# Differential privacy for symmetric log-concave mechanisms

arXiv: https://arxiv.org/abs/2202.11393 · HTML: https://mlsanity.com/paper/2202.11393/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 34 references that are in the map.
- First posted on arXiv 23 Feb 2022.

## Builds on (most cited first, 8 of 8)

- [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)
- [Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoising](https://mlsanity.com/paper/1805.06530/) (2018)
- [Concentrated Differential Privacy](https://mlsanity.com/paper/1603.01887/) (2016)
- [The Discrete Gaussian for Differential Privacy](https://mlsanity.com/paper/2004.00010/) (2020)
- [A Central Limit Theorem for Differentially Private Query Answering](https://mlsanity.com/paper/2103.08721/) (2021)

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

- [Optimality of Staircase Mechanisms for Vector Queries under Differential Privacy](https://mlsanity.com/paper/2601.14597/) (2026)

## Abstract (arXiv)

Adding random noise to database query results is an important tool for achieving privacy. A challenge is to minimize this noise while still meeting privacy requirements. Recently, a sufficient and necessary condition for (ε, δ)-differential privacy for Gaussian noise was published. This condition allows the computation of the minimum privacy-preserving scale for this distribution. We extend this work and provide a sufficient and necessary condition for (ε, δ)-differential privacy for all symmetric and log-concave noise densities. Our results allow fine-grained tailoring of the noise distribution to the dimensionality of the query result. We demonstrate that this can yield significantly lower mean squared errors than those incurred by the currently used Laplace and Gaussian mechanisms for the same ε and δ.