An adaptive approach for online monitoring of large-scale data streams
提出一种自适应top-r方法，通过并行运行局部检测程序并利用Benjamini-Hochberg错误发现率控制程序，自适应估计变化数据流的数量，用于监测大规模数据流中的变化。
In this article, we propose an adaptive top-r method to monitor large-scale data streams where the change may affect a set of unknown data streams at some unknown time. Motivated by parallel and distributed computing, we propose to develop global monitoring schemes by parallel running local detection procedures and then use the Benjamin–Hochberg false discovery rate control procedure to estimate the number of changed data streams adaptively. Our approach is illustrated in two concrete examples: one is a homogeneous case when all data streams are independent and identically distributed with the same known pre-change and post-change distributions. The other is when all data are normally distributed, and the mean shifts are unknown and can be positive or negative. Theoretically, we show that when the pre-change and post-change distributions are completely specified, our proposed method can estimate the number of changed data streams for both the pre-change and post-change status. Moreover, we perform simulations and two case studies to show its detection efficiency.