Online Change Point Detection for Multivariate Poisson Point Processes

Xiaokai Luo, Carlos Misael Madrid Padilla, Haotian Xu, OSCAR HERNAN MADRID PADILLA

Keywords: Online change point detection, poisson processes, false alarm control, and detection delay

Abstract: We study online change point detection for multivariate inhomogeneous Poisson point process data streams. Although this setting is common in applications such as earthquake seismology, climate monitoring, and epidemic surveillance, it remains largely underexplored in the statistics and data science literature. We propose a method that uses low-rank matrices to represent the multivariate Poisson intensity function, resulting in an adaptive procedure to detect local changes in a nonparametric setting. Our algorithm processes the stream in a single-pass, and the per-observation cost is a constant independent of the elapsed stream length. We also provide theoretical guarantees to control the overall false alarm probability and quantify the detection delay. Numerical experiments demonstrate that our method is statistically robust and computationally efficient.

Primary Area: learning theory

Submission Number: 8042