# Private Mean Estimation of Heavy-Tailed Distributions

@article{Kamath2020PrivateME, title={Private Mean Estimation of Heavy-Tailed Distributions}, author={Gautam Kamath and Vikrant Singhal and Jonathan Ullman}, journal={ArXiv}, year={2020}, volume={abs/2002.09464} }

We give new upper and lower bounds on the minimax sample complexity of differentially private mean estimation of distributions with bounded $k$-th moments. Roughly speaking, in the univariate case, we show that $n = \Theta\left(\frac{1}{\alpha^2} + \frac{1}{\alpha^{\frac{k}{k-1}}\varepsilon}\right)$ samples are necessary and sufficient to estimate the mean to $\alpha$-accuracy under $\varepsilon$-differential privacy, or any of its common relaxations. This result demonstrates a qualitatively… CONTINUE READING