Differentially Private Confidence Intervals

TL;DR

This paper introduces five practical algorithms for constructing differentially private confidence intervals for the population mean of normally distributed data, demonstrating significantly improved accuracy over previous methods through experimental analysis.

Contribution

The paper presents five new algorithms for differentially private confidence intervals and provides a comprehensive comparison showing their superior accuracy.

Findings

Our algorithms produce much smaller confidence intervals than prior work.

In a specific setting, our interval is only 1/15th the size of previous methods.

Experimental results confirm improved accuracy of the proposed algorithms.

Abstract

Confidence intervals for the population mean of normally distributed data are some of the most standard statistical outputs one might want from a database. In this work we give practical differentially private algorithms for this task. We provide five algorithms and then compare them to each other and to prior work. We give concrete, experimental analysis of their accuracy and find that our algorithms provide much more accurate confidence intervals than prior work. For example, in one setting (with {\epsilon} = 0.1 and n = 2782) our algorithm yields an interval that is only 1/15th the size of the standard set by prior work.