Optimal Parallel Sequential Change Detection Under Generalized Performance Measures
Optimal Parallel Sequential Change Detection Under Generalized Performance Measures
复制标题
DOI：
10.1109/tsp.2022.3231521
复制
发表时间：
2022-06
影响因子：
5.4
通讯作者：
Zexian Lu;Yunxiao Chen;Xiaoou Li
中科院分区：
文献类型：
--
作者：
Zexian Lu;Yunxiao Chen;Xiaoou Li
本文考虑并行数据流中的变化点检测，这是分析大规模实时流数据时经常遇到的问题。每个流可能有自己的变化点，在那里它的数据具有分布变化。对于连续观察的数据，决策者需要声明在每个时间点流是否已经发生了变化。一旦流被声明为已更改，它将被永久停用，以便不再收集其未来的数据。这是一个复合决策问题，因为决策者可能希望优化某些涉及所有流作为一个整体的复合性能指标。因此，对于不同的流，决策不是独立的。我们的贡献是三方面的。首先，我们提出了一个通用的框架，复合性能指标，包括在现有的作品中考虑的特殊情况下，并引入新的连接密切的性能指标，单流顺序变化检测和大规模的假设检验。第二，数据驱动的决策程序在这个框架下开发。最后，最优性结果建立建议的决策程序。所提出的方法和理论进行了评估模拟研究和案例研究。
This paper considers the detection of change points in parallel data streams, a problem widely encountered when analyzing large-scale real-time streaming data. Each stream may have its own change point, at which its data has a distributional change. With sequentially observed data, a decision maker needs to declare whether changes have already occurred to the streams at each time point. Once a stream is declared to have changed, it is deactivated permanently so that its future data will no longer be collected. This is a compound decision problem in the sense that the decision maker may want to optimize certain compound performance metrics that concern all the streams as a whole. Thus, the decisions are not independent for different streams. Our contribution is three-fold. First, we propose a general framework for compound performance metrics that includes the ones considered in the existing works as special cases and introduces new ones that connect closely with the performance metrics for single-stream sequential change detection and large-scale hypothesis testing. Second, data-driven decision procedures are developed under this framework. Finally, optimality results are established for the proposed decision procedures. The proposed methods and theory are evaluated by simulation studies and a case study.