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We derive concentration inequalities for differentially private median and mean estimators building on the "Propose, Test, Release" (PTR) mechanism introduced by Dwork and Lei (2009).
The accuracy of the gaussian approximation to the sum of independent variates
Andrew C Berry · 1941
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The notion of breakdown point
David L Donoho and Peter J Huber · 1983
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Problem complexity and method efficiency in optimization
Arkadiĭ S. Nemirovsky and David B. Yudin · 1983
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Calibrating noise to sensitivity in private data analysis
Cynthia Dwork, Frank McSherry, Kobbi Nissim, and Adam Smith · 2006
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Smooth sensitivity and sampling in private data analysis
Kobbi Nissim, Sofya Raskhodnikova, and Adam Smith · 2007
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Differential privacy and robust statistics
Cynthia Dwork and Jing Lei · 2009
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Robust Statistics
Peter J. Huber and Elvezio Ronchetti · 2009
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A statistical framework for differential privacy
Larry Wasserman and Shuheng Zhou · 2010
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Differentially private M-estimators
Jing Lei · 2011
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Robust empirical mean estimators
Matthieu Lerasle and Roberto I Oliveira · 2011
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Privacy-preserving statistical estimation with optimal convergence rates
Adam Smith · 2011
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Challenging the empirical mean and empirical variance: a deviation study
Olivier Catoni · 2012
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Convergence rates for differentially private statistical estimation
Kamalika Chaudhuri and Daniel Hsu · 2012
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Private convex empirical risk minimization and high-dimensional regression
Daniel Kifer, Adam Smith, and Abhradeep Thakurta · 2012
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Bandits with heavy tail
Sébastien Bubeck, Nicolo Cesa-Bianchi, and Gábor Lugosi · 2013
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Private empirical risk minimization: Efficient algorithms and tight error bounds
Raef Bassily, Adam Smith, and Abhradeep Thakurta · 2014
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The algorithmic foundations of differential privacy
Cynthia Dwork and Aaron Roth · 2014
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Inference using noisy degrees: Differentially private beta-model and synthetic graphs
Vishesh Karwa and Aleksandra Slavković · 2016
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Algorithms for differentially private multi-armed bandits
Aristide CY Tossou and Christos Dimitrakakis · 2016
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Differentially private ordinary least squares
Or Sheffet · 2017
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Minimax optimal procedures for locally private estimation
John C Duchi, Michael I Jordan, and Martin J Wainwright · 2018
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Certified robustness to adversarial examples with differential privacy
Mathias Lecuyer, Vaggelis Atlidakis, Roxana Geambasu, Daniel Hsu, and Suman Jana · 2018
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Differentially private contextual linear bandits
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(nearly) optimal differentially private stochastic multi-arm bandits
Nikita Mishra and Abhradeep Thakurta · 2015
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Nearly optimal private lasso
Kunal Talwar, Abhradeep Guha Thakurta, and Li Zhang · 2015
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Deep learning with differential privacy
Martin Abadi, Andy Chu, Ian Goodfellow, H Brendan McMahan, Ilya Mironov, Kunal Talwar, and Li Zhang · 2016
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Differentially private chi-squared hypothesis testing: Goodness of fit and independence testing
Marco Gaboardi, Hyun-Woo Lim, Ryan M Rogers, and Salil P Vadhan · 2016
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Roshan Shariff and Or Sheffet · 2018
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Differentially private significance tests for regression coefficients
Andrés F Barrientos, Jerome P Reiter, Ashwin Machanavajjhala, and Yan Chen · 2019
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The cost of privacy: optimal rates of convergence for paramer estimaion with differential privacy
Tony T. Cai, Yichen Wang, and Linjun Zhang · 2019
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Distributed statistical estimation and rates of convergence in normal approximation
Stanislav Minsker · 2019
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Privacy-preserving parametric inference: a case for robust statistics
Marco Avella-Medina · 2020
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