Interpreting the Error of Differentially Private Median Queries through Randomization Intervals

TL;DR

This paper introduces PostRI, a method for computing confidence intervals for differentially private medians, improving interpretability and utility over prior approaches by providing meaningful error bounds.

Contribution

PostRI is a novel post-processing technique that computes randomization intervals for DP medians, enhancing utility while maintaining narrow error bounds.

Findings

PostRI achieves 14%-850% higher utility than previous methods.

PostRI provides narrow and meaningful error bounds for DP medians.

The method improves interpretability of DP median queries.

Abstract

It can be difficult for practitioners to interpret the quality of differentially private (DP) statistics due to the added noise. One method to help analysts understand the amount of error introduced by DP is to return a Randomization Interval (RI), along with the statistic. A RI is a type of confidence interval that bounds the error introduced by DP. For queries where the noise distribution depends on the input, such as the median, prior work degrades the quality of the median itself to obtain a high-quality RI. In this work, we propose PostRI, a solution to compute a RI after the median has been estimated. PostRI enables a median estimation with 14%-850% higher utility than related work, while maintaining a narrow RI.