Exact Privacy Analysis of the Gaussian Sparse Histogram Mechanism

TL;DR

This paper provides an exact privacy analysis of the Gaussian sparse histogram mechanism, offering precise differential privacy guarantees and comparing them to previous overestimated bounds to assess their tightness.

Contribution

It introduces an exact differential privacy analysis for the Gaussian sparse histogram mechanism, improving understanding of its privacy guarantees over prior overestimates.

Findings

Exact $oldsymbol{ ext{epsilon}, ext{delta}}$ privacy guarantees derived.

Comparison shows previous bounds are looser than the exact analysis.

Quantifies the impact of overestimating privacy parameters.

Abstract

Sparse histogram methods can be useful for returning differentially private counts of items in large or infinite histograms, large group-by queries, and more generally, releasing a set of statistics with sufficient item counts. We consider the Gaussian version of the sparse histogram mechanism and study the exact $\epsilon,\delta$ differential privacy guarantees satisfied by this mechanism. We compare these exact $\epsilon,\delta$ parameters to the simpler overestimates used in prior work to quantify the impact of their looser privacy bounds.