基于条件FDR的高维数据流的在线监控  

Online Monitoring of High-Dimensional Data Streams Based on Conditional FDR

作　　者：齐德全 马辰瑶 施三支[1] 毕利 QI Dequan;MA Chenyao;SHI Sanzhi;BI Li(School of Mathematics and Statistics,Changchun University of Science and Technology,Changchun 130022)

机构地区：[1]长春理工大学数学与统计学院,长春130022

出　　处：《长春理工大学学报（自然科学版）》2024年第6期121-126,共6页Journal of Changchun University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金面上项目(12271271)。

摘　　要：传统的通过控制图监控高维数据流的方法,可能每时每刻都发出警报。在高维数据流之间具有一定相关结构、数据流可进可出的情况下,利用统计过程控制特点,提出了条件错误发现率(FDR)的思想,给出了在线监控高维数据流均值是否发生漂移的稳健方法。针对非正态高维数据流,通过将样本分割、聚合,结合SDA与EWMA构造满足对称性的监控统计量,通过条件错误发现率(FDR)确定动态的阈值进行在线监控。采用AR(1)模型来刻画数据流间的相关性,通过蒙特卡罗模拟从错误发现率与累积功效水平的角度研究了所提出方法的性能。数值模拟结果表明,该方法能达到较好的监控效果。In traditional methods for monitoring high-dimensional data streams using control charts,alarms are often triggered constantly,even when there is no significant change.In the case of high-dimensional data streams with inherent correlations and the flexibility of data entering and exiting over time,a robust approach for online monitoring is required.This paper introduces the concept of Conditional False Discovery Rate(FDR)to address this issue,proposing a method for robustly detecting shifts in the mean of high-dimensional data streams.For non-normal high-dimensional data streams,t he method involves partitioning and aggregating the samples,and then constructing monitoring statistics that satisfy symmetry by combining Sample Data Aggregation(SDA)with Exponentially Weighted Moving Average(EWMA)techniques.Dynamic thresholds for online monitoring are determined through the Conditional FDR approach.An AR(1)model is employed to capture the correlation structure between data streams.The performance of the proposed method is evaluated through Monte Carlo simulations,f ocusing on the trade-off between false discovery rate and power.Numerical simulation results indicate that the proposed method achieves satisfactory monitoring performance,providing a robust and effective solution for online monitoring of high-dimensional data streams.

关 键 词：高维数据流 错误发现率 对称数据聚合 统计过程控制 

分 类 号：O212[理学—概率论与数理统计] O213[理学—数学]