One-Shot Private Confidence Regions via Resampling
A one-shot resampling method builds differentially private confidence regions without privatizing every resample.
The paper presents a one-shot method for differentially private confidence regions that adds noise only to the final resampling quantile. Under with-replacement sampling, the privacy cost is logarithmic in the number of resamples, and under subsampling it is independent of that number, avoiding a square-root penalty. Nonasymptotic Gaussian differential privacy and utility guarantees cover mean-like estimators, quantiles, and degenerate U-statistics, including cases where the private error is smaller than the non-private error.
- Noise is added once to the final resampling quantile.
- With-replacement privacy cost grows only logarithmically with resample count B.
- Subsampling privacy cost is independent of the number of resamples.
- Guarantees cover means, quantiles, and degenerate U-statistics.
From the original article
1 min read at arxiv.orgWe 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.
By Shourya Pandey · arxiv.org
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