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We establish a simple connection between robust and differentially-private algorithms: private mechanisms which perform well with very high probability are automatically robust in the sense that they retain accuracy even if a constant fraction of the samples they receive are adversarially corrupted.
A robust version of the probability ratio test
Peter J Huber · 1965
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John W Tukey · 1975
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Michel Ledoux and Michel Talagrand · 1991
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Toward efficient agnostic learning
Michael J Kearns, Robert E Schapire, and Linda M Sellie · 1994
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Testing that distributions are close
Tugkan Batu, Lance Fortnow, Ronitt Rubinfeld, Warren D Smith, and Patrick White · 2000
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Some optimal inapproximability results
Johan Håstad · 2001
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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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Mechanism design via differential privacy
Frank McSherry and Kunal Talwar · 2007
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Smooth sensitivity and sampling in private data analysis
Kobbi Nissim, Sofya Raskhodnikova, and Adam Smith · 2007
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Resolving individuals contributing trace amounts of dna to highly complex mixtures using high-density snp genotyping microarrays
Nils Homer, Szabolcs Szelinger, Margot Redman, David Duggan, Waibhav Tembe, Jill Muehling, John V Pearson, Dietrich A Stephan, Stanley F Nelson, and David W Craig · 2008
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Differential privacy and robust statistics
Cynthia Dwork and Jing Lei · 2009
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Lower bounds for sparse recovery
Khanh Do Ba, Piotr Indyk, Eric Price, and David P Woodruff · 2010
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On the geometry of differential privacy
Moritz Hardt and Kunal Talwar · 2010
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Robust statistics
Peter J Huber · 2011
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What can we learn privately?
Shiva Prasad Kasiviswanathan, Homin K Lee, Kobbi Nissim, Sofya Raskhodnikova, and Adam Smith · 2011
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Pcps and the hardness of generating private synthetic data
Jonathan Ullman and Salil Vadhan · 2011
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Lower bounds in differential privacy
Anindya De · 2012
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Optimal hypothesis testing for high dimensional covariance matrices
T Tony Cai and Zongming Ma · 2013
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Privately releasing conjunctions and the statistical query barrier
Anupam Gupta, Moritz Hardt, Aaron Roth, and Jonathan Ullman · 2013
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Differentially private feature selection via stability arguments, and the robustness of the lasso
Abhradeep Guha Thakurta and Adam Smith · 2013
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Sum-of-squares proofs and the quest toward optimal algorithms
Boaz Barak and David Steurer · 2014
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Between pure and approximate differential privacy
Thomas Steinke and Jonathan Ullman · 2015
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Concentrated differential privacy: Simplifications, extensions, and lower bounds
Mark Bun and Thomas Steinke · 2016
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Reducibility and statistical-computational gaps from secret leakage
Matthew Brennan and Guy Bresler · 2020
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A computational separation between private learning and online learning
Mark Bun · 2020
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Robust and heavy-tailed mean estimation made simple, via regret minimization
Sam Hopkins, Jerry Li, and Fred Zhang · 2020
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Mean estimation with sub-gaussian rates in polynomial time
Samuel B Hopkins · 2020
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Private mean estimation of heavy-tailed distributions
Gautam Kamath, Vikrant Singhal, and Jonathan Ullman · 2020
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Covariance-aware private mean estimation without private covariance estimation
Gavin Brown, Marco Gaboardi, Adam Smith, Jonathan Ullman, and Lydia Zakynthinou · 2021
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Answering nˆ2+o(1) counting queries with differential privacy is hard
Jonathan Ullman · 2016
Cited alongside, same era.
Computationally efficient robust sparse estimation in high dimensions
Sivaraman Balakrishnan, Simon S Du, Jerry Li, and Aarti Singh · 2017
Cited alongside, same era.
Statistical query lower bounds for robust estimation of high-dimensional gaussians and gaussian mixtures
Ilias Diakonikolas, Daniel M Kane, and Alistair Stewart · 2017
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Finite sample differentially private confidence intervals
Vishesh Karwa and Salil Vadhan · 2017
Cited alongside, same era.
The total variation distance between high-dimensional gaussians
Luc Devroye, Abbas Mehrabian, and Tommy Reddad · 2018
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Differentially private false discovery rate control
Cynthia Dwork, Weijie J Su, and Li Zhang · 2018
Cited alongside, same era.
High dimensional estimation via sum-of-squares proofs
Prasad Raghavendra, Tselil Schramm, and David Steurer · 2018
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The cost of privacy: Optimal rates of convergence for parameter estimation with differential privacy
T Tony Cai, Yichen Wang, and Linjun Zhang · 2021
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The sample complexity of robust covariance testing
Ilias Diakonikolas and Daniel M Kane · 2021
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Efficient mean estimation with pure differential privacy via a sum-of-squares exponential mechanism
Samuel B Hopkins, Gautam Kamath, and Mahbod Majid · 2021
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Private robust estimation by stabilizing convex relaxations
Pravesh K Kothari, Pasin Manurangsi, and Ameya Velingker · 2021
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Robust and differentially private mean estimation
Xiyang Liu, Weihao Kong, Sham Kakade, and Sewoong Oh · 2021
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Differential privacy and robust statistics in high dimensions
Xiyang Liu, Weihao Kong, and Sewoong Oh · 2021
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Oren Mangoubi and Nisheeth K Vishnoi · 2021
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Geographic spines in the 2020 census disclosure avoidance system topdown algorithm
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Learning to be adversarially robust and differentially private
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