# Modeling Inter-Dependence Between Time and Mark in Multivariate Temporal Point Processes

arXiv: https://arxiv.org/abs/2210.15294 · HTML: https://mlsanity.com/paper/2210.15294/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 38 references that are in the map.
- First posted on arXiv 27 Oct 2022.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Predicting Dynamic Embedding Trajectory in Temporal Interaction Networks](https://mlsanity.com/paper/1908.01207/) (2019)
- [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)
- [Modeling The Intensity Function Of Point Process Via Recurrent Neural Networks](https://mlsanity.com/paper/1705.08982/) (2017)
- [Neural Spatio-Temporal Point Processes](https://mlsanity.com/paper/2011.04583/) (2020)
- [Identifying Coordinated Accounts on Social Media through Hidden Influence and Group Behaviours](https://mlsanity.com/paper/2008.11308/) (2020)
- [Wasserstein Learning of Deep Generative Point Process Models](https://mlsanity.com/paper/1705.08051/) (2017)
- [Learning Temporal Point Processes via Reinforcement Learning](https://mlsanity.com/paper/1811.05016/) (2018)
- [Neural Temporal Point Processes For Modelling Electronic Health Records](https://mlsanity.com/paper/2007.13794/) (2020)
- [Deep Reinforcement Learning of Marked Temporal Point Processes](https://mlsanity.com/paper/1805.09360/) (2018)
- [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)
- [Long Horizon Forecasting With Temporal Point Processes](https://mlsanity.com/paper/2101.02815/) (2021)
- [Shaping Social Activity by Incentivizing Users](https://mlsanity.com/paper/1408.0406/) (2014)
- [VigDet: Knowledge Informed Neural Temporal Point Process for Coordination Detection on Social Media](https://mlsanity.com/paper/2110.15454/) (2021)

## Built on by (most cited first, 7 of 7)

- [On the Predictive Accuracy of Neural Temporal Point Process Models for Continuous-time Event Data](https://mlsanity.com/paper/2306.17066/) (2023)
- [Distribution-Free Conformal Joint Prediction Regions for Neural Marked Temporal Point Processes](https://mlsanity.com/paper/2401.04612/) (2024)
- [Time-Aware Attention for Enhanced Electronic Health Records Modeling](https://mlsanity.com/paper/2507.14847/) (2025)
- [Interpretable Neural Temporal Point Processes for Modelling Electronic Health Records](https://mlsanity.com/paper/2404.08007/) (2024)
- [Cumulative Hazard Function Based Efficient Multivariate Temporal Point Process Learning](https://mlsanity.com/paper/2404.13663/) (2024)
- [Preventing Conflicting Gradients in Neural Marked Temporal Point Processes](https://mlsanity.com/paper/2412.08590/) (2024)
- [Addressing Mark Imbalance in Integration-free Neural Marked Temporal Point Processes](https://mlsanity.com/paper/2510.20414/) (2025)

## Abstract (arXiv)

Temporal Point Processes (TPP) are probabilistic generative frameworks. They model discrete event sequences localized in continuous time. Generally, real-life events reveal descriptive information, known as marks. Marked TPPs model time and marks of the event together for practical relevance. Conditioned on past events, marked TPPs aim to learn the joint distribution of the time and the mark of the next event. For simplicity, conditionally independent TPP models assume time and marks are independent given event history. They factorize the conditional joint distribution of time and mark into the product of individual conditional distributions. This structural limitation in the design of TPP models hurt the predictive performance on entangled time and mark interactions. In this work, we model the conditional inter-dependence of time and mark to overcome the limitations of conditionally independent models. We construct a multivariate TPP conditioning the time distribution on the current event mark in addition to past events. Besides the conventional intensity-based models for conditional joint distribution, we also draw on flexible intensity-free TPP models from the literature. The proposed TPP models outperform conditionally independent and dependent models in standard prediction tasks. Our experimentation on various datasets with multiple evaluation metrics highlights the merit of the proposed approach.