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

arXiv: https://arxiv.org/abs/2308.02360 · HTML: https://mlsanity.com/paper/2308.02360/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 22 references that are in the map.
- First posted on arXiv 4 Aug 2023.

## Builds on (most cited first, 10 of 10)

- [Transformer Hawkes Process](https://mlsanity.com/paper/2002.09291/) (2020)
- [Intensity-Free Learning of Temporal Point Processes](https://mlsanity.com/paper/1909.12127/) (2019)
- [Fully Neural Network based Model for General Temporal Point Processes](https://mlsanity.com/paper/1905.09690/) (2019)
- [Neural Spatio-Temporal Point Processes](https://mlsanity.com/paper/2011.04583/) (2020)
- [SEISMIC: A Self-Exciting Point Process Model for Predicting Tweet Popularity](https://mlsanity.com/paper/1506.02594/) (2015)
- [Lecture Notes: Temporal Point Processes and the Conditional Intensity Function](https://mlsanity.com/paper/1806.00221/) (2018)
- [Neural Temporal Point Processes For Modelling Electronic Health Records](https://mlsanity.com/paper/2007.13794/) (2020)
- [Uncertainty on Asynchronous Time Event Prediction](https://mlsanity.com/paper/1911.05503/) (2019)
- [Noise-Contrastive Estimation for Multivariate Point Processes](https://mlsanity.com/paper/2011.00717/) (2020)
- [Learning Hawkes Processes from a Handful of Events](https://mlsanity.com/paper/1911.00292/) (2019)

## Abstract (arXiv)

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 (underlineIntensity-underlinefree underlineIntegral-underlinebased 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 urlhttps://github.com/StepinSilence/IFIB.