False Discovery Rate Control For Structured Multiple Testing: Asymmetric Rules And Conformal <i>Q</i>-values

The effective utilization of structural information in data while ensuring statistical validity poses a significant challenge in false discovery rate (FDR) analyses. Conformal inference provides rigorous theory for grounding complex machine learning methods without relying on strong assumptions or highly idealized models. However, existing conformal methods have limitations in handling structured multiple testing, as their validity often requires the deployment of symmetric decision rules, which assume the exchangeability of data points and permutation-invariance of fitting algorithms. To overcome these limitations, we introduce the pseudo local index of significance (PLIS) procedure, which is capable of accommodating <i>asymmetric rules</i> and requires only <i>pairwise exchangeability</i> between the null conformity scores. We demonstrate that PLIS offers finite-sample guarantees in FDR control and the ability to assign higher weights to relevant data points. Numerical results confirm the effectiveness and robustness of PLIS and demonstrate improvements in power compared to existing model-free methods in various scenarios. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

在错误发现率（false discovery rate, FDR）分析领域，如何在确保统计有效性的同时高效利用数据中的结构信息，是一项重大挑战。共形推断（conformal inference）可为复杂机器学习方法提供严谨的理论支撑，无需依赖强假设或高度理想化的模型。然而，现有共形方法在处理结构化多重检验时存在局限：其有效性通常需要采用对称决策规则，而该规则假定数据点具备可交换性，且拟合算法具有置换不变性。为克服上述局限，我们提出了伪局部显著性指数（pseudo local index of significance, PLIS）流程，该方法能够兼容非对称规则（asymmetric rules），且仅要求零假设一致性得分之间满足两两可交换性（pairwise exchangeability）。我们证明，PLIS可实现错误发现率控制的有限样本保证，并能为相关数据点分配更高权重。数值实验结果验证了PLIS的有效性与鲁棒性，且相较于现有无模型方法，在多种场景下均展现出更优的检验功效。本文的补充材料可在线获取，其中包含了可用于复现研究成果的标准化材料说明。

搜集汇总

背景与挑战

背景概述

该数据集为一项关于结构化多重检验中错误发现率控制的研究，提出了一种名为PLIS的新方法，能够处理不对称规则并仅需两两可交换性假设，在有限样本下保证FDR控制并提高数据点权重分配。数据集包含论文的补充材料，如代码和文档，适用于生物化学、社会学等跨学科领域。