# Cumulative Hazard Function Based Efficient Multivariate Temporal Point Process Learning

arXiv: https://arxiv.org/abs/2404.13663 · HTML: https://mlsanity.com/paper/2404.13663/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 42 references that are in the map.
- First posted on arXiv 21 Apr 2024.

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [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 Temporal Point Processes: A Review](https://mlsanity.com/paper/2104.03528/) (2021)
- [EasyTPP: Towards Open Benchmarking Temporal Point Processes](https://mlsanity.com/paper/2307.08097/) (2023)
- [Survival Regression with Proper Scoring Rules and Monotonic Neural Networks](https://mlsanity.com/paper/2103.14755/) (2021)
- [COEVOLVE: A Joint Point Process Model for Information Diffusion and Network Co-evolution](https://mlsanity.com/paper/1507.02293/) (2015)
- [Deep Reinforcement Learning of Marked Temporal Point Processes](https://mlsanity.com/paper/1805.09360/) (2018)
- [Neural Likelihoods via Cumulative Distribution Functions](https://mlsanity.com/paper/1811.00974/) (2018)
- [An Empirical Study: Extensive Deep Temporal Point Process](https://mlsanity.com/paper/2110.09823/) (2021)
- [Modeling Inter-Dependence Between Time and Mark in Multivariate Temporal Point Processes](https://mlsanity.com/paper/2210.15294/) (2022)
- [Learning Point Processes using Recurrent Graph Network](https://mlsanity.com/paper/2208.05736/) (2022)
- [Link-aware link prediction over temporal graph by pattern recognition](https://mlsanity.com/paper/2402.07199/) (2024)
- [Interpretable Neural Temporal Point Processes for Modelling Electronic Health Records](https://mlsanity.com/paper/2404.08007/) (2024)

## Built on by (most cited first, 2 of 2)

- [Advances in Temporal Point Processes: Bayesian, Neural, and LLM Approaches](https://mlsanity.com/paper/2501.14291/) (2025)
- [Efficient Temporal Point Processes via Monotone Alternating Splines](https://mlsanity.com/paper/2607.01752/) (2026)

## Abstract (arXiv)

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.