New method creates private confidence regions with less noise
One-Shot Private Confidence Regions via Resampling
Cryptography and Security
Summary
When analysts want to estimate how confident they are in their results while keeping individual data private, it usually involves adding noise many times, which increases errors. The authors propose a way to add noise just once to the final combined estimate instead of each intermediate step. This method keeps the privacy guarantees while reducing the amount of extra noise added, making these confidence regions more accurate and efficient. It works well with common sampling methods and a broad class of estimators.
What this means in practice
- •For data privacy engineers: Construct differentially private confidence intervals with less noise and computational cost in privacy-sensitive data analyses using resampling.
- •For statistical software developers: Implement efficient private uncertainty quantification tools that add noise only once, improving performance of privacy-preserving statistical packages.
Authors
Shourya Pandey, Purnamrita Sarkar, Po-Ling Loh, Debepsita Mukherjee
Abstract
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.