Structure–Adaptive Sequential Testing for Online False Discovery Rate Control
Structure–Adaptive Sequential Testing for Online False Discovery Rate Control
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DOI：
10.1080/01621459.2021.1955688
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发表时间：
2020-02
影响因子：
3.7
通讯作者：
Bowen Gang;Wenguang Sun;Weinan Wang
中科院分区：
文献类型：
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作者：
Bowen Gang;Wenguang Sun;Weinan Wang
摘要考虑一系列假设的在线测试，其中必须在下一个数据点到达之前做出实时决策。要求在所有决策点控制错误率。由于更严格的误差约束和未来数据的缺乏，传统的同时测试规则不再适用。此外，当总错误预算或阿尔法财富耗尽时，在线决策过程可能会停止。提出了一类新的结构自适应序贯测试(SAST)规则，用于在线控制错误发现率(FDR)。我们提案中的一个关键要素是一种新的阿尔法投资算法，它准确地表征了顺序决策中的得失。SAST捕获数据流的时变结构，以持续的方式自适应地学习最优阈值，并优化不同时间段的阿尔法财富分配。我们给出了理论和数值结果，表明SAST对于在线FDR控制是渐近有效的，并且比现有的在线测试规则获得了显著的功率增益。
Abstract Consider the online testing of a stream of hypotheses where a real-time decision must be made before the next data point arrives. The error rate is required to be controlled at all decision points. Conventional simultaneous testing rules are no longer applicable due to the more stringent error constraints and absence of future data. Moreover, the online decision-making process may come to a halt when the total error budget, or alpha-wealth, is exhausted. This work develops a new class of structure-adaptive sequential testing (SAST) rules for online false discovery rate (FDR) control. A key element in our proposal is a new alpha-investing algorithm that precisely characterizes the gains and losses in sequential decision making. SAST captures time varying structures of the data stream, learns the optimal threshold adaptively in an ongoing manner and optimizes the alpha-wealth allocation across different time periods. We present theory and numerical results to show that SAST is asymptotically valid for online FDR control and achieves substantial power gain over existing online testing rules.