mlsanityData to 7 Oct 2026

Differentially Private Bootstrap: New Privacy Analysis and Inference Strategies

arXiv 2210.06140 ↗First posted 12 Oct 2022stat.ML cs.CR cs.DScited by 9

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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.

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 24 of its 60 references that are in the map. First posted on arXiv 12 Oct 2022.

Builds on

24 of 60 references.

References · 24

  1. 2021Convex optimizationcited by 2,479
  2. 2017Renyi Differential Privacycited by 643
  3. 2016Concentrated Differential Privacy: Simplifications, Extensions, and Lower Boundscited by 339
  4. 2018Privacy Amplification by Subsampling: Tight Analyses via Couplings and Divergencescited by 237
  5. 2018Subsampled R'enyi Differential Privacy and Analytical Moments Accountantcited by 234
  6. 2018Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoisingcited by 216
  7. 2021Numerical Composition of Differential Privacycited by 174
  8. 2016Concentrated Differential Privacycited by 139
  9. 2017Finite Sample Differentially Private Confidence Intervalscited by 103
  10. 2021Optimal Accounting of Differential Privacy via Characteristic Functioncited by 83
  11. 2020CoinPress: Practical Private Mean and Covariance Estimationcited by 74
  12. 2015Differentially Private Ordinary Least Squarescited by 36
12 more
  1. 2020Differentially Private Confidence Intervalscited by 20
  2. 2020Parametric Bootstrap for Differentially Private Confidence Intervalscited by 19
  3. 2021Unbiased Statistical Estimation and Valid Confidence Intervals Under Differential Privacycited by 15
  4. 2020Sharp Composition Bounds for Gaussian Differential Privacy via Edgeworth Expansioncited by 13
  5. 2018Differentially Private Confidence Intervals for Empirical Risk Minimizationcited by 11
  6. 2019Benefits and Pitfalls of the Exponential Mechanism with Applications to Hilbert Spaces and Functional PCAcited by 10
  7. 2019KNG: The K-Norm Gradient Mechanismcited by 8
  8. 2021Canonical Noise Distributions and Private Hypothesis Testscited by 8
  9. 2021Non-parametric Differentially Private Confidence Intervals for the Mediancited by 7
  10. 2019Differentially Private Inference for Binomial Datacited by 4
  11. 2020Deconvoluting Kernel Density Estimation and Regression for Locally Differentially Private Datacited by 3
  12. 2014Bayesian Semiparametric Multivariate Density Deconvolutioncited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 2; 2025: 3; 2026: 2.

9 papers.

  1. 2023Unified Enhancement of Privacy Bounds for Mixture Mechanisms via f-Differential Privacycited by 13
  2. 2024Private Gradient Descent for Linear Regression: Tighter Error Bounds and Instance-Specific Uncertainty Estimationcited by 11
  3. 2026How Much is Left? LLMs Linearly Encode Their Remaining Output Lengthcited by 2
  4. 2024Uncertainty quantification by block bootstrap for differentially private stochastic gradient descentcited by 1
  5. 2025Gaussian Differential Private Bootstrap by Subsamplingcited by 1
  6. 2023Enhancing Trade-offs in Privacy, Utility, and Computational Efficiency through MUltistage Sampling Technique (MUST)cited by 0
  7. 2025Optimal Survey Design for Private Mean Estimationcited by 0
  8. 2025Differentially Private Nonparametric Confidence Intervals Under Minimal Distributional Assumptionscited by 0
  9. 2026Noise-Calibrated Inference from Differentially Private Sufficient Statistics in Exponential Familiescited by 0