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arXiv 1809.09231cs.ITmath.IT
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信息泄漏的可调测度及其在隐私-效用权衡中的应用

Tunable Measures for Information Leakage and Applications to Privacy-Utility Tradeoffs

Jiachun Liao, Oliver Kosut, Lalitha Sankar, Flavio du Pin Calmon

摘要:

我们引入了一个可调的信息泄漏措施,称为最大α泄漏。该度量量化了对手从数据的发布中推断数据集的任何(潜在随机)函数的最大收益。对手的推理能力,反过来,量化的一类对抗损失函数,我们引入$α$ -损失,$α\in[1,\infty]$。$α$的选择决定了具体的对抗行动,范围从细化$α=1$的信念(关于数据的任何函数)到猜测$α=\infty$的最可能值,同时细化介于两者之间的$α$的信念的$α^{th}$矩。最大α泄漏然后量化在数据的所有可能函数上的$α$损失下的对抗增益。特别地,对于$α=1$和$α=\infty$的极值,最大α泄漏分别简化为互信息和最大泄漏。对于$α\in(1,\infty)$,该测量被示出为阶为$α$的Arimoto信道容量。我们表明,最大的α-泄漏满足数据处理不等式和次加性属性,从而允许一个弱的组合物的结果。在这些属性的基础上,我们使用最大α泄漏作为隐私措施和研究的问题,数据发布的隐私保证,其中发布的数据的效用是通过一个硬失真约束确保。与平均失真不同,硬失真提供了保真度的确定性保证。我们表明,在硬失真约束下,对于$α>1$的最佳机制是独立的$α$,因此,得到的最佳折衷是相同的所有值的$α>1$。最后,最大阿尔法泄漏作为隐私措施的可调性也说明了平均汉明失真作为实用措施的二进制数据。

英文摘要:

We introduce a tunable measure for information leakage called maximal alpha-leakage. This measure quantifies the maximal gain of an adversary in inferring any (potentially random) function of a dataset from a release of the data. The inferential capability of the adversary is, in turn, quantified by a class of adversarial loss functions that we introduce as $α$-loss, $α\in[1,\infty]$. The choice of $α$ determines the specific adversarial action and ranges from refining a belief (about any function of the data) for $α=1$ to guessing the most likely value for $α=\infty$ while refining the $α^{th}$ moment of the belief for $α$ in between. Maximal alpha-leakage then quantifies the adversarial gain under $α$-loss over all possible functions of the data. In particular, for the extremal values of $α=1$ and $α=\infty$, maximal alpha-leakage simplifies to mutual information and maximal leakage, respectively. For $α\in(1,\infty)$ this measure is shown to be the Arimoto channel capacity of order $α$. We show that maximal alpha-leakage satisfies data processing inequalities and a sub-additivity property thereby allowing for a weak composition result. Building upon these properties, we use maximal alpha-leakage as the privacy measure and study the problem of data publishing with privacy guarantees, wherein the utility of the released data is ensured via a hard distortion constraint. Unlike average distortion, hard distortion provides a deterministic guarantee of fidelity. We show that under a hard distortion constraint, for $α>1$ the optimal mechanism is independent of $α$, and therefore, the resulting optimal tradeoff is the same for all values of $α>1$. Finally, the tunability of maximal alpha-leakage as a privacy measure is also illustrated for binary data with average Hamming distortion as the utility measure.

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