Corpus ID: 211252621

Private Mean Estimation of Heavy-Tailed Distributions

  title={Private Mean Estimation of Heavy-Tailed Distributions},
  author={Gautam Kamath and Vikrant Singhal and Jonathan Ullman},
  • Gautam Kamath, Vikrant Singhal, Jonathan Ullman
  • Published 2020
  • Mathematics, Computer Science
  • ArXiv
  • 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

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