Optimal Parallel Sequential Change Detection under Generalized Performance Measures

TL;DR

This paper develops a comprehensive framework for parallel change detection in multiple data streams, introducing new performance metrics, data-driven decision procedures, and establishing their optimality, with validation through simulations and a case study.

Contribution

It proposes a unified framework for compound performance metrics, develops data-driven decision procedures, and proves their optimality in parallel change detection.

Findings

Framework includes existing and new performance metrics.

Decision procedures are shown to be optimal.

Methods are validated through simulations and a case study.

Abstract

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.