Improved Utility Analysis of Private CountSketchDownload PDF

Published: 31 Oct 2022, Last Modified: 12 Oct 2022NeurIPS 2022 AcceptReaders: Everyone
Keywords: sketching, dimension reduction, sparsity, differential privacy, countsketch
TL;DR: CountSketch made private using the Gaussian mechanism has essentially optimal utility
Abstract: 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.
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