Online Change-Point Detection in High-Dimensional Covariance Structure with Application to Dynamic Networks
Online Change-Point Detection in High-Dimensional Covariance Structure with Application to Dynamic Networks
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发表时间：
2019-11
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通讯作者：
Lingjun Li;Jun Li
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作者：
Lingjun Li;Jun Li
在线数据分析中的一项重要任务是检测网络变化，如社区的分离或新社区的形成。针对这类应用，我们开发了一种高维数据协方差结构中的在线变点检测方法。为了在网络发生变化时尽早终止进程，提出了一种新的停止规则。该停止规则融合了空间和时间相关性，并且可以应用于非高斯数据。推导出了平均行程长度的显式表达式，使得无需运行耗时的蒙特卡罗模拟就可以很容易地获得停止规则中的阈值水平。我们还建立了期望检测延迟(EDD)的上界，它的表达式表明了数据相关性和协方差结构变化的大小的影响。通过仿真研究，验证了理论结果的准确性。通过在静息状态fMRI数据集中检测大脑网络的变化，说明了该方法的实用性。
One important task in online data analysis is detecting network change, such as dissociation of communities or formation of new communities. Targeting on this type of application, we develop an online change-point detection procedure in the covariance structure of high-dimensional data. A new stopping rule is proposed to terminate the process as early as possible when a network change occurs. The stopping rule incorporates spatial and temporal dependence, and can be applied to non-Gaussian data. An explicit expression for the average run length (ARL) is derived, so that the level of threshold in the stopping rule can be easily obtained with no need to run time-consuming Monte Carlo simulations. We also establish an upper bound for the expected detection delay (EDD), the expression of which demonstrates the impact of data dependence and magnitude of change in the covariance structure. Simulation studies are provided to confirm accuracy of the theoretical results. The practical usefulness of the proposed procedure is illustrated by detecting brain's network change in a resting-state fMRI dataset.