We introduce a family of information leakage measures called maximal $(\alpha,\beta)$-leakage, parameterized by non-negative real numbers $\alpha$ and $\beta$. The measure is formalized via an operational definition involving an adversary guessing an unknown (randomized) function of the data given the released data. We obtain a simplified computable expression for the measure and show that it satisfies several basic properties such as monotonicity in $\beta$ for a fixed $\alpha$, non-negativity, data processing inequalities, and additivity over independent releases. We highlight the relevance of this family by showing that it bridges several known leakage measures, including maximal $\alpha$-leakage $(\beta=1)$, maximal leakage $(\alpha=\infty,\beta=1)$, local differential privacy [LDP] $(\alpha=\infty,\beta=\infty)$, and local Renyi differential privacy [LRDP] $(\alpha=\beta)$, thereby giving an operational interpretation to local Renyi differential privacy. We also study a conditional version of maximal $(\alpha,\beta)$-leakage on leveraging which we recover differential privacy and Renyi differential privacy. A new variant of LRDP, which we call maximal Renyi leakage, appears as a special case of maximal $(\alpha,\beta)$-leakage for $\alpha=\infty$ that smoothly tunes between maximal leakage ($\beta=1$) and LDP ($\beta=\infty$). Finally, we show that a vector form of the maximal Renyi leakage relaxes differential privacy under Gaussian and Laplacian mechanisms.

翻译：我们提出了一系列信息泄漏度量，称为最大$(\alpha,\beta)$-泄漏，由非负实数参数$\alpha$和$\beta$刻画。该度量通过一个操作性定义形式化，涉及敌手根据已发布数据猜测数据的未知（随机化）函数。我们得到了该度量的简化可计算表达式，并证明其满足若干基本性质，如固定$\alpha$下关于$\beta$的单调性、非负性、数据处理不等式以及独立发布下的可加性。我们通过展示该度量族桥接了若干已知泄漏度量（包括最大$\alpha$-泄漏$(\beta=1)$、最大泄漏$(\alpha=\infty,\beta=1)$、本地差分隐私[LDP]$(\alpha=\infty,\beta=\infty)$和本地Rényi差分隐私[LRDP]$(\alpha=\beta)$）来强调其相关性，从而为本地Rényi差分隐私提供了操作性解释。我们还研究了最大$(\alpha,\beta)$-泄漏的条件版本，利用该版本我们恢复了差分隐私和Rényi差分隐私。一种新的LRDP变体——我们称之为最大Rényi泄漏——作为最大$(\alpha,\beta)$-泄漏在$\alpha=\infty$时的特例出现，该变体可在最大泄漏$(\beta=1)$和LDP$(\beta=\infty)$之间平滑调节。最后，我们证明了最大Rényi泄漏的向量形式在高斯和拉普拉斯机制下松弛了差分隐私。