# The Multivariate Hawkes Process in High Dimensions: Beyond Mutual Excitation

arXiv: https://arxiv.org/abs/1707.04928 · HTML: https://mlsanity.com/paper/1707.04928/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jul 2017.

## Built on by (most cited first, 9 of 9)

- [Granger Causality: A Review and Recent Advances](https://mlsanity.com/paper/2105.02675/) (2021)
- [On the Predictive Accuracy of Neural Temporal Point Process Models for Continuous-time Event Data](https://mlsanity.com/paper/2306.17066/) (2023)
- [Maximum Likelihood Estimation for Hawkes Processes with self-excitation or inhibition](https://mlsanity.com/paper/2103.05299/) (2021)
- [Spatiotemporal Clustering with Neyman-Scott Processes via Connections to Bayesian Nonparametric Mixture Models](https://mlsanity.com/paper/2201.05044/) (2022)
- [Scalable Marked Point Processes for Exchangeable and Non-Exchangeable Event Sequences](https://mlsanity.com/paper/2105.14574/) (2021)
- [Causal Discovery in High-Dimensional Point Process Networks with Hidden Nodes](https://mlsanity.com/paper/2109.10947/) (2021)
- [Joint Estimation and Inference for Multi-Experiment Networks of High-Dimensional Point Processes](https://mlsanity.com/paper/2109.11634/) (2021)
- [Scalable and adaptive variational Bayes methods for Hawkes processes](https://mlsanity.com/paper/2212.00293/) (2022)
- [Latent Factor Point Processes for Patient Representation in Electronic Health Records](https://mlsanity.com/paper/2508.20327/) (2025)

## Abstract (arXiv)

The Hawkes process is a class of point processes whose future depends on their own history. Previous theoretical work on the Hawkes process is limited to a special case in which a past event can only increase the occurrence of future events, and the link function is linear. However, in neuronal networks and other real-world applications, inhibitory relationships may be present, and the link function may be non-linear. In this paper, we develop a new approach for investigating the properties of the Hawkes process without the restriction to mutual excitation or linear link functions. To this end, we employ a thinning process representation and a coupling construction to bound the dependence coefficient of the Hawkes process. Using recent developments on weakly dependent sequences, we establish a concentration inequality for second-order statistics of the Hawkes process. We apply this concentration inequality to cross-covariance analysis in the high-dimensional regime, and we verify the theoretical claims with simulation studies.