Sequential change point detection for multivariate autocorrelated data is a very common problem in practice. However, when the sensing resources are limited, only a subset of variables from the multivariate system can be observed at each sensing time point. This raises the problem of partially observable multi-sensor sequential change point detection. For it, we propose a detection scheme called adaptive upper confidence region with state space model (AUCRSS). It models multivariate time series via a state space model (SSM), and uses an adaptive sampling policy for efficient change point detection and localization. A partially-observable Kalman filter algorithm is developed for online inference of SSM, and accordingly, a change point detection scheme based on a generalized likelihood ratio test is developed. How its detection power relates to the adaptive sampling strategy is analyzed. Meanwhile, by treating the detection power as a reward, its connection with the online combinatorial multi-armed bandit (CMAB) problem is formulated and an adaptive upper confidence region algorithm is proposed for adaptive sampling policy design. Theoretical analysis of the asymptotic average detection delay is performed, and thorough numerical studies with synthetic data and real-world data are conducted to demonstrate the effectiveness of our method.

翻译：针对多变量自相关数据的序列变点检测是实际应用中常见问题。然而，当传感资源受限时，每个检测时刻仅能观测多变量系统中的部分变量，由此产生部分可观测多传感器序列变点检测问题。为此，我们提出一种基于状态空间模型的自适应置信上界检测方案（AUCRSS）。该方案采用状态空间模型对多变量时间序列进行建模，并通过自适应采样策略实现高效的变点检测与定位。我们开发了部分可观测卡尔曼滤波算法用于状态空间模型的在线推理，并据此构建基于广义似然比检验的变点检测方法。本文分析了检测效能与自适应采样策略之间的关联，同时将检测效能视为回报，建立了与在线组合多臂老虎机（CMAB）问题的联系，提出用于自适应采样策略设计的自适应置信上界算法。完成了渐近平均检测延迟的理论分析，并通过合成数据与真实数据的全面数值实验验证了方法的有效性。