A unified interpretation of the Gaussian mechanism for differential privacy through the sensitivity index
This work provides a unified framework for practitioners to interpret and compare privacy guarantees in differential privacy, though it is incremental as it builds on existing interpretations.
The authors tackled the problem of interpreting Gaussian mechanisms for differential privacy by introducing a single parameter called the sensitivity index, which unifies three existing interpretations and characterizes the mechanism's properties through sensitivity and noise magnitude.
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 $(\varepsilon, δ)$-DP, f-DP and Rényi DP can be expressed by using a single parameter $ψ$, which we term the sensitivity index. $ψ$ 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, $ψ$ offers the practitioner a powerful method for interpreting, comparing and communicating the privacy guarantees of Gaussian mechanisms.