Consider a data publishing setting for a dataset composed by both private and non-private features. The publisher uses an empirical distribution, estimated from $n$ i.i.d. samples, to design a privacy mechanism which is applied to new fresh samples afterward. In this paper, we study the discrepancy between the privacy-utility guarantees for the empirical distribution, used to design the privacy mechanism, and those for the true distribution, experienced by the privacy mechanism in practice. We first show that, for any privacy mechanism, these discrepancies vanish at speed $O(1/\sqrt {n})$ with high probability. These bounds follow from our main technical results regarding the Lipschitz continuity of the considered information leakage measures. Then we prove that the optimal privacy mechanisms for the empirical distribution approach the corresponding mechanisms for the true distribution as the sample size $n$ increases, thereby establishing the statistical consistency of the optimal privacy mechanisms. Finally, we introduce and study uniform privacy mechanisms which, by construction, provide privacy to all the distributions within a neighborhood of the estimated distribution and, thereby, guarantee privacy for the true distribution with high probability.

中文翻译：

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论信息理论隐私措施和机制的稳健性

考虑由私有和非私有特征组成的数据集的数据发布设置。出版商使用经验分布，估计从 $n$ iid 样本，以设计一种隐私机制，然后应用于新的新鲜样本。在本文中，我们研究了用于设计隐私机制的经验分布的隐私效用保证与隐私机制在实践中经历的真实分布的隐私效用保证之间的差异。我们首先证明，对于任何隐私机制，这些差异都会迅速消失 $O(1/\sqrt {n})$ 很有可能。这些界限来自我们关于所考虑的信息泄漏措施的 Lipschitz 连续性的主要技术结果。然后我们证明经验分布的最优隐私机制接近真实分布的相应机制作为样本量 $n$ 增加，从而建立最优隐私机制的统计一致性。最后，我们介绍和研究统一的隐私机制 它通过构造为估计分布的邻域内的所有分布提供隐私，从而以高概率保证真实分布的隐私。