# Grafting Laplace and Gaussian distributions: A new noise mechanism for differential privacy

arXiv: https://arxiv.org/abs/2212.09657 · HTML: https://mlsanity.com/paper/2212.09657/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Dec 2022.

## Built on by (most cited first, 3 of 3)

- [PrivateXR: Defending Privacy Attacks in Extended Reality Through Explainable AI-Guided Differential Privacy](https://mlsanity.com/paper/2512.16851/) (2025)
- [Optimality of Staircase Mechanisms for Vector Queries under Differential Privacy](https://mlsanity.com/paper/2601.14597/) (2026)
- [On the Optimal Number of Grids for Differentially Private Non-Interactive K-Means Clustering](https://mlsanity.com/paper/2603.26963/) (2026)

## Abstract (arXiv)

The framework of differential privacy protects an individual's privacy while publishing query responses on congregated data. In this work, a new noise addition mechanism for differential privacy is introduced where the noise added is sampled from a hybrid density that resembles Laplace in the centre and Gaussian in the tail. With a sharper centre and light, sub-Gaussian tail, this density has the best characteristics of both distributions. We theoretically analyze the proposed mechanism, and we derive the necessary and sufficient condition in one dimension and a sufficient condition in high dimensions for the mechanism to guarantee (ε,δ)-differential privacy. Numerical simulations corroborate the efficacy of the proposed mechanism compared to other existing mechanisms in achieving a better trade-off between privacy and accuracy.