We study the relationship between adversarial robustness and differential privacy in high-dimensional algorithmic statistics. We give the first black-box reduction from privacy to robustness which can produce private estimators with optimal tradeoffs among sample complexity, accuracy, and privacy for a wide range of fundamental high-dimensional parameter estimation problems, including mean and covariance estimation. We show that this reduction can be implemented in polynomial time in some important special cases. In particular, using nearly-optimal polynomial-time robust estimators for the mean and covariance of high-dimensional Gaussians which are based on the Sum-of-Squares method, we design the first polynomial-time private estimators for these problems with nearly-optimal samples-accuracy-privacy tradeoffs. Our algorithms are also robust to a constant fraction of adversarially-corrupted samples.

翻译：我们研究了高维算法统计数据中对抗性强强性和隐私差异之间的关系。 我们第一次从隐私到稳健度的黑箱减少黑箱,这可以产生私人估计器,在抽样复杂度、准确度和隐私之间作出最佳的权衡,解决一系列基本高维参数估计问题,包括平均和共变估计。 我们表明,这种缩减可以在一些重要的特殊情况下的多元时段实施。 特别是,我们使用以平方法为基础的高维测算器的平均值和共变差的几乎最佳的多元时段稳健估测器,我们设计了第一个多维时私人估计器,用近于最佳的样品-准确度-均变差的权衡来解决这些问题。 我们的算法也很强于持续部分的对抗性腐蚀性样本。