Partially-Observable Sequential Change-Point Detection for
  Autocorrelated Data via Upper Confidence Region
Haijie Xu Xiaochen Xian Chen Zhang Kaibo Liu
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.