A Bandit Approach to Multiple Testing with False Discovery Control
A Bandit Approach to Multiple Testing with False Discovery Control
复制标题
通过错误发现控制进行多重测试的强盗方法
DOI：
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发表时间：
2018
期刊：
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通讯作者：
Lalit P. Jain
中科院分区：
文献类型：
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作者：
Kevin G. Jamieson;Lalit P. Jain
我们提出了一种用于多次测试的自适应抽样方法，该方法旨在最大化统计能力，同时确保随时进行错误发现控制。我们考虑$n$分布，其平均值按它们是否低于或等于基线(空值)与高于基线(实际正值)进行划分。此外，可以对每个分布进行顺序和重复采样。受多臂强盗文献的启发，我们提供了一种算法，它使用尽可能少的样本来超过目标真阳性比例(即发现的实际阳性比例)，同时随时控制错误发现比例(预测为实际阳性的空值)。我们的样本复杂度结果与已知信息理论下界相符，通过仿真，我们显示出比均匀采样和自适应消去式算法有显著的性能改善。鉴于该方法的简单性和样本效率，该方法有望在生物科学、药物发现的临床测试和在线A/B/N测试问题中广泛采用。
We propose an adaptive sampling approach for multiple testing which aims to maximize statistical power while ensuring anytime false discovery control. We consider $n$ distributions whose means are partitioned by whether they are below or equal to a baseline (nulls), versus above the baseline (actual positives). In addition, each distribution can be sequentially and repeatedly sampled. Inspired by the multi-armed bandit literature, we provide an algorithm that takes as few samples as possible to exceed a target true positive proportion (i.e. proportion of actual positives discovered) while giving anytime control of the false discovery proportion (nulls predicted as actual positives). Our sample complexity results match known information theoretic lower bounds and through simulations we show a substantial performance improvement over uniform sampling and an adaptive elimination style algorithm. Given the simplicity of the approach, and its sample efficiency, the method has promise for wide adoption in the biological sciences, clinical testing for drug discovery, and online A/B/n testing problems.