Exact Privacy Analysis of the Gaussian Sparse Histogram Mechanism

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.