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。