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Gaussian Noise is Nearly Instance Optimal for Private Unbiased Mean Estimation. (arXiv:2301.13850v1 [math.ST])
cs.CR updates on arXiv.org arxiv.org
We investigate unbiased high-dimensional mean estimators in differential
privacy. We consider differentially private mechanisms whose expected output
equals the mean of the input dataset, for every dataset drawn from a fixed
convex domain $K$ in $\mathbb{R}^d$. In the setting of concentrated
differential privacy, we show that, for every input such an unbiased mean
estimator introduces approximately at least as much error as a mechanism that
adds Gaussian noise with a carefully chosen covariance. This is true when the
error is …
differential privacy domain error high input instance math noise privacy private