We construct differentially private estimators with low sample complexity that estimate the median of an arbitrary distribution over $\mathbb{R}$ satisfying very mild moment conditions. Our result stands in contrast to the surprising negative result of Bun et al. (FOCS 2015) that showed there is no differentially private estimator with any finite sample complexity that returns any non-trivial approximation to the median of an arbitrary distribution.

翻译：我们构造了样本复杂度较低的差分隐私估计器，用于估计满足极弱矩条件的 $\mathbb{R}$ 上任意分布的中位数。这一结果与 Bun 等人（FOCS 2015）令人惊讶的负面结论形成鲜明对比——该结论表明，对于任意分布的中位数，不存在任何有限样本复杂度的差分隐私估计器能够给出非平凡的近似估计。