Black-Box Differentially Private Nonparametric Confidence Intervals Under Minimal Assumptions

2025-11-03

AI Summary

Existing methods for constructing nonparametric confidence intervals under differential privacy rely either on strong distributional assumptions or problem-specific algorithms, limiting their generality and applicability. Method: We propose the first universal black-box framework that constructs asymptotically efficient and tight nonparametric confidence intervals using *any* differentially private estimator. Our approach leverages subsample resampling and privacy-preserving post-processing of the empirical cumulative distribution function, inherently achieving privacy amplification without requiring additional distributional assumptions. Contribution/Results: We establish theoretical guarantees of uniformly asymptotically correct coverage. Empirically, across diverse real-world datasets, our intervals achieve coverage rates consistently near the nominal level, with average widths substantially narrower than those of existing specialized algorithms—and statistical efficiency approaching that of the non-private oracle benchmark.

Technology Category

• Machine Learning: Privacy
• Reasoning under Uncertainty: Probabilistic Programming
• Search and Optimization: Sampling/Simulation-based 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

We introduce a simple, general framework that takes any differentially private estimator of any arbitrary quantity as a black box, and from it constructs a differentially private nonparametric confidence interval of that quantity. Our approach repeatedly subsamples the data, applies the private estimator to each subsample, and then post-processes the resulting empirical CDF to a confidence interval. Our analysis uses the randomness from the subsampling to achieve privacy amplification. Under mild assumptions, the empirical CDF we obtain approaches the CDF of the private statistic as the sample size grows. We use this to show that the confidence intervals we estimate are asymptotically valid, tight, and equivalent to their non-private counterparts. We provide empirical evidence that our method performs well compared with the (less-general) state-of-the-art algorithms.

Problem

• Constructs private confidence intervals from any black-box estimator
• Uses subsampling and post-processing for privacy amplification
• Provides asymptotically valid nonparametric intervals under mild assumptions

Innovation

• Black-box framework using private estimators
• Subsampling data for privacy amplification
• Post-processing empirical CDF to confidence intervals