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：我们研究了多元非齐次泊松点过程时间序列的在线变点检测问题。该设定在地震学、气候监测和流行病监测等应用中普遍存在，但在机器学习和统计学文献中尚未得到充分探索。我们提出了一种方法，利用低秩矩阵表示多元泊松强度函数，从而得到自适应的非参数检测程序。该算法为单遍算法，每次新观测仅需恒定计算成本，与已观测时间序列长度无关。我们提供了控制整体误报概率的理论保证，并刻画了时间依赖下的检测延迟特性。此外，针对时间依赖的泊松点过程时间序列，我们推导了新的矩阵伯恩斯坦不等式，该结果可能具有独立的研究价值。数值实验表明，我们的方法在统计稳健性和计算效率方面均表现优异。