Online Change-Point Detection in High-Dimensional Covariance Structure with Application to Dynamic Networks
Lingjun Li, Jun Li; 24(51):1−44, 2023.
Abstract
This paper presents a novel approach for online change-point detection in high-dimensional data, specifically focusing on the covariance structure. The proposed method incorporates a stopping rule that allows for the detection of changes in covariance structure in real-time. The stopping rule is designed to accommodate spatial and temporal dependence, making it applicable to non-Gaussian data. Furthermore, an explicit expression for the average run length is derived, eliminating the need for time-consuming Monte Carlo simulations to determine the threshold level in the stopping rule. Additionally, an upper bound for the expected detection delay is established, providing insights into the impact of data dependence and the magnitude of change in the covariance structure. The accuracy of the theoretical results is confirmed through simulation studies. To demonstrate the practical utility of the proposed procedure, it is applied to detect changes in the brain’s covariance network using a resting-state fMRI dataset. The R package OnlineCOV provides the implementation of this methodology.
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