Finite Sample Differentially Private Confidence Intervals

TL;DR

This paper develops differentially private algorithms for finite sample confidence intervals of a normal mean, ensuring finite sample coverage without requiring bounded data, and proves their near-optimality.

Contribution

It introduces new private algorithms for confidence intervals with finite sample guarantees and no bounded domain assumptions, along with matching lower bounds.

Findings

Algorithms guarantee finite sample coverage

No bounded domain requirement for data

Parameters are nearly optimal up to polylogarithmic factors

Abstract

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.