Optimal parallel sequential change detection under generalized performance measures

Zexian Lu, Yunxiao Chen and Xiaoou Li

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

Keywords: large-scale inference; multiple change detection; sequential analysis; multiple hypothesis testing (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 15 pages
Date: 2022-12-22
New Economics Papers: this item is included in nep-ecm
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Published in IEEE Transactions on Signal Processing, 22, December, 2022, 70, pp. 5967 - 5981. ISSN: 1053-587X

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