# SMURF-THP: Score Matching-based UnceRtainty quantiFication for Transformer Hawkes Process

arXiv: https://arxiv.org/abs/2310.16336 · HTML: https://mlsanity.com/paper/2310.16336/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 31 references that are in the map.
- First posted on arXiv 25 Oct 2023.

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [Transformer Hawkes Process](https://mlsanity.com/paper/2002.09291/) (2020)
- [Fully Neural Network based Model for General Temporal Point Processes](https://mlsanity.com/paper/1905.09690/) (2019)
- [Supervised Reinforcement Learning with Recurrent Neural Network for Dynamic Treatment Recommendation](https://mlsanity.com/paper/1807.01473/) (2018)
- [Modeling The Intensity Function Of Point Process Via Recurrent Neural Networks](https://mlsanity.com/paper/1705.08982/) (2017)
- [SEISMIC: A Self-Exciting Point Process Model for Predicting Tweet Popularity](https://mlsanity.com/paper/1506.02594/) (2015)
- [Mirrored Langevin Dynamics](https://mlsanity.com/paper/1802.10174/) (2018)
- [Learning Temporal Point Processes via Reinforcement Learning](https://mlsanity.com/paper/1811.05016/) (2018)
- [Deep Reinforcement Learning of Marked Temporal Point Processes](https://mlsanity.com/paper/1805.09360/) (2018)
- [Noise-Contrastive Estimation for Multivariate Point Processes](https://mlsanity.com/paper/2011.00717/) (2020)
- [Generalized Score Matching for General Domains](https://mlsanity.com/paper/2009.11428/) (2020)
- [Uncertainty Quantification for Inferring Hawkes Networks](https://mlsanity.com/paper/2006.07506/) (2020)

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

- [Is Score Matching Suitable for Estimating Point Processes?](https://mlsanity.com/paper/2410.04037/) (2024)
- [Advances in Temporal Point Processes: Bayesian, Neural, and LLM Approaches](https://mlsanity.com/paper/2501.14291/) (2025)
- [Enhancing Temporal Awareness in LLMs for Temporal Point Processes](https://mlsanity.com/paper/2601.00845/) (2025)
- [Score-Based Change-Point Detection and Region Localization for Spatio-Temporal Point Processes](https://mlsanity.com/paper/2602.04798/) (2026)
- [Preventing Conflicting Gradients in Neural Marked Temporal Point Processes](https://mlsanity.com/paper/2412.08590/) (2024)
- [Bridging Discrete Marks and Continuous Dynamics: Dual-Path Cross-Interaction for Marked Temporal Point Processes](https://mlsanity.com/paper/2603.11462/) (2026)
- [Efficient Temporal Point Processes via Monotone Alternating Splines](https://mlsanity.com/paper/2607.01752/) (2026)

## Abstract (arXiv)

Transformer Hawkes process models have shown to be successful in modeling event sequence data. However, most of the existing training methods rely on maximizing the likelihood of event sequences, which involves calculating some intractable integral. Moreover, the existing methods fail to provide uncertainty quantification for model predictions, e.g., confidence intervals for the predicted event's arrival time. To address these issues, we propose SMURF-THP, a score-based method for learning Transformer Hawkes process and quantifying prediction uncertainty. Specifically, SMURF-THP learns the score function of events' arrival time based on a score-matching objective that avoids the intractable computation. With such a learned score function, we can sample arrival time of events from the predictive distribution. This naturally allows for the quantification of uncertainty by computing confidence intervals over the generated samples. We conduct extensive experiments in both event type prediction and uncertainty quantification of arrival time. In all the experiments, SMURF-THP outperforms existing likelihood-based methods in confidence calibration while exhibiting comparable prediction accuracy.