Approximate Differential Privacy of the $\ell_2$ Mechanism
Abstract
We study the $\ell_2$ mechanism for computing a $d$-dimensional statistic with bounded $\ell_2$ sensitivity under approximate differential privacy. Across a range of privacy parameters, we find that the $\ell_2$ mechanism obtains error approaching that of the Laplace mechanism as $d \to 1$ and approaching that of the Gaussian mechanism as $d \to \infty$; however, it dominates both in between.
Cite
Text
Joseph et al. "Approximate Differential Privacy of the $\ell_2$ Mechanism." Proceedings of the 42nd International Conference on Machine Learning, 2025.Markdown
[Joseph et al. "Approximate Differential Privacy of the $\ell_2$ Mechanism." Proceedings of the 42nd International Conference on Machine Learning, 2025.](https://mlanthology.org/icml/2025/joseph2025icml-approximate/)BibTeX
@inproceedings{joseph2025icml-approximate,
title = {{Approximate Differential Privacy of the $\ell_2$ Mechanism}},
author = {Joseph, Matthew and Kulesza, Alex and Yu, Alexander},
booktitle = {Proceedings of the 42nd International Conference on Machine Learning},
year = {2025},
pages = {28377-28392},
volume = {267},
url = {https://mlanthology.org/icml/2025/joseph2025icml-approximate/}
}