A1705
Title: Online change point detection for multivariate inhomogeneous Poisson processes time series
Authors: Xiaokai Luo - University of Notre Dame (United States)
Haotian Xu - Auburn University (United States)
Carlos Misael Madrid Padilla - Washington University in St Louis (United States) [presenting]
Oscar Hernan Madrid Padilla - UCLA (United States)
Abstract: Change point detection in streaming data is a fundamental problem in statistics and machine learning, with important applications in areas such as seismology, climate monitoring, and epidemic surveillance. The problem of online change point detection for multivariate inhomogeneous Poisson point process time series is studied, a setting that captures event-based data with complex temporal and spatial structure. A novel method is introduced that leverages low-rank Matrix representations of multivariate intensity functions, enabling flexible nonparametric modeling while maintaining computational scalability. The proposed procedure operates in a single-pass online fashion, requiring only constant computational cost per incoming observation, independent of the length of the time series. On the theoretical side, guarantees are established for controlling the false alarm probability and the detection delay is characterized under temporal dependence. A key technical contribution is a new Matrix Bernstein inequality for temporally dependent Poisson point processes, which may be of independent interest. Numerical experiments demonstrate the statistical robustness and computational efficiency of the proposed approach in realistic scenarios.
