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.