For mean estimation, a simple thresholding operator on privacy budgets matches the performance of fully personalized differential privacy mechanisms up to constant factors.
Average-case averages: Private algorithms for smooth sensitivity and mean estimation.Advances in Neural Information Processing Systems, 32
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Limits of Personalizing Differential Privacy Budgets
For mean estimation, a simple thresholding operator on privacy budgets matches the performance of fully personalized differential privacy mechanisms up to constant factors.