# THP: Topological Hawkes Processes for Learning Causal Structure on Event Sequences

arXiv: https://arxiv.org/abs/2105.10884 · HTML: https://mlsanity.com/paper/2105.10884/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 39 references that are in the map.
- First posted on arXiv 23 May 2021.

## Builds on (most cited first, 13 of 13)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [SEISMIC: A Self-Exciting Point Process Model for Predicting Tweet Popularity](https://mlsanity.com/paper/1506.02594/) (2015)
- [Learning Granger Causality for Hawkes Processes](https://mlsanity.com/paper/1602.04511/) (2016)
- [Uncovering Causality from Multivariate Hawkes Integrated Cumulants](https://mlsanity.com/paper/1607.06333/) (2016)
- [CAUSE: Learning Granger Causality from Event Sequences using Attribution Methods](https://mlsanity.com/paper/2002.07906/) (2020)
- [Shaping Social Activity by Incentivizing Users](https://mlsanity.com/paper/1408.0406/) (2014)
- [Learning Network of Multivariate Hawkes Processes: A Time Series Approach](https://mlsanity.com/paper/1603.04319/) (2016)
- [Efficient Non-parametric Bayesian Hawkes Processes](https://mlsanity.com/paper/1810.03730/) (2018)
- [Learning Hawkes Processes from a Handful of Events](https://mlsanity.com/paper/1911.00292/) (2019)
- [Large-scale directed network inference with multivariate transfer entropy and hierarchical statistical testing](https://mlsanity.com/paper/1902.06828/) (2019)
- [An information-theoretic framework to measure the dynamic interaction between neural spike trains](https://mlsanity.com/paper/2012.08667/) (2020)

## Built on by (most cited first, 19 of 19)

- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [Structural Hawkes Processes for Learning Causal Structure from Discrete-Time Event Sequences](https://mlsanity.com/paper/2305.05986/) (2023)
- [Nonparametric Conditional Local Independence Testing](https://mlsanity.com/paper/2203.13559/) (2022)
- [Identification of Causal Structure in the Presence of Missing Data with Additive Noise Model](https://mlsanity.com/paper/2312.12206/) (2023)
- [TNPAR: Topological Neural Poisson Auto-Regressive Model for Learning Granger Causal Structure from Event Sequences](https://mlsanity.com/paper/2306.14114/) (2023)
- [Causal Discovery from Poisson Branching Structural Causal Model Using High-Order Cumulant with Path Analysis](https://mlsanity.com/paper/2403.16523/) (2024)
- [Advances in Temporal Point Processes: Bayesian, Neural, and LLM Approaches](https://mlsanity.com/paper/2501.14291/) (2025)
- [EDGE: Error Dependency Graph-Guided Multi-Error Attribution in Multi-Agent LLM Systems](https://mlsanity.com/paper/2609.01360/) (2026)
- [OCDB: Revisiting Causal Discovery with a Comprehensive Benchmark and Evaluation Framework](https://mlsanity.com/paper/2406.04598/) (2024)
- [Heterogeneous Causal Discovery of Repeated Undesirable Health Outcomes](https://mlsanity.com/paper/2503.11477/) (2025)
- [Local Independence Testing for Point Processes](https://mlsanity.com/paper/2110.12709/) (2021)
- [Scalable Structure Learning of Bayesian Networks by Learning Algorithm Ensembles](https://mlsanity.com/paper/2506.22848/) (2025)
- [TempOpt -- Unsupervised Alarm Relation Learning for Telecommunication Networks](https://mlsanity.com/paper/2508.08814/) (2025)
- [Causal Structure Learning in Hawkes Processes with Complex Latent Confounder Networks](https://mlsanity.com/paper/2508.11727/) (2025)
- [LMT: A Bayesian Framework for Causal Discovery from Textual Alarm Records in Manufacturing Systems](https://mlsanity.com/paper/2606.09892/) (2026)
- [EvoCause: LLM-Guided Evolution of Causal Graphs for Root Cause Analysis](https://mlsanity.com/paper/2607.27290/) (2026)
- [Resilient Concurrent Causal Discovery for Topological Event Sequences](https://mlsanity.com/paper/2608.21815/) (2026)
- [Replicating TRACE: A Practitioner's Guide to Its Threshold and Particle Budget](https://mlsanity.com/paper/2609.01108/) (2026)
- [Inferring Causal Relations between Two Sequences of Events with Language Models](https://mlsanity.com/paper/2609.39406/) (2026)

## Abstract (arXiv)

Learning causal structure among event types on multi-type event sequences is an important but challenging task. Existing methods, such as the Multivariate Hawkes processes, mostly assumed that each sequence is independent and identically distributed. However, in many real-world applications, it is commonplace to encounter a topological network behind the event sequences such that an event is excited or inhibited not only by its history but also by its topological neighbors. Consequently, the failure in describing the topological dependency among the event sequences leads to the error detection of the causal structure. By considering the Hawkes processes from the view of temporal convolution, we propose a Topological Hawkes process (THP) to draw a connection between the graph convolution in the topology domain and the temporal convolution in time domains. We further propose a causal structure learning method on THP in a likelihood framework. The proposed method is featured with the graph convolution-based likelihood function of THP and a sparse optimization scheme with an Expectation-Maximization of the likelihood function. Theoretical analysis and experiments on both synthetic and real-world data demonstrate the effectiveness of the proposed method