Private Means and the Curious Incident of the Free Lunch

TL;DR

This paper introduces a method to release linear queries like sum, mean, and count with less noise by projecting data onto a simplex, enabling additional free queries within the same privacy budget.

Contribution

It presents a novel projection technique onto a simplex that reduces noise in differentially private linear query releases, allowing multiple queries within the same privacy constraints.

Findings

Reduced noise in releasing sums, means, and counts.

Enabling multiple queries without additional privacy loss.

Improved accuracy of differentially private data releases.

Abstract

We show that the most well-known and fundamental building blocks of DP implementations -- sum, mean, count (and many other linear queries) -- can be released with substantially reduced noise for the same privacy guarantee. We achieve this by projecting individual data with worst-case sensitivity $R$ onto a simplex where all data now has a constant norm $R$. In this simplex, additional ``free'' queries can be run that are already covered by the privacy-loss of the original budgeted query, and which algebraically give additional estimates of counts or sums.