Sequential Change-Point Detection for Hawkes Processes Over Networks

• Activity Number: 124 - Algorithms for Threat Detection
• Type: Topic-Contributed
• Date/Time: Monday, August 9, 2021 : 1:30 PM to 3:20 PM
• Sponsor: Section on Statistics in Defense and National Security
• Author(s): Yao Xie* and Haoyun Wang and Liyan Xie and Simon Mak and Alex Cuozzo
• Companies: Georgia Institute of Technology and Georgia Institute of Technology and Georgia Institute of Technology and Duke University and Duke University
• Keywords: Change-point detection; Hawkes processes; Networks; CUSUM; Sequential data

Abstract

Hawkes processes over networks are becoming very popular due to their flexibility in modeling the complex dependence between discrete events data and wide applications in social networks and human activity data (such as crime data). Despite the rapid progress in establishing point estimates, much less has been studied for sequential change detection for Hawkes processes over networks, which is critical for threat and anomaly detection. We developed a new likelihood-based CUSUM procedure for detecting abrupt changes in the Hawkes processes, particularly tackling the challenge posed by complex temporal dependency. We also show its competitive performance with several alternatives, such as the generalized likelihood ratio statistic and the score statistics using numerical simulations and real data.