# Differentially Private Bootstrap: New Privacy Analysis and Inference Strategies arXiv: https://arxiv.org/abs/2210.06140 · HTML: https://mlsanity.com/paper/2210.06140/ ## Key facts - Cited by 10 papers in the map (data through 14 Oct 2026). - Builds on 24 of its 60 references that are in the map. - First posted on arXiv 12 Oct 2022. ## Builds on (most cited first, 24 of 24) - [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021) - [Renyi Differential Privacy](https://mlsanity.com/paper/1702.07476/) (2017) - [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016) - [Privacy Amplification by Subsampling: Tight Analyses via Couplings and Divergences](https://mlsanity.com/paper/1807.01647/) (2018) - [Subsampled R'enyi Differential Privacy and Analytical Moments Accountant](https://mlsanity.com/paper/1808.00087/) (2018) - [Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoising](https://mlsanity.com/paper/1805.06530/) (2018) - [Numerical Composition of Differential Privacy](https://mlsanity.com/paper/2106.02848/) (2021) - [Concentrated Differential Privacy](https://mlsanity.com/paper/1603.01887/) (2016) - [Finite Sample Differentially Private Confidence Intervals](https://mlsanity.com/paper/1711.03908/) (2017) - [Optimal Accounting of Differential Privacy via Characteristic Function](https://mlsanity.com/paper/2106.08567/) (2021) - [CoinPress: Practical Private Mean and Covariance Estimation](https://mlsanity.com/paper/2006.06618/) (2020) - [Differentially Private Ordinary Least Squares](https://mlsanity.com/paper/1507.02482/) (2015) - [Differentially Private Confidence Intervals](https://mlsanity.com/paper/2001.02285/) (2020) - [Parametric Bootstrap for Differentially Private Confidence Intervals](https://mlsanity.com/paper/2006.07749/) (2020) - [Unbiased Statistical Estimation and Valid Confidence Intervals Under Differential Privacy](https://mlsanity.com/paper/2110.14465/) (2021) - [Sharp Composition Bounds for Gaussian Differential Privacy via Edgeworth Expansion](https://mlsanity.com/paper/2003.04493/) (2020) - [Differentially Private Confidence Intervals for Empirical Risk Minimization](https://mlsanity.com/paper/1804.03794/) (2018) - [Benefits and Pitfalls of the Exponential Mechanism with Applications to Hilbert Spaces and Functional PCA](https://mlsanity.com/paper/1901.10864/) (2019) - [KNG: The K-Norm Gradient Mechanism](https://mlsanity.com/paper/1905.09436/) (2019) - [Canonical Noise Distributions and Private Hypothesis Tests](https://mlsanity.com/paper/2108.04303/) (2021) - [Non-parametric Differentially Private Confidence Intervals for the Median](https://mlsanity.com/paper/2106.10333/) (2021) - [Differentially Private Inference for Binomial Data](https://mlsanity.com/paper/1904.00459/) (2019) - [Deconvoluting Kernel Density Estimation and Regression for Locally Differentially Private Data](https://mlsanity.com/paper/2008.12466/) (2020) - [Bayesian Semiparametric Multivariate Density Deconvolution](https://mlsanity.com/paper/1404.6462/) (2014) ## Built on by (most cited first, 10 of 10) - [Unified Enhancement of Privacy Bounds for Mixture Mechanisms via f-Differential Privacy](https://mlsanity.com/paper/2310.19973/) (2023) - [Private Gradient Descent for Linear Regression: Tighter Error Bounds and Instance-Specific Uncertainty Estimation](https://mlsanity.com/paper/2402.13531/) (2024) - [Gaussian Differential Private Bootstrap by Subsampling](https://mlsanity.com/paper/2505.01197/) (2025) - [How Much is Left? LLMs Linearly Encode Their Remaining Output Length](https://mlsanity.com/paper/2607.05316/) (2026) - [Enhancing Trade-offs in Privacy, Utility, and Computational Efficiency through MUltistage Sampling Technique (MUST)](https://mlsanity.com/paper/2312.13389/) (2023) - [Uncertainty quantification by block bootstrap for differentially private stochastic gradient descent](https://mlsanity.com/paper/2405.12553/) (2024) - [Differentially Private Nonparametric Confidence Intervals Under Minimal Distributional Assumptions](https://mlsanity.com/paper/2511.01303/) (2025) - [Optimal Survey Design for Private Mean Estimation](https://mlsanity.com/paper/2501.18121/) (2025) - [Noise-Calibrated Inference from Differentially Private Sufficient Statistics in Exponential Families](https://mlsanity.com/paper/2603.02010/) (2026) - [One-Shot Private Confidence Regions via Resampling](https://mlsanity.com/paper/2610.08460/) (2026) ## Abstract (arXiv) Differentially private (DP) mechanisms protect individual-level information by introducing randomness into the statistical analysis procedure. Despite the availability of numerous DP tools, there remains a lack of general techniques for conducting statistical inference under DP. We examine a DP bootstrap procedure that releases multiple private bootstrap estimates to infer the sampling distribution and construct confidence intervals (CIs). Our privacy analysis presents new results on the privacy cost of a single DP bootstrap estimate, applicable to any DP mechanism, and identifies some misapplications of the bootstrap in the existing literature. For the composition of the DP bootstrap, we present a numerical method to compute the exact privacy cost of releasing multiple DP bootstrap estimates, and using the Gaussian-DP (GDP) framework (Dong et al., 2022), we show that the release of B DP bootstrap estimates from mechanisms satisfying (μ/√(2-2/e)B)-GDP asymptotically satisfies μ-GDP as B goes to infinity. Then, we perform private statistical inference by post-processing the DP bootstrap estimates. We prove that our point estimates are consistent, our standard CIs are asymptotically valid, and both enjoy optimal convergence rates. To further improve the finite performance, we use deconvolution with DP bootstrap estimates to accurately infer the sampling distribution. We derive CIs for tasks such as population mean estimation, logistic regression, and quantile regression, and we compare them to existing methods using simulations and real-world experiments on 2016 Canada Census data. Our private CIs achieve the nominal coverage level and offer the first approach to private inference for quantile regression.