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arXiv · 2109.10528

A unified interpretation of the Gaussian mechanism for differential privacy through the sensitivity index

Georgios Kaissis·Moritz Knolle·Friederike Jungmann·Alexander Ziller·Dmitrii Usynin·Daniel Rueckert
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Abstract

The Gaussian mechanism (GM) represents a universally employed tool for achieving differential privacy (DP), and a large body of work has been devoted to its analysis. We argue that the three prevailing interpretations of the GM, namely $(\varepsilon, \delta)$-DP, f-DP and R\'enyi DP can be expressed by using a single parameter $\psi$, which we term the sensitivity index. $\psi$ uniquely characterises the GM and its properties by encapsulating its two fundamental quantities: the sensitivity of the query and the magnitude of the noise perturbation. With strong links to the ROC curve and the hypothesis-testing interpretation of DP, $\psi$ offers the practitioner a powerful method for interpreting, comparing and communicating the privacy guarantees of Gaussian mechanisms.

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Georgios Kaissis, Moritz Knolle, Friederike Jungmann, Alexander Ziller, Dmitrii Usynin, Daniel Rueckert. 2021-09-22. A unified interpretation of the Gaussian mechanism for differential privacy through the sensitivity index. https://arxiv.org/abs/2109.10528

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