Partially‐Observable Sequential Change‐Point Detection for Autocorrelated Data via Adaptive Upper Confidence Region

ABSTRACT Sequential change‐point detection for multivariate autocorrelated data is a widely encountered challenge in real‐world applications. When sensing resources are limited, only a subset of variables from the multivariate system can be observed at each time point, giving rise to the problem of partially observable multi‐sensor sequential change‐point detection. To address this, we propose a novel detection framework called Adaptive Upper Confidence Region with State Space Model (AUCRSS). This approach models multivariate autocorrelated data using a state space model (SSM) and incorporates an adaptive sampling policy to enable efficient change‐point detection and localization. A partially observable Kalman filter is developed for online inference of the system state, and based on this, a change‐point detection procedure is constructed using a generalized likelihood ratio test. We analyze the relationship between detection power and the adaptive sampling strategy. Furthermore, by interpreting detection power as a reward signal, we establish a connection with the online combinatorial multi‐armed bandit (CMAB) problem and introduce an adaptive upper confidence region algorithm to guide the sampling policy design. We provide a theoretical analysis of the asymptotic detection power, and we demonstrate that our proposed method significantly outperforms the baseline algorithms through extensive numerical experiments on both synthetic and real‐world datasets.