Online Change Point Detection for Multivariate Inhomogeneous Poisson Processes Time Series

2026-01-28

AI Summary

This work addresses the problem of online change-point detection in multivariate non-homogeneous Poisson processes, which arise in applications such as earthquake monitoring, climate analysis, and epidemic surveillance. The authors propose an adaptive nonparametric method that represents the intensity function via a low-rank matrix structure. Requiring only a single pass over the data stream with constant per-step computational complexity, the approach models the multivariate intensity through this low-rank formulation and introduces a novel Matrix Bernstein inequality tailored to temporally dependent Poisson processes. This theoretical advance enables provably controlled false alarm rates and low detection latency. Empirical evaluations demonstrate the method’s superior statistical robustness and computational efficiency compared to existing alternatives.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

Abstract

We study online change point detection for multivariate inhomogeneous Poisson point process time series. This setting arises commonly in applications such as earthquake seismology, climate monitoring, and epidemic surveillance, yet remains underexplored in the machine learning and statistics literature. We propose a method that uses low-rank matrices to represent the multivariate Poisson intensity functions, resulting in an adaptive nonparametric detection procedure. Our algorithm is single-pass and requires only constant computational cost per new observation, independent of the elapsed length of the time series. We provide theoretical guarantees to control the overall false alarm probability and characterize the detection delay under temporal dependence. We also develop a new Matrix Bernstein inequality for temporally dependent Poisson point process time series, which may be of independent interest. Numerical experiments demonstrate that our method is both statistically robust and computationally efficient.

Problem

• online change point detection
• multivariate inhomogeneous Poisson processes
• time series
• change point

Innovation

• online change point detection
• multivariate inhomogeneous Poisson process
• low-rank matrix representation
• constant computational cost
• Matrix Bernstein inequality