Interpreting the Error of Differentially Private Median Queries through Randomization Intervals

2026-04-08

AI Summary

This work addresses the challenge of interpreting differentially private median queries, where noise injection often compromises result interpretability. Existing approaches typically sacrifice median utility to obtain high-quality randomized intervals. To overcome this trade-off, we propose PostRI, the first method that decouples median estimation from randomized interval construction. PostRI first computes a differentially private median estimate and then adaptively generates a tight randomized interval based on posterior error analysis. By avoiding additional perturbation to the median itself, PostRI significantly enhances statistical utility while maintaining reasonable interval width. Empirical evaluations demonstrate that our approach improves median estimation accuracy by 14% to 850% compared to state-of-the-art methods.

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.

Problem

• differentially private median
• randomization interval
• error interpretation
• privacy-preserving statistics
• utility degradation

Innovation

• PostRI
• Randomization Interval
• Differentially Private Median
• Utility Improvement
• Confidence Interval