文采用神经网络模型一个灵活但具有明确定义的累积风险函数，从而降低参数复杂性，并在六个数据集上的实验结果表明，该模型在数据拟合和事件预测任务中取得了最先进的性能，同时参数和内存使用量显著减少。

基于累积危险函数的高效多变量时间点过程学习

Cumulative Hazard Function Based Efficient Multivariate Temporal Point  Process Learning

These short lecture notes contain a not too technical introduction to point
processes on the time line. The focus lies on defining these processes using
the conditional intensity function. Furthermore, likelihood inference, methods
of simulation and residual analysis for temporal point processes specified by a
conditional intensity function are considered.

这篇论文介绍了时间线上点过程的概念和应用，重点是通过条件强度函数定义这些过程，讨论了基于条件强度函数建模的方法和相关推断、模拟和残差分析。

讲义：时间点过程与条件强度函数

Lecture Notes: Temporal Point Processes and the Conditional Intensity  Function

A novel point process model continuous in space-time is proposed for
quantifying the transmission dynamics of the two most common meningococcal
antigenic sequence types observed in Germany 2002-2008. Modelling is based on
the conditional intensity function (CIF) which is described by a superposition
of additive and multiplicative components. As an epidemiological interesting
finding, spread behaviour was shown to depend on type in addition to age: basic
reproduction numbers were 0.25 (95% CI 0.19-0.34) and 0.11 (95% CI 0.07-0.17)
for types B:P1.7-2,4:F1-5 and C:P1.5,2:F3-3, respectively. Altogether, the
proposed methodology represents a comprehensive and universal regression
framework for the modelling, simulation and inference of self-exciting
spatio-temporal point processes based on the CIF. Usability of the modelling in
biometric practice is promoted by an implementation in the R package
surveillance.

研究了德国 2002-2008 年发生的两个最常见的脑膜炎球菌抗原序列类型的传输动力学， 提出一种新的连续时空点过程模型，通过条件强度函数描述和建模，发现传播行为除年龄外还与类型有关，基础再生数分别为 0.25 和 0.11，所提出的方法可用于自激励时空点过程的建模、模拟和推断。