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

arXiv: https://arxiv.org/abs/2109.10528 · HTML: https://mlsanity.com/paper/2109.10528/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 41 references that are in the map.
- First posted on arXiv 22 Sep 2021.

## Builds on (most cited first, 17 of 17)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Renyi Differential Privacy](https://mlsanity.com/paper/1702.07476/) (2017)
- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [The Composition Theorem for Differential Privacy](https://mlsanity.com/paper/1311.0776/) (2013)
- [RAPPOR: Randomized Aggregatable Privacy-Preserving Ordinal Response](https://mlsanity.com/paper/1407.6981/) (2014)
- [Privacy Amplification by Subsampling: Tight Analyses via Couplings and Divergences](https://mlsanity.com/paper/1807.01647/) (2018)
- [Differentially Private Learning Needs Better Features (or Much More Data)](https://mlsanity.com/paper/2011.11660/) (2020)
- [Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoising](https://mlsanity.com/paper/1805.06530/) (2018)
- [R'enyi Differential Privacy of the Sampled Gaussian Mechanism](https://mlsanity.com/paper/1908.10530/) (2019)
- [Numerical Composition of Differential Privacy](https://mlsanity.com/paper/2106.02848/) (2021)
- [Concentrated Differential Privacy](https://mlsanity.com/paper/1603.01887/) (2016)
- [Deep Learning with Gaussian Differential Privacy](https://mlsanity.com/paper/1911.11607/) (2019)
- [Optimal Accounting of Differential Privacy via Characteristic Function](https://mlsanity.com/paper/2106.08567/) (2021)
- [Hypothesis Testing Interpretations and Renyi Differential Privacy](https://mlsanity.com/paper/1905.09982/) (2019)
- [Privacy Loss in Apple's Implementation of Differential Privacy on MacOS 10.12](https://mlsanity.com/paper/1709.02753/) (2017)
- [Understanding the Sparse Vector Technique for Differential Privacy](https://mlsanity.com/paper/1603.01699/) (2016)
- [Three Variants of Differential Privacy: Lossless Conversion and Applications](https://mlsanity.com/paper/2008.06529/) (2020)

## Built on by (most cited first, 1 of 1)

- [SoK: Differential Privacy on Graph-Structured Data](https://mlsanity.com/paper/2203.09205/) (2022)

## Abstract (arXiv)

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 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.