Online Change Point Detection for Multivariate Inhomogeneous Poisson Processes Time Series

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.

Many important systems generate streams of events: earthquakes occur at different locations and depths, disease cases appear across regions, and climate extremes emerge over time. In these settings, scientists often need to detect quickly when the pattern of events changes, because a delay may mean missing early signs of a new hazard or outbreak. This paper studies how to detect such changes automatically while the data are still arriving. We design a method that represents complicated event patterns in a compact way, allowing it to adapt to different spatial and temporal structures without making overly rigid assumptions. The method processes each new observation only once and keeps the computing cost stable, even as the time series becomes very long. We also provide mathematical guarantees showing that the method can limit false alarms and detect real changes with controlled delay, even when observations over time are dependent. Experiments show that the method is reliable and computationally efficient. This work can help build faster monitoring tools for applications such as seismology, climate science, and epidemic surveillance.