Resampling methods for Private Statistical Inference

We consider the task of constructing confidence intervals with differential privacy. We propose two private variants of the non-parametric bootstrap, which privately compute the median of the results of multiple ``little'' bootstraps run on partitions of the data and give asymptotic bounds on the coverage error of the resulting confidence intervals. For a fixed differential privacy parameter $\epsilon$, our methods enjoy the same error rates as that of the non-private bootstrap to within logarithmic factors in the sample size $n$. …

bootstrap compute confidence coverage cs.cr cs.lg data differential differential privacy error inference multiple non-parametric parametric privacy resampling statistical stat.me stat.ml variants