提出可动态调整的因果选择方法,让研究者根据数据自主权衡筛选数量与错误率。
Beyond Fixed False Discovery Rates: Post-Hoc Conformal Selection with E-Variables

- 基于校准数据生成多阶段候选集,每阶段附带数据驱动的错误发现比例估计
- 在真实数据上验证,可满足用户设定的效用约束,同时保持可靠的错误率控制
- 适用于基因组、神经影像等需灵活决策的领域,支持事后调整筛选标准
共形选择(CS)利用校准数据识别测试输入中可能满足预设最低质量要求的样本,同时控制假发现率(FDR)。现有方法在观察数据前固定目标FDR水平,无法根据实际数据情况动态调整筛选数量与错误率之间的平衡。例如,在基因组或神经影像研究中,研究者常依据统计量分布判断证据强度,并据此决定后续资源投入策略。为此,本文提出事后共形选择(PH-CS),生成一系列候选集路径,每个路径点均配有数据驱动的假发现比例(FDP)估计值。用户可根据自身效用函数任意选取路径上的操作点,以灵活权衡选择规模与FDR。PH-CS基于共形e-变量与e-Benjamini-Hochberg(e-BH)过程,证明其在有限样本下具有事后可靠性保证:估计的FDP与真实FDP之比的平均值不超过1,即估计值在第一阶意义上是真实FDR的有效上界。该方法还可扩展至控制一般风险下的质量要求。在合成与真实数据集上的实验表明,相较于传统CS,PH-CS能持续满足用户设定的效用约束,提供可靠FDP估计,并保持竞争性的FDR控制性能。
原文摘要 · Abstract (English)
Conformal selection (CS) uses calibration data to identify test inputs whose unobserved outcomes are likely to satisfy a pre-specified minimal quality requirement, while controlling the false discovery rate (FDR). Existing methods fix the target FDR level before observing data, which prevents the user from adapting the balance between number of selected test inputs and FDR to downstream needs and constraints based on the available data. For example, in genomics or neuroimaging, researchers often inspect the distribution of test statistics, and decide how aggressively to pursue candidates based on observed evidence strength and available follow-up resources. To address this limitation, we introduce post-hoc CS (PH-CS), which generates a path of candidate selection sets, each paired with a data-driven false discovery proportion (FDP) estimate. PH-CS lets the user select any operating point on this path by maximizing a user-specified utility, arbitrarily balancing selection size and FDR. Building on conformal e-variables and the e-Benjamini-Hochberg (e-BH) procedure, PH-CS is proved to provide a finite-sample post-hoc reliability guarantee whereby the ratio between estimated FDP level and true FDP is, on average, upper bounded by 1, so that the average estimated FDP is, to first order, a valid upper bound on the true FDR. PH-CS is extended to control quality defined in terms of a general risk. Experiments on synthetic and real-world datasets demonstrate that, unlike CS, PH-CS can consistently satisfy user-imposed utility constraints while producing reliable FDP estimates and maintaining competitive FDR control.
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