Approximate Differential Privacy of the $\ell_2$ Mechanism

Matthew Joseph, Alex Kulesza, Alexander Yu
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:28377-28392, 2025.

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 this Paper

BibTeX
@InProceedings{pmlr-v267-joseph25a, 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}, pages = {28377--28392}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/joseph25a/joseph25a.pdf}, url = {https://proceedings.mlr.press/v267/joseph25a.html}, 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.} }
Endnote
%0 Conference Paper %T Approximate Differential Privacy of the $\ell_2$ Mechanism %A Matthew Joseph %A Alex Kulesza %A Alexander Yu %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-joseph25a %I PMLR %P 28377--28392 %U https://proceedings.mlr.press/v267/joseph25a.html %V 267 %X 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.
APA
Joseph, M., Kulesza, A. & Yu, A.. (2025). Approximate Differential Privacy of the $\ell_2$ Mechanism. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:28377-28392 Available from https://proceedings.mlr.press/v267/joseph25a.html.

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