Finite Sample Differentially Private Confidence Intervals
This work addresses the need for reliable statistical inference with privacy guarantees in data analysis, offering a non-asymptotic solution that is more practical for real-world applications.
The authors tackled the problem of estimating finite sample confidence intervals for the mean of a normal population under differential privacy constraints, achieving algorithms that guarantee finite sample coverage without requiring bounded sample domains and proving near-optimal lower bounds on interval size.
We study the problem of estimating finite sample confidence intervals of the mean of a normal population under the constraint of differential privacy. We consider both the known and unknown variance cases and construct differentially private algorithms to estimate confidence intervals. Crucially, our algorithms guarantee a finite sample coverage, as opposed to an asymptotic coverage. Unlike most previous differentially private algorithms, we do not require the domain of the samples to be bounded. We also prove lower bounds on the expected size of any differentially private confidence set showing that our the parameters are optimal up to polylogarithmic factors.