# Granger Causal Inference in Multivariate Hawkes Processes by Minimum Message Length

arXiv: https://arxiv.org/abs/2309.02027 · HTML: https://mlsanity.com/paper/2309.02027/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 43 references that are in the map.
- First posted on arXiv 5 Sep 2023.

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

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [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)
- [Truncated Matrix Power Iteration for Differentiable DAG Learning](https://mlsanity.com/paper/2208.14571/) (2022)
- [Sparse and low-rank multivariate Hawkes processes](https://mlsanity.com/paper/1501.00725/) (2015)
- [Cardinality-Regularized Hawkes-Granger Model](https://mlsanity.com/paper/2208.10671/) (2022)
- [Causal Discovery in Hawkes Processes by Minimum Description Length](https://mlsanity.com/paper/2206.06124/) (2022)
- [A Study of Error Variance Estimation in Lasso Regression](https://mlsanity.com/paper/1311.5274/) (2013)
- [Uncertainty Quantification for Inferring Hawkes Networks](https://mlsanity.com/paper/2006.07506/) (2020)
- [Granger Causal Chain Discovery for Sepsis-Associated Derangements via Continuous-Time Hawkes Processes](https://mlsanity.com/paper/2209.04480/) (2022)
- [Causal Graph Discovery from Self and Mutually Exciting Time Series](https://mlsanity.com/paper/2301.11197/) (2023)

## Built on by (most cited first, 3 of 3)

- [Advances in Temporal Point Processes: Bayesian, Neural, and LLM Approaches](https://mlsanity.com/paper/2501.14291/) (2025)
- [Causal Structure Learning in Hawkes Processes with Complex Latent Confounder Networks](https://mlsanity.com/paper/2508.11727/) (2025)
- [Resilient Concurrent Causal Discovery for Topological Event Sequences](https://mlsanity.com/paper/2608.21815/) (2026)

## Abstract (arXiv)

Multivariate Hawkes processes (MHPs) are versatile probabilistic tools used to model various real-life phenomena: earthquakes, operations on stock markets, neuronal activity, virus propagation and many others. In this paper, we focus on MHPs with exponential decay kernels and estimate connectivity graphs, which represent the Granger causal relations between their components. We approach this inference problem by proposing an optimization criterion and model selection algorithm based on the minimum message length (MML) principle. MML compares Granger causal models using the Occam's razor principle in the following way: even when models have a comparable goodness-of-fit to the observed data, the one generating the most concise explanation of the data is preferred. While most of the state-of-art methods using lasso-type penalization tend to overfitting in scenarios with short time horizons, the proposed MML-based method achieves high F1 scores in these settings. We conduct a numerical study comparing the proposed algorithm to other related classical and state-of-art methods, where we achieve the highest F1 scores in specific sparse graph settings. We illustrate the proposed method also on G7 sovereign bond data and obtain causal connections, which are in agreement with the expert knowledge available in the literature.