SUP: An Inferable Private Multiple Testing Framework with Super Uniformity

2025-12-03

AI Summary

In privacy-preserving multiple testing on genomic and health data, existing differential privacy (DP) mechanisms violate the super-uniformity of p-values, undermining post-selection inference. To address this, we propose the generic SUP framework, which jointly applies p-value transformations compatible with diverse DP mechanisms and a reverse-stripping algorithm to rigorously preserve p-value super-uniformity under ε-differential privacy. SUP further introduces an adaptive rejection threshold that requires no pre-specified privacy budget, enabling unified control of both family-wise error rate (FWER) and false discovery rate (FDR). We provide theoretical guarantees showing SUP dominates existing private methods in statistical power. Extensive simulations and real-data analyses demonstrate that SUP tightly controls Type I error while substantially mitigating power loss compared to state-of-the-art private multiple testing approaches.

Technology Category

• Machine Learning: Privacy
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Security and Privacy: Data transparency and provenance
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

Multiple testing is widely applied across scientific fields, particularly in genomic and health data analysis, where protecting sensitive personal information is imperative. However, developing private multiple testing algorithms for super uniform $p$-values remains an open question, as privacy mechanisms introduce intricate dependence among the peeled $p$-values and disrupt their super uniformity, complicating post-selection inference. To address this, we introduce a general Super Uniform Private (SUP) multiple testing framework with three key components. First, we develop a novel ( p )-value transformation that is compatible with diverse privacy regimes while retaining the super uniformity. Next, a reversed peeling algorithm is designed to reduce privacy budgets while facilitating inference. Then, we provide diverse rejection thresholds that are privacy-parameter-free and tailored for different Type-I errors, including the family-wise error rate (FWER) and the false discovery rate (FDR). Building upon these, we advance adaptive techniques to determine the peeling number and boost thresholds. Theoretically, we propose a technique overcoming the post-selection obstacle to Type-I error control, quantify the privacy-induced power loss of SUP relative to its non-private counterpart, and demonstrate that SUP surpasses existing private methods in terms of power. The results of extensive simulations and a real data application validate our theories.

Problem

• Develop private multiple testing for super uniform p-values
• Address privacy-induced dependence disrupting super uniformity
• Provide privacy-parameter-free thresholds for Type-I error control

Innovation

• Novel p-value transformation preserving super uniformity
• Reversed peeling algorithm optimizing privacy budget usage
• Privacy-parameter-free thresholds for FWER and FDR control