不同的私人Assouad，Fano和Le Cam
Differentially Private Assouad, Fano, and Le Cam
摘要：
Le Cam方法、Fano不等式和Assouad引理是证明统计估计任务下界的三种广泛使用的技术。在中心差分隐私下，我们提出了它们的类似物。我们的结果是简单的，易于应用，我们用它们来建立样本的复杂性界限在几个估计任务。在全变差距离和$\ell_2$距离下，建立了离散分布估计的最优样本复杂度.我们还提供了其他几个分布类的下限，包括产品分布和高斯混合是紧密的对数因子。我们论文的技术部分将分布之间的耦合与差分隐私下估计的样本复杂性联系起来。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
