# Learning Granger Causality for Hawkes Processes

arXiv: https://arxiv.org/abs/1602.04511 · HTML: https://mlsanity.com/paper/1602.04511/

## Key facts

- Cited by 69 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Feb 2016.

## Built on by (most cited first, 30 of 69)

- [Transformer Embeddings of Irregularly Spaced Events and Their Participants](https://mlsanity.com/paper/2201.00044/) (2021)
- [Granger Causality: A Review and Recent Advances](https://mlsanity.com/paper/2105.02675/) (2021)
- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [Exploring Generative Neural Temporal Point Process](https://mlsanity.com/paper/2208.01874/) (2022)
- [Counterfactual Temporal Point Processes](https://mlsanity.com/paper/2111.07603/) (2021)
- [THP: Topological Hawkes Processes for Learning Causal Structure on Event Sequences](https://mlsanity.com/paper/2105.10884/) (2021)
- [Deep Graph Memory Networks for Forgetting-Robust Knowledge Tracing](https://mlsanity.com/paper/2108.08105/) (2021)
- [Cardinality-Regularized Hawkes-Granger Model](https://mlsanity.com/paper/2208.10671/) (2022)
- [Structural Hawkes Processes for Learning Causal Structure from Discrete-Time Event Sequences](https://mlsanity.com/paper/2305.05986/) (2023)
- [Mitigating Performance Saturation in Neural Marked Point Processes: Architectures and Loss Functions](https://mlsanity.com/paper/2107.03354/) (2021)
- [Learning with Asymmetric Kernels: Least Squares and Feature Interpretation](https://mlsanity.com/paper/2202.01397/) (2022)
- [Causal Discovery in Hawkes Processes by Minimum Description Length](https://mlsanity.com/paper/2206.06124/) (2022)
- [An Empirical Study: Extensive Deep Temporal Point Process](https://mlsanity.com/paper/2110.09823/) (2021)
- [In-Context Learning of Temporal Point Processes with Foundation Inference Models](https://mlsanity.com/paper/2509.24762/) (2025)
- [Nonparametric Conditional Local Independence Testing](https://mlsanity.com/paper/2203.13559/) (2022)
- [Learning Granger Causality from Instance-wise Self-attentive Hawkes Processes](https://mlsanity.com/paper/2402.03726/) (2024)
- [Granger Causal Chain Discovery for Sepsis-Associated Derangements via Continuous-Time Hawkes Processes](https://mlsanity.com/paper/2209.04480/) (2022)
- [Neuro-Symbolic Temporal Point Processes](https://mlsanity.com/paper/2406.03914/) (2024)
- [Temporal Attention Augmented Transformer Hawkes Process](https://mlsanity.com/paper/2112.14472/) (2021)
- [FaDIn: Fast Discretized Inference for Hawkes Processes with General Parametric Kernels](https://mlsanity.com/paper/2210.04635/) (2022)
- [Universal Transformer Hawkes Process with Adaptive Recursive Iteration](https://mlsanity.com/paper/2112.14479/) (2021)
- [TNPAR: Topological Neural Poisson Auto-Regressive Model for Learning Granger Causal Structure from Event Sequences](https://mlsanity.com/paper/2306.14114/) (2023)
- [Granger Causal Inference in Multivariate Hawkes Processes by Minimum Message Length](https://mlsanity.com/paper/2309.02027/) (2023)
- [Unveiling Latent Causal Rules: A Temporal Point Process Approach for Abnormal Event Explanation](https://mlsanity.com/paper/2402.05946/) (2024)
- [TEE4EHR: Transformer Event Encoder for Better Representation Learning in Electronic Health Records](https://mlsanity.com/paper/2402.06367/) (2024)
- [Advances in Temporal Point Processes: Bayesian, Neural, and LLM Approaches](https://mlsanity.com/paper/2501.14291/) (2025)
- [Scalable Marked Point Processes for Exchangeable and Non-Exchangeable Event Sequences](https://mlsanity.com/paper/2105.14574/) (2021)
- [DriPP: Driven Point Processes to Model Stimuli Induced Patterns in M/EEG Signals](https://mlsanity.com/paper/2112.06652/) (2021)
- [VAC2: Visual Analysis of Combined Causality in Event Sequences](https://mlsanity.com/paper/2206.05420/) (2022)
- [Online Learning for Mixture of Multivariate Hawkes Processes](https://mlsanity.com/paper/2208.07961/) (2022)

## Abstract (arXiv)

Learning Granger causality for general point processes is a very challenging task. In this paper, we propose an effective method, learning Granger causality, for a special but significant type of point processes --- Hawkes process. We reveal the relationship between Hawkes process's impact function and its Granger causality graph. Specifically, our model represents impact functions using a series of basis functions and recovers the Granger causality graph via group sparsity of the impact functions' coefficients. We propose an effective learning algorithm combining a maximum likelihood estimator (MLE) with a sparse-group-lasso (SGL) regularizer. Additionally, the flexibility of our model allows to incorporate the clustering structure event types into learning framework. We analyze our learning algorithm and propose an adaptive procedure to select basis functions. Experiments on both synthetic and real-world data show that our method can learn the Granger causality graph and the triggering patterns of the Hawkes processes simultaneously.