Online Score Statistics for Detecting Clustered Change in Network Point Processes

TL;DR

This paper introduces an online detection method for local changes in network point processes, specifically Hawkes processes, using scan score statistics to efficiently identify shifts in data distribution with controlled false alarms.

Contribution

It develops a novel scan score statistic-based detection procedure for multivariate Hawkes processes that does not require post-change parameter estimation, improving computational efficiency.

Findings

Effective detection of change points in simulated data

Successful application to real stock exchange data

Controlled false discovery rate via importance sampling

Abstract

We consider online monitoring of the network event data to detect local changes in a cluster when the affected data stream distribution shifts from one point process to another with different parameters. Specifically, we are interested in detecting a change point that causes a shift of the underlying data distribution that follows a multivariate Hawkes process with exponential decay temporal kernel, whereby the Hawkes process is considered to account for spatio-temporal correlation between observations. The proposed detection procedure is based on scan score statistics. We derive the asymptotic distribution of the statistic, which enables the self-normalizing property and facilitates the approximation of the instantaneous false alarm probability and the average run length. When detecting a change in the Hawkes process with non-vanishing self-excitation, the procedure does not require estimating the post-change network parameter while assuming the temporal decay parameter, which enjoys computational efficiency. We further present an efficient procedure to accurately determine the false discovery rate via importance sampling, as validated by numerical examples. Using simulated and real stock exchange data, we show the effectiveness of the proposed method in detecting change while enjoying computational efficiency.