结构化假设空间中的有限资源错误发现率控制
Finite Resources False Discovery Rate Control in Structured Hypothesis Spaces
AI总结：
针对有限空分布样本和结构化假设空间，提出基于再生核的框架，通过两种决策规则在精确FDR控制与统计功效间权衡，并优化资源分配。
摘要：
科学发现依赖于大规模假设检验。然而，在控制错误发现的同时识别真正发现的能力面临重大挑战：获取相关参考数据（零分布）是资源密集型的，留下有限数据的不确定性，并且当假设空间存在固有结构时，程序应考虑该结构。在这里，我们提出了一个框架，用于在以下两种情况下控制错误发现率：当每个假设仅由有限数量的空分布样本支持，导致其p值不确定时；以及当假设空间具有任意结构时，仅要求通过合适的再生核表示该结构。我们提出了两种决策规则，它们对结构错误指定都具有鲁棒性，但在精确FDR控制和统计功效之间提供了不同的权衡。第一个规则保证精确的FDR控制；第二个规则通过将镜像统计控制适应到计数空间来最大化功效，利用分析框架在精确镜像对称放松时评估FDR控制。此外，RKHS框架带来的可处理性使我们能够直接研究有限数据的不确定性，我们利用这一点提出了一种有效分配零分布样本的策略。
英文摘要：
Scientific discovery relies on large-scale hypothesis testing. However, the capacity to identify true discoveries while controlling false discovery faces major challenges: obtaining relevant reference data (the null distribution) is resource-intensive, leaving finite-data uncertainty, and the procedure should account for the inherent structure in the hypothesis space, when such structure exists. Here, we present a framework for controlling the false discovery rate both when each hypothesis is evidenced only by a finite count of null draws, leaving its p-value uncertain, and when the hypothesis space carries arbitrary structure, requiring only that the structure be represented through a suitable reproducing kernel. We present two decision rules that are both robust to structural mis-specification, yet offer a distinct trade-off between exact FDR control and statistical power. The first rule guarantees exact FDR control; the second maximizes power by adapting mirror-statistic control into count space, utilizing an analytical framework to assess FDR control when exact mirror symmetry is relaxed. Furthermore, the tractability gained by the RKHS framework allows us to directly investigate finite-data uncertainties, which we leverage to suggest a policy for the efficient allocation of null distribution samples.
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