Learning continuous-time point processes is essential to many discrete event
forecasting tasks. However, integration poses a major challenge, particularly
for spatiotemporal point processes (STPPs), as it involves calculating the
likelihood through triple integrals over space and time. Existing methods for
integrating STPP either assume a parametric form of the intensity function,
which lacks flexibility; or approximating the intensity with Monte Carlo
sampling, which introduces numerical errors. Recent work by Omi et al. [2019]
proposes a dual network or AutoInt approach for efficient integration of
flexible intensity function. However, the method only focuses on the 1D
temporal point process. In this paper, we introduce a novel paradigm: AutoSTPP
(Automatic Integration for Spatiotemporal Neural Point Processes) that extends
the AutoInt approach to 3D STPP. We show that direct extension of the previous
work overly constrains the intensity function, leading to poor performance. We
prove consistency of AutoSTPP and validate it on synthetic data and benchmark
real world datasets, showcasing its significant advantage in recovering complex
intensity functions from irregular spatiotemporal events, particularly when the
intensity is sharply localized.

AutoSTPP 是一种用于恢复复杂强度函数的自动化空时神经点过程的方法，它扩展了 AutoInt 方法至三维空时点过程，证明了其一致性，并在合成数据和基准真实数据集上验证了其显著优势，特别是在强度函数明显局部化的不规则空时事件中。

时空神经点过程的自动整合

Automatic Integration for Spatiotemporal Neural Point Processes

In the marked temporal point processes (MTPP), a core problem is to
parameterize the conditional joint PDF (probability distribution function)
$p^*(m,t)$ for inter-event time $t$ and mark $m$, conditioned on the history.
The majority of existing studies predefine intensity functions. Their utility
is challenged by specifying the intensity function's proper form, which is
critical to balance expressiveness and processing efficiency. Recently, there
are studies moving away from predefining the intensity function -- one models
$p^*(t)$ and $p^*(m)$ separately, while the other focuses on temporal point
processes (TPPs), which do not consider marks. This study aims to develop
high-fidelity $p^*(m,t)$ for discrete events where the event marks are either
categorical or numeric in a multi-dimensional continuous space. We propose a
solution framework IFIB (\underline{I}ntensity-\underline{f}ree
\underline{I}ntegral-\underline{b}ased process) that models conditional joint
PDF $p^*(m,t)$ directly without intensity functions. It remarkably simplifies
the process to compel the essential mathematical restrictions. We show the
desired properties of IFIB and the superior experimental results of IFIB on
real-world and synthetic datasets. The code is available at
https://github.com/StepinSilence/IFIB.

通过 IFIB（无强度积分型进程）提出了一种在离散事件中高度准确建模条件联合概率密度 $p^*(m,t)$ 的解决方案，其中事件标记可以是分类的或连续多维空间的数值，该方法极大地简化了过程以满足数学约束条件，并通过在真实数据和合成数据集上展示出的优越实验结果进行验证。

基于积分的标记时态点过程的无强度学习

Intensity-free Integral-based Learning of Marked Temporal Point  Processes

A temporal point process is a stochastic process that predicts which type of
events is likely to happen and when the event will occur given a history of a
sequence of events. There are various examples of occurrence dynamics in the
daily life, and it is important to train the temporal dynamics and solve two
different prediction problems, time and type predictions. Especially, deep
neural network based models have outperformed the statistical models, such as
Hawkes processes and Poisson processes. However, many existing approaches
overfit to specific events, instead of learning and predicting various event
types. Therefore, such approaches could not cope with the modified
relationships between events and fail to predict the intensity functions of
temporal point processes very well. In this paper, to solve these problems, we
propose a variational neural temporal point process (VNTPP). We introduce the
inference and the generative networks, and train a distribution of latent
variable to deal with stochastic property on deep neural network. The intensity
functions are computed using the distribution of latent variable so that we can
predict event types and the arrival times of the events more accurately. We
empirically demonstrate that our model can generalize the representations of
various event types. Moreover, we show quantitatively and qualitatively that
our model outperforms other deep neural network based models and statistical
processes on synthetic and real-world datasets.

本文提出了一种变分神经时间点过程（VNTPP），通过引入推理和生成网络，训练深度神经网络中的潜变量分布以应对时间点过程的随机特性，并利用潜变量分布计算强度函数，从而更准确地预测事件类型和到达时间，实验证明该模型可以广义地表示各种事件类型，并在合成和实际数据集上表现优异。