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

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