Large-scale multiple testing: Fundamental limits of false discovery rate control and compound oracle
大规模多重检验：错误发现率控制的基本界限与复合预言规则AI 解读 ↓
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大规模多重检验：错误发现率控制的基本界限与复合预言规则
- 研究问题
- 在大量假设的检验中，错误发现率与错误未发现率之间能达到怎样的最优权衡，逐项决策是否足够？
- 方法与思路
- 作者在两组随机混合模型中研究假设数量趋于无穷时的最优权衡，比较复合规则、可分离规则及不同错误控制准则。
- 材料陈述的贡献
- 摘要称，最优 FDR–FNR 权衡需要复合规则；控制 FDP 的高概率权衡则与边际错误率准则下的权衡一致。
- 阅读关注点
- 应核对混合模型与规则类别的定义、预言规则使用哪些已知信息，以及期望控制和高概率控制的理论差异。
- 阅读边界
- 索引摘要版本未注明，未给出最优曲线、模型条件或可实施算法；不能将渐近预言结论视为有限样本保证。
原文摘要
The false discovery rate (FDR) and the false nondiscovery rate (FNR), defined as the expected false discovery proportion (FDP) and the false nondiscovery proportion (FNP), are the most popular benchmarks for multiple testing. Despite the theoretical and algorithmic advances in recent years, the optimal trade-off between the FDR and the FNR has been largely unknown, except for certain restricted classes of decision rules, for example, separable rules, or for other performance metrics, for example, the marginal FDR and the marginal FNR (mFDR and mFNR). In this paper we determine the asymptotically optimal FDR-FNR trade-off under the two-group random mixture model when the number of hypotheses tends to infinity. Distinct from the optimal mFDR-mFNR trade-off, which is achieved by separable decision rules, the optimal FDR-FNR trade-off requires compound rules, even in the large-sample limit and for models as simple as the Gaussian location model. This suboptimality of separable rules also holds for other objectives, such as maximizing the expected number of true discoveries. Finally, to address the limitation of the FDR, which only controls the expectation but not the fluctuation of the FDP, we also determine the optimal tradeoff when the FDP is controlled with high probability and show it coincides with that of the mFDR and the mFNR. Extensions to models with a fixed nonnull proportion are also obtained.