Approximate Differential Privacy of the $\ell_2$ Mechanism

Matthew Joseph, Alex Kulesza, Alexander Yu

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.

Lay Summary: For a certain kind of statistic, we provide a new algorithm that computes the statistic with a quantitative privacy guarantee, with lower error than previous such algorithms.

Link To Code: https://github.com/google-research/google-research/tree/master/dp_l2

Primary Area: Social Aspects->Privacy

Keywords: differential privacy

Submission Number: 4032