Title: Online Change Point Detection for Multivariate Poisson Point Processes
Primary area: learning theory
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.