# Causal Discovery in Hawkes Processes by Minimum Description Length

arXiv: https://arxiv.org/abs/2206.06124 · HTML: https://mlsanity.com/paper/2206.06124/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 30 references that are in the map.
- First posted on arXiv 10 Jun 2022.

## Builds on (most cited first, 5 of 5)

- [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)
- [Minimum Description Length Revisited](https://mlsanity.com/paper/1908.08484/) (2019)
- [Telling Cause from Effect using MDL-based Local and Global Regression](https://mlsanity.com/paper/1709.08915/) (2017)
- [Causal Inference on Multivariate and Mixed-Type Data](https://mlsanity.com/paper/1702.06385/) (2017)

## Built on by (most cited first, 11 of 11)

- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [Granger Causal Inference in Multivariate Hawkes Processes by Minimum Message Length](https://mlsanity.com/paper/2309.02027/) (2023)
- [Advances in Temporal Point Processes: Bayesian, Neural, and LLM Approaches](https://mlsanity.com/paper/2501.14291/) (2025)
- [Your Autoregressive Model Already Reveals the Causal Graph](https://mlsanity.com/paper/2602.01135/) (2026)
- [Consistency evaluation of benchmarks used for causal discovery](https://mlsanity.com/paper/2606.01789/) (2026)
- [Explainable History Distillation by Marked Temporal Point Process](https://mlsanity.com/paper/2311.07797/) (2023)
- [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)
- [Generating Causal Temporal Interaction Graphs for Counterfactual Validation of Temporal Link Prediction](https://mlsanity.com/paper/2602.02161/) (2026)
- [Resilient Concurrent Causal Discovery for Topological Event Sequences](https://mlsanity.com/paper/2608.21815/) (2026)
- [Inferring Causal Relations between Two Sequences of Events with Language Models](https://mlsanity.com/paper/2609.39406/) (2026)

## Abstract (arXiv)

Hawkes processes are a special class of temporal point processes which exhibit a natural notion of causality, as occurrence of events in the past may increase the probability of events in the future. Discovery of the underlying influence network among the dimensions of multi-dimensional temporal processes is of high importance in disciplines where a high-frequency data is to model, e.g. in financial data or in seismological data. This paper approaches the problem of learning Granger-causal network in multi-dimensional Hawkes processes. We formulate this problem as a model selection task in which we follow the minimum description length (MDL) principle. Moreover, we propose a general algorithm for MDL-based inference using a Monte-Carlo method and we use it for our causal discovery problem. We compare our algorithm with the state-of-the-art baseline methods on synthetic and real-world financial data. The synthetic experiments demonstrate superiority of our method incausal graph discovery compared to the baseline methods with respect to the size of the data. The results of experiments with the G-7 bonds price data are consistent with the experts knowledge.