Sequential change-point detection for mutually exciting point processes over networks

TL;DR

This paper introduces a new online CUSUM method for detecting change-points in Hawkes networks, improving efficiency and accuracy over existing techniques, with applications in neuronal, sensor, and social networks.

Contribution

The paper develops a computationally efficient, recursive CUSUM procedure for online change-point detection in Hawkes networks, with theoretical guarantees and superior performance.

Findings

Proposed CUSUM outperforms Shewhart, GLR, and score-based methods.

Method is memory-efficient and suitable for real-time applications.

Validated through simulations and neuronal network data.

Abstract

We present a new CUSUM procedure for sequentially detecting change-point in the self and mutual exciting processes, a.k.a. Hawkes networks using discrete events data. Hawkes networks have become a popular model for statistics and machine learning due to their capability in modeling irregularly observed data where the timing between events carries a lot of information. The problem of detecting abrupt changes in Hawkes networks arises from various applications, including neuronal imaging, sensor network, and social network monitoring. Despite this, there has not been a computationally and memory-efficient online algorithm for detecting such changes from sequential data. We present an efficient online recursive implementation of the CUSUM statistic for Hawkes processes, both decentralized and memory-efficient, and establish the theoretical properties of this new CUSUM procedure. We then show that the proposed CUSUM method achieves better performance than existing methods, including the Shewhart procedure based on count data, the generalized likelihood ratio (GLR) in the existing literature, and the standard score statistic. We demonstrate this via a simulated example and an application to population code change-detection in neuronal networks.