Non-parametric Differentially Private Confidence Intervals for the Median

TL;DR

This paper introduces methods for constructing valid differentially private confidence intervals for the median, emphasizing direct estimation of interval bounds and addressing multiple sources of uncertainty, with extensive simulations and real data application.

Contribution

It proposes novel strategies for differentially private median confidence intervals, focusing on direct interval estimation and combined uncertainty management, improving statistical inference under privacy constraints.

Findings

Direct estimation of interval bounds outperforms traditional methods.

Simultaneous handling of sampling and privacy-induced uncertainty yields better intervals.

Algorithms perform well across various parameters in simulations and real census data.

Abstract

Differential privacy is a restriction on data processing algorithms that provides strong confidentiality guarantees for individual records in the data. However, research on proper statistical inference, that is, research on properly quantifying the uncertainty of the (noisy) sample estimate regarding the true value in the population, is currently still limited. This paper proposes and evaluates several strategies to compute valid differentially private confidence intervals for the median. Instead of computing a differentially private point estimate and deriving its uncertainty, we directly estimate the interval bounds and discuss why this approach is superior if ensuring privacy is important. We also illustrate that addressing both sources of uncertainty--the error from sampling and the error from protecting the output--simultaneously should be preferred over simpler approaches that incorporate the uncertainty in a sequential fashion. We evaluate the performance of the different algorithms under various parameter settings in extensive simulation studies and demonstrate how the findings could be applied in practical settings using data from the 1940 Decennial Census.