# Structural Hawkes Processes for Learning Causal Structure from Discrete-Time Event Sequences

arXiv: https://arxiv.org/abs/2305.05986 · HTML: https://mlsanity.com/paper/2305.05986/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 67 references that are in the map.
- First posted on arXiv 10 May 2023.

## Builds on (most cited first, 12 of 12)

- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasets](https://mlsanity.com/paper/2003.03685/) (2020)
- [Learning Granger Causality for Hawkes Processes](https://mlsanity.com/paper/1602.04511/) (2016)
- [Artificial Intelligence and Statistics](https://mlsanity.com/paper/1712.03779/) (2017)
- [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)
- [A Unified View of Causal and Non-causal Feature Selection](https://mlsanity.com/paper/1802.05844/) (2018)
- [THP: Topological Hawkes Processes for Learning Causal Structure on Event Sequences](https://mlsanity.com/paper/2105.10884/) (2021)
- [Learning causal representations for robust domain adaptation](https://mlsanity.com/paper/2011.06317/) (2020)
- [Shaping Social Activity by Incentivizing Users](https://mlsanity.com/paper/1408.0406/) (2014)
- [Learning Hawkes Processes from a Handful of Events](https://mlsanity.com/paper/1911.00292/) (2019)
- [Cardinality-Regularized Hawkes-Granger Model](https://mlsanity.com/paper/2208.10671/) (2022)

## Built on by (most cited first, 14 of 14)

- [Identification of Causal Structure in the Presence of Missing Data with Additive Noise Model](https://mlsanity.com/paper/2312.12206/) (2023)
- [Towards Practical Multi-label Causal Discovery in High-Dimensional Event Sequences via One-Shot Graph Aggregation](https://mlsanity.com/paper/2509.19112/) (2025)
- [One-Shot Multi-Label Causal Discovery in High-Dimensional Event Sequences](https://mlsanity.com/paper/2509.23213/) (2025)
- [Where and How to Attack? A Causality-Inspired Recipe for Generating Counterfactual Adversarial Examples](https://mlsanity.com/paper/2312.13628/) (2023)
- [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)
- [Your Autoregressive Model Already Reveals the Causal Graph](https://mlsanity.com/paper/2602.01135/) (2026)
- [CDFM: Towards a General-Purpose Causal Discovery Foundation Model](https://mlsanity.com/paper/2607.11508/) (2026)
- [Causal Structure Learning in Hawkes Processes with Complex Latent Confounder Networks](https://mlsanity.com/paper/2508.11727/) (2025)
- [MOCHA: Discovering Multi-Order Dynamic Causality in Temporal Point Processes](https://mlsanity.com/paper/2508.18873/) (2025)
- [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)
- [seq2cause: One Autoregressive Backbone, Four Causal Discovery Tasks in Event Sequences](https://mlsanity.com/paper/2609.31801/) (2026)

## Abstract (arXiv)

Learning causal structure among event types from discrete-time event sequences is a particularly important but challenging task. Existing methods, such as the multivariate Hawkes processes based methods, mostly boil down to learning the so-called Granger causality which assumes that the cause event happens strictly prior to its effect event. Such an assumption is often untenable beyond applications, especially when dealing with discrete-time event sequences in low-resolution; and typical discrete Hawkes processes mainly suffer from identifiability issues raised by the instantaneous effect, i.e., the causal relationship that occurred simultaneously due to the low-resolution data will not be captured by Granger causality. In this work, we propose Structure Hawkes Processes (SHPs) that leverage the instantaneous effect for learning the causal structure among events type in discrete-time event sequence. The proposed method is featured with the minorization-maximization of the likelihood function and a sparse optimization scheme. Theoretical results show that the instantaneous effect is a blessing rather than a curse, and the causal structure is identifiable under the existence of the instantaneous effect. Experiments on synthetic and real-world data verify the effectiveness of the proposed method.