TY - GEN
T1 - Improved Utility Analysis of Private CountSketch
AU - Pagh, Rasmus
AU - Thorup, Mikkel
PY - 2022
Y1 - 2022
N2 - Sketching is an important tool for dealing with high-dimensional vectors that are sparse (or well-approximated by a sparse vector), especially useful in distributed, parallel, and streaming settings.It is known that sketches can be made differentially private by adding noise according to the sensitivity of the sketch, and this has been used in private analytics and federated learning settings.The post-processing property of differential privacy implies that \emph{all} estimates computed from the sketch can be released within the given privacy budget.In this paper we consider the classical CountSketch, made differentially private with the Gaussian mechanism, and give an improved analysis of its estimation error.Perhaps surprisingly, the privacy-utility trade-off is essentially the best one could hope for, independent of the number of repetitions in CountSketch:The error is almost identical to the error from non-private CountSketch plus the noise needed to make the vector private in the original, high-dimensional domain.
AB - Sketching is an important tool for dealing with high-dimensional vectors that are sparse (or well-approximated by a sparse vector), especially useful in distributed, parallel, and streaming settings.It is known that sketches can be made differentially private by adding noise according to the sensitivity of the sketch, and this has been used in private analytics and federated learning settings.The post-processing property of differential privacy implies that \emph{all} estimates computed from the sketch can be released within the given privacy budget.In this paper we consider the classical CountSketch, made differentially private with the Gaussian mechanism, and give an improved analysis of its estimation error.Perhaps surprisingly, the privacy-utility trade-off is essentially the best one could hope for, independent of the number of repetitions in CountSketch:The error is almost identical to the error from non-private CountSketch plus the noise needed to make the vector private in the original, high-dimensional domain.
M3 - Article in proceedings
T3 - Advances in Neural Information Processing Systems
BT - Advances in Neural Information Processing Systems 35 (NeurIPS 2022)
PB - NeurIPS Proceedings
Y2 - 28 November 2022 through 9 December 2022
ER -