In this work we study the problem of differentially private (DP) quantiles, in which given dataset $X$ and quantiles $q_1, ..., q_m \in [0,1]$, we want to output $m$ quantile estimations which are as close as possible to the true quantiles and preserve DP. We describe a simple recursive DP algorithm, which we call ApproximateQuantiles (AQ), for this task. We give a worst case upper bound on its error, and show that its error is much lower than of previous implementations on several different datasets. Furthermore, it gets this low error while running time two orders of magnitude faster that the best previous implementation.

翻译：在这项工作中,我们研究了差异化的私有(DP)量子的问题,其中给数据集以X$和四分位数$_1,...,...,q_m\\ in [0,1,1],我们想要输出尽可能接近真量化值的四分位数估计值,并保存DP。我们描述一个简单的递归式DP算法,我们称之为“Apprbly 量子(AQ) ”,用于这项任务。我们给出了一个最差的错误,并显示其错误远小于以前在多个不同数据集上执行的错误。此外,它得到这个低误差,同时运行的时间两个数量级速度要快于以往的最佳执行速度。