A Bias-Variance-Privacy Trilemma for Statistical Estimation. (arXiv:2301.13334v1 [math.ST])

The canonical algorithm for differentially private mean estimation is to
first clip the samples to a bounded range and then add noise to their empirical
mean. Clipping controls the sensitivity and, hence, the variance of the noise
that we add for privacy. But clipping also introduces statistical bias. We
prove that this tradeoff is inherent: no algorithm can simultaneously have low
bias, low variance, and low privacy loss for arbitrary distributions.

On the positive side, we show that unbiased mean …

algorithm bias canonical controls distributions loss low math noise privacy private prove