Differentially Private Bootstrap: New Privacy Analysis and Inference Strategies

2024-12-31 · Source: JMLR · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Cybersecurity & Data Privacy · Depth: Expert, quick

Summary

Zhanyu Wang, Guang Cheng, and Jordan Awan introduce a differentially private (DP) bootstrap procedure designed to facilitate statistical inference while protecting individual-level information. Their work, published in 2025, addresses the scarcity of general techniques for statistical inference under DP. The authors provide a new privacy analysis for a single DP bootstrap estimate, applicable across various DP mechanisms, and identify misapplications in existing literature. For composing multiple DP bootstrap estimates, they present a numerical method for exact privacy cost computation and demonstrate that releasing B estimates from mechanisms satisfying $(\mu/\sqrt{(2-2/\mathrm{e})B})$-GDP asymptotically meets $\mu$-GDP as B approaches infinity. They prove consistency and asymptotic validity for their point estimates and standard confidence intervals (CIs), achieving optimal convergence rates. The procedure also employs deconvolution to enhance finite performance and derives CIs for tasks like population mean estimation, logistic regression, and quantile regression, validated through simulations and experiments on 2016 Canada Census data.

Key takeaway

For research scientists developing privacy-preserving statistical methods, this work offers a robust framework for conducting inference with differential privacy. You should consider integrating this DP bootstrap procedure to achieve asymptotically valid confidence intervals and consistent point estimates, particularly for tasks like quantile regression where private inference was previously challenging. The provided code can help you implement these techniques effectively.

Key insights

A new differentially private bootstrap method enables robust statistical inference with strong privacy guarantees.

Principles

• DP bootstrap estimates can infer sampling distributions.
• Gaussian-DP framework quantifies privacy cost.
• Deconvolution improves finite performance of CIs.

Method

The method involves releasing multiple DP bootstrap estimates, computing exact privacy costs numerically, and using deconvolution for accurate sampling distribution inference to construct asymptotically valid confidence intervals.

In practice

• Construct CIs for population mean estimation.
• Apply to logistic regression tasks.
• Perform private inference for quantile regression.

Topics

• Differentially Private Bootstrap
• Differential Privacy
• Statistical Inference
• Confidence Intervals
• Quantile Regression

Code references

• Zhanyu-Wang/Differentially_Private_Bootstrap
• JmlrOrg/v26

Best for: Research Scientist, AI Researcher, AI Scientist, Data Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by JMLR.