# Uncertainty Quantification for Inferring Hawkes Networks

arXiv: https://arxiv.org/abs/2006.07506 · HTML: https://mlsanity.com/paper/2006.07506/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2020.

## Built on by (most cited first, 8 of 8)

- [Sequential change-point detection for mutually exciting point processes over networks](https://mlsanity.com/paper/2102.05724/) (2021)
- [SMURF-THP: Score Matching-based UnceRtainty quantiFication for Transformer Hawkes Process](https://mlsanity.com/paper/2310.16336/) (2023)
- [Granger Causal Chain Discovery for Sepsis-Associated Derangements via Continuous-Time Hawkes Processes](https://mlsanity.com/paper/2209.04480/) (2022)
- [Bayesian Neural Hawkes Process for Event Uncertainty Prediction](https://mlsanity.com/paper/2112.14474/) (2021)
- [Granger Causal Inference in Multivariate Hawkes Processes by Minimum Message Length](https://mlsanity.com/paper/2309.02027/) (2023)
- [PERCEPT: a new online change-point detection method using topological data analysis](https://mlsanity.com/paper/2203.04246/) (2022)
- [Deep spatio-temporal point processes: Advances and new directions](https://mlsanity.com/paper/2504.06364/) (2025)
- [Fine-Grained ε-Margin Closed-Form Stabilization of Parametric Hawkes Processes](https://mlsanity.com/paper/2105.03800/) (2021)

## Abstract (arXiv)

Multivariate Hawkes processes are commonly used to model streaming networked event data in a wide variety of applications. However, it remains a challenge to extract reliable inference from complex datasets with uncertainty quantification. Aiming towards this, we develop a statistical inference framework to learn causal relationships between nodes from networked data, where the underlying directed graph implies Granger causality. We provide uncertainty quantification for the maximum likelihood estimate of the network multivariate Hawkes process by providing a non-asymptotic confidence set. The main technique is based on the concentration inequalities of continuous-time martingales. We compare our method to the previously-derived asymptotic Hawkes process confidence interval, and demonstrate the strengths of our method in an application to neuronal connectivity reconstruction.