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2019

R\'enyi Differential Privacy of the Sampled Gaussian Mechanism

Mironov, Ilya, Talwar, Kunal, Zhang, Li

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The Sampled Gaussian Mechanism (SGM)---a composition of subsampling and the additive Gaussian noise---has been successfully used in a number of machine learning applications.

The mechanism's unexpected power is derived from privacy amplification by sampling where the privacy cost of a single evaluation diminishes quadratically, rather than linearly, with the sampling rate.
Characterizing the precise privacy properties of SGM motivated development of several relaxations of the notion of differential privacy.
This work unifies and fills in gaps in published results on SGM.

R\'enyi Differential Privacy of the Sampled Gaussian Mechanism · Around

Built on

Our data, ourselves: Privacy via distributed noise generation
Cynthia Dwork, Krishnaram Kenthapadi, Frank McSherry, Ilya Mironov, and Moni Naor · 2006
Earlier work this paper cites.
Calibrating noise to sensitivity in private data analysis
Cynthia Dwork, Frank McSherry, Kobbi Nissim, and Adam Smith · 2006
Earlier work this paper cites.
Differential privacy
Cynthia Dwork · 2006
Earlier work this paper cites.
Differential privacy and the secrecy of the sample
Adam D. Smith · 2009
Earlier work this paper cites.

Similar

What can we learn privately?
Shiva Prasad Kasiviswanathan, Homin K. Lee, Kobbi Nissim, Sofya Raskhodnikova, and Adam Smith · 2011
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Rényi divergence and Kullback-Leibler divergence
Tim van Erven and Peter Harremoës · 2014
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Deep learning with differential privacy
Martín Abadi, Andy Chu, Ian Goodfellow, H. Brendan McMahan, Ilya Mironov, Kunal Talwar, and Li Zhang · 2016
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Concentrated differential privacy: Simplifications, extensions, and lower bounds
Mark Bun and Thomas Steinke · 2016
Cited alongside, same era.

Then

Concentrated differential privacy
Original
Cynthia Dwork and Guy N. Rothblum · 2016
Later among the works it cites.
Rényi differential privacy
Ilya Mironov · 2017
Later among the works it cites.
Composable and versatile privacy via Truncated CDP
Mark Bun, Cynthia Dwork, Guy N. Rothblum, and Thomas Steinke · 2018
Later among the works it cites.

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