发表机构
University of Texas at Austin; University of Cambridge（德克萨斯大学奥斯汀分校; 剑桥大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
我们提出一次性重采样框架，仅对最终分位数加噪实现差分隐私置信区域，避免√B因子，提供GDP与效用保证，适用于均值类、分位数及退化U统计量，显著降低隐私与计算成本。
AI 中文摘要
我们提出了一个简单框架，用于一次性构建差分隐私置信区域，即仅向最终的重采样分位数添加噪声，而不是对每次重采样计算出的估计量进行私有化。在我们提出的过程中，隐私成本在有效回置抽样（m-out-of-n抽样）下仅与重采样次数B的对数成正比，而在无回置抽样（子抽样）下与B无关，从而避免了先前工作中出现的√B因子。我们为子抽样和m-out-of-n重采样提供了非渐近高斯差分隐私（GDP）和效用保证，涵盖了具有较小全局敏感度的均值类估计量，以及具有可高效计算的平滑敏感度界限的估计量，包括分位数和退化U统计量。这使得我们还能为退化U统计量获得私有置信区域，其中私有误差远小于非私有误差。总之，我们提供了一个工具箱，用于在流行的重采样策略下广泛适用的DP不确定性量化程序，同时避免了私有化许多中间重采样统计量的计算和隐私成本。
英文摘要
We propose a simple framework for constructing differentially private confidence regions \textit{in one shot}, i.e., by adding noise only to the final resampling quantile instead of privatizing the estimator computed on each resample. The cost of privacy of our procedure is only logarithmic in the number of resamples $B$ under with-replacement ($m$-out-of-$n$) sampling and independent of $B$ under without replacement sampling (subsampling), avoiding the $\sqrt{B}$ factor that arises in previous works. We provide nonasymptotic Gaussian Differential Privacy (GDP) and utility guarantees for both subsampling and $m$-out-of-$n$ resampling, covering mean-like estimators with small global sensitivity as well as estimators admitting efficiently computable smooth sensitivity bounds, including quantiles and degenerate U-statistics. This allows us to also obtain private confidence regions for degenerate U-statistics where the private error is much smaller than the non-private error. In all, we provide a toolbox for widely applicable DP uncertainty quantification procedures under popular resampling strategies while avoiding the computational and privacy costs of privatizing many intermediate resample statistics.
CommentsAccepted at NeurIPS 2026
