We present a differentially private algorithm for releasing the sequence of $k$ elements with the highest counts from a data domain of $d$ elements. The algorithm is a "joint" instance of the exponential mechanism, and its output space consists of all $O(d^k)$ length-$k$ sequences. Our main contribution is a method to sample this exponential mechanism in time $O(dk\log(k) + d\log(d))$ and space $O(dk)$. Experiments show that this approach outperforms existing pure differential privacy methods and improves upon even approximate differential privacy methods for moderate $k$.

翻译：我们提出了一种差别化的私人算法,用于从以美元计数的数据域中释放以美元计数的以美元计数的元素序列。算法是指数机制的一个“联合”实例,其输出空间由所有美元(d ⁇ k)的长度-k美元序列组成。我们的主要贡献是用一种方法来抽取这个指数机制的时间(o)(dk\log(k)+dlog(d))美元和空间(o(dk)美元)。实验表明,这一方法优于现有的纯粹的差别隐私方法,并且甚至改进了中值(k)的近似差别隐私方法。