论文标题
差异化私人Assouad，Fano和Le Cam
Differentially Private Assouad, Fano, and Le Cam
论文作者
论文摘要
Le Cam的方法，Fano的不平等和Assouad的引理是三种广泛使用的技术，可以证明用于统计估计任务的下限。我们在中央差异隐私下提出了类似物。我们的结果简单，易于应用，我们使用它们在几个估计任务中建立样本复杂性界限。我们在总变化距离和$ \ ell_2 $距离下建立了离散分布估计的最佳样本复杂性。我们还为其他几个分配类别提供了下限，包括产品分布和高斯混合物，这些混合物紧密地符合对数因素。本文的技术组成部分将分布之间的耦合与差异隐私下的样本复杂性之间的耦合联系起来。
Le Cam's method, Fano's inequality, and Assouad's lemma are three widely used techniques to prove lower bounds for statistical estimation tasks. We propose their analogues under central differential privacy. Our results are simple, easy to apply and we use them to establish sample complexity bounds in several estimation tasks. We establish the optimal sample complexity of discrete distribution estimation under total variation distance and $\ell_2$ distance. We also provide lower bounds for several other distribution classes, including product distributions and Gaussian mixtures that are tight up to logarithmic factors. The technical component of our paper relates coupling between distributions to the sample complexity of estimation under differential privacy.
