Offset-Symmetric Gaussians for Differential Privacy

The Gaussian distribution is widely used in mechanism design for differential privacy (DP). Thanks to its sub-Gaussian tail, it significantly reduces the chance of outliers when responding queries. However, can only provide approximate (ε,δ(ε))-DP. In practice, δ(ε) must be much smaller than size dataset, which may limit use large datasets with strong requirements. this paper, we introduce and analyze a new DP that based on distribution, but has improved performance. so-called offset-symmetric tail (OSGT) obtained through using normalized tails two symmetric Gaussians around zero. Consequently, still have lend itself analytical derivations. We analytically derive variance OSGT random variable single-dimensional mechanism. extend k-dimensional queries, iteratively compute δk(ε), Rényi privacy, study composition. Numerical results show offer better privacy-utility performance compared Laplace mechanisms. also method post processing output query minimum mean square error (MMSE) estimation technique. simulation such confirm efficacy over