# Differential Privacy with Higher Utility by Exploiting Coordinate-wise Disparity: Laplace Mechanism Can Beat Gaussian in High Dimensions

arXiv: https://arxiv.org/abs/2302.03511 · HTML: https://mlsanity.com/paper/2302.03511/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2023.

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

- [Robust Learnability of Sample-Compressible Distributions under Noisy or Adversarial Perturbations](https://mlsanity.com/paper/2506.06613/) (2025)
- [Lap2: Revisiting Laplace DP-SGD for High Dimensions via Majorization Theory](https://mlsanity.com/paper/2602.23516/) (2026)
- [Jacobian-Guided Anisotropic Noise Reshaping for Enhancing Representation Utility under Local Differential Privacy](https://mlsanity.com/paper/2605.16812/) (2026)

## Abstract (arXiv)

Conventionally, in a differentially private additive noise mechanism, independent and identically distributed (i.i.d.) noise samples are added to each coordinate of the response. In this work, we formally present the addition of noise that is independent but not identically distributed (i.n.i.d.) across the coordinates to achieve tighter privacy-accuracy trade-off by exploiting coordinate-wise disparity in privacy leakage. In particular, we study the i.n.i.d. Gaussian and Laplace mechanisms and obtain the conditions under which these mechanisms guarantee privacy. The optimal choice of parameters that ensure these conditions are derived considering (weighted) mean squared and ℓpp-errors as measures of accuracy. Theoretical analyses and numerical simulations demonstrate that the i.n.i.d. mechanisms achieve higher utility for the given privacy requirements compared to their i.i.d. counterparts. One of the interesting observations is that the Laplace mechanism outperforms Gaussian even in high dimensions, as opposed to the popular belief, if the irregularity in coordinate-wise sensitivities is exploited. We also demonstrate how the i.n.i.d. noise can improve the performance in private (a) coordinate descent, (b) principal component analysis, and (c) deep learning with group clipping.