# Detecting Structural Shifts in Multivariate Hawkes Processes with Fr'echet Statistics

arXiv: https://arxiv.org/abs/2308.06769 · HTML: https://mlsanity.com/paper/2308.06769/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 26 references that are in the map.
- First posted on arXiv 13 Aug 2023.

## Builds on (most cited first, 11 of 11)

- [Fr'echet Regression for Random Objects with Euclidean Predictors](https://mlsanity.com/paper/1608.03012/) (2016)
- [Uncovering Causality from Multivariate Hawkes Integrated Cumulants](https://mlsanity.com/paper/1607.06333/) (2016)
- [Discovering Latent Network Structure in Point Process Data](https://mlsanity.com/paper/1402.0914/) (2014)
- [Learning Network of Multivariate Hawkes Processes: A Time Series Approach](https://mlsanity.com/paper/1603.04319/) (2016)
- [Sequential change-point detection for mutually exciting point processes over networks](https://mlsanity.com/paper/2102.05724/) (2021)
- [Cumulants of Hawkes point processes](https://mlsanity.com/paper/1409.5353/) (2014)
- [Fr'echet Change Point Detection](https://mlsanity.com/paper/1911.11864/) (2019)
- [Online Detection Of Supply Chain Network Disruptions Using Sequential Change-Point Detection for Hawkes Processes](https://mlsanity.com/paper/2211.12091/) (2022)
- [Stein Variational Online Changepoint Detection with Applications to Hawkes Processes and Neural Networks](https://mlsanity.com/paper/1901.07987/) (2019)
- [Controlling Segregation in Social Network Dynamics as an Edge Formation Game](https://mlsanity.com/paper/2108.12741/) (2021)
- [Fr'echet Statistics Based Change Point Detection in Dynamic Social Networks](https://mlsanity.com/paper/2303.10753/) (2023)

## Abstract (arXiv)

This paper proposes a new approach for change point detection in multivariate Hawkes processes using Fr'echet statistic of a network. The method splits the point process into overlapping windows, estimates kernel matrices in each window, and reconstructs the signed Laplacians by treating the kernel matrices as the adjacency matrices of the causal network. We demonstrate the effectiveness of our method through experiments on both simulated and cryptocurrency datasets. Our results show that our method is capable of accurately detecting and characterizing changes in the causal structure of multivariate Hawkes processes, and may have potential applications in fields such as finance and neuroscience. The proposed method is an extension of previous work on Fr'echet statistics in point process settings and represents an important contribution to the field of change point detection in multivariate point processes.