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

TL;DR

This paper introduces a novel hybrid noise mechanism combining Laplace and Gaussian distributions for differential privacy, offering improved privacy-accuracy trade-offs through theoretical analysis and simulations.

Contribution

It proposes a new hybrid noise mechanism for differential privacy that combines Laplace and Gaussian distributions, with theoretical guarantees and empirical validation.

Findings

Mechanism guarantees (${\epsilon}$,${\delta}$)-differential privacy.

Outperforms existing mechanisms in privacy-accuracy trade-offs.

Theoretical conditions derived for one and high dimensions.

Abstract

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 (${\epsilon}$,${\delta}$)-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.