论文标题
在广义绩效指标下的最佳平行顺序更改检测
Optimal Parallel Sequential Change Detection under Generalized Performance Measures
论文作者
论文摘要
本文考虑了并行数据流中变更点的检测，这是分析大型实时流数据时广泛遇到的问题。每个流可能具有其自身的变更点，其数据具有分布更改。通过顺序观察到的数据，决策者需要声明是否在每个时间点都已经发生了变化。一旦宣布流进行了变更，它将被永久停用，以便不再收集其未来数据。从某种意义上说，这是一个复合决策问题，即决策者可能希望优化与整个流有关所有流有关的某些复合性能指标。因此，对于不同的流而言，这些决策不是独立的。我们的贡献是三倍。首先，我们为复合性能指标提出了一个一般框架，其中包括现有作品中的特殊情况下考虑的框架，并引入了与单个流程顺序更改检测和大规模假设测试的性能指标紧密相关的新框架。其次，数据驱动的决策程序是在此框架下制定的。最后，为拟议的决策程序建立了最佳结果。提出的方法和理论通过仿真研究和案例研究评估。
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.
