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.

翻译：本文研究多元非齐次泊松点过程时间序列的在线变点检测问题。该设定常见于地震学、气候监测和流行病监测等应用领域，但在机器学习与统计学文献中尚未得到充分探索。我们提出一种利用低秩矩阵表示多元泊松强度函数的方法，从而形成一种自适应的非参数检测流程。所提算法为单次遍历算法，对每个新观测值仅需恒定计算成本，与时间序列的已观测长度无关。我们提供了控制整体误报概率的理论保证，并刻画了时间依赖性条件下的检测延迟。此外，我们针对具有时间依赖性的泊松点过程时间序列提出了一种新的矩阵伯恩斯坦不等式，该不等式本身可能具有独立的研究价值。数值实验表明，所提方法在统计上具有鲁棒性，在计算上具有高效性。