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We give new upper and lower bounds on the minimax sample complexity of differentially private mean estimation of distributions with bounded $k$-th moments.
Rates of convergence of minimum distance estimators and Kolmogorov’s entropy
Yannis G. Yatracos · 1985
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A universally acceptable smoothing factor for kernel density estimation
Luc Devroye and Gábor Lugosi · 1996
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Nonasymptotic universal smoothing factors, kernel complexity and Yatracos classes
Luc Devroye and Gábor Lugosi · 1997
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Combinatorial methods in density estimation
Luc Devroye and Gábor Lugosi · 2001
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Practical privacy: The SuLQ framework
Avrim Blum, Cynthia Dwork, Frank McSherry, and Kobbi Nissim · 2005
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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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Density estimation in linear time
Satyaki Mahalanabis and Daniel Stefankovic · 2008
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Boosting and differential privacy
Cynthia Dwork, Guy N. Rothblum, and Salil Vadhan · 2010
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Privacy-preserving statistical estimation with optimal convergence rates
Adam Smith · 2011
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Learning Poisson binomial distributions
Constantinos Daskalakis, Ilias Diakonikolas, and Rocco A. Servedio · 2012
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Local privacy and statistical minimax rates
John C. Duchi, Michael I. Jordan, and Martin J. Wainwright · 2013
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Sorting with adversarial comparators and application to density estimation
Jayadev Acharya, Ashkan Jafarpour, Alon Orlitsky, and Ananda Theertha Suresh · 2014
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Privacy and statistical risk: Formalisms and minimax bounds, 2014
Rina Foygel Barber and John C. Duchi · 2014
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Fingerprinting codes and the price of approximate differential privacy
Mark Bun, Jonathan Ullman, and Salil Vadhan · 2014
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Faster and sample near-optimal algorithms for proper learning mixtures of Gaussians
Constantinos Daskalakis and Gautam Kamath · 2014
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RAPPOR: Randomized aggregatable privacy-preserving ordinal response
Úlfar Erlingsson, Vasyl Pihur, and Aleksandra Korolova · 2014
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Near-optimal-sample estimators for spherical Gaussian mixtures
Ananda Theertha Suresh, Alon Orlitsky, Jayadev Acharya, and Ashkan Jafarpour · 2014
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Differentially private release and learning of threshold functions
Mark Bun, Kobbi Nissim, Uri Stemmer, and Salil Vadhan · 2015
Cited alongside, same era.
Differentially private learning of structured discrete distributions
Ilias Diakonikolas, Moritz Hardt, and Ludwig Schmidt · 2015
Cited alongside, same era.
Robust traceability from trace amounts
Cynthia Dwork, Adam Smith, Thomas Steinke, Jonathan Ullman, and Salil Vadhan · 2015
Cited alongside, same era.
Interactive fingerprinting codes and the hardness of preventing false discovery
Thomas Steinke and Jonathan Ullman · 2015
Cited alongside, same era.
Simultaneous private learning of multiple concepts
Mark Bun, Kobbi Nissim, and Uri Stemmer · 2016
Cited alongside, same era.
Concentrated differential privacy: Simplifications, extensions, and lower bounds
Mark Bun and Thomas Steinke · 2016
Differentially private sub-Gaussian location estimators
Marco Avella-Medina and Victor-Emmanuel Brunel · 2019
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The optimal approximation factor in density estimation
Olivier Bousquet, Daniel M. Kane, and Shay Moran · 2019
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Private hypothesis selection
Mark Bun, Gautam Kamath, Thomas Steinke, and Zhiwei Steven Wu · 2019
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Average-case averages: Private algorithms for smooth sensitivity and mean estimation
Mark Bun and Thomas Steinke · 2019
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Differential privacy on finite computers
Victor Balcer and Salil Vadhan · 2019
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Fast mean estimation with sub-Gaussian rates
Yeshwanth Cherapanamjeri, Nicolas Flammarion, and Peter L. Bartlett · 2019
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Cited alongside, same era.
Robust estimators in high dimensions without the computational intractability
Ilias Diakonikolas, Gautam Kamath, Daniel M. Kane, Jerry Li, Ankur Moitra, and Alistair Stewart · 2016
Cited alongside, same era.
Learning with privacy at scale
Differential Privacy Team, Apple · 2017
Cited alongside, same era.
Minimax optimal procedures for locally private estimation
John C. Duchi, Michael I. Jordan, and Martin J. Wainwright · 2017
Cited alongside, same era.
Being robust (in high dimensions) can be practical
Ilias Diakonikolas, Gautam Kamath, Daniel M. Kane, Jerry Li, Ankur Moitra, and Alistair Stewart · 2017
Cited alongside, same era.
Collecting telemetry data privately
Bolin Ding, Janardhan Kulkarni, and Sergey Yekhanin · 2017
Cited alongside, same era.
The modernization of statistical disclosure limitation at the U.S. census bureau, 2017
Aref N. Dajani, Amy D. Lauger, Phyllis E. Singer, Daniel Kifer, Jerome P. Reiter, Ashwin Machanavajjhala, Simson L. Garfinkel, Scot A. Dahl, Matthew Graham, Vishesh Karwa, Hang Kim, Philip Lelerc, Ian M. Schmutte, William N. Sexton, Lars Vilhuber, and John M. Abowd · 2017
Cited alongside, same era.
Later among the works it cites.
The cost of privacy: Optimal rates of convergence for parameter estimation with differential privacy
T. Tony Cai, Yichen Wang, and Linjun Zhang · 2019
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Robust subgaussian estimation of a mean vector in nearly linear time
Jules Depersin and Guillaume Lecué · 2019
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Locally private confidence intervals: Z-test and tight confidence intervals
Marco Gaboardi, Ryan Rogers, and Or Sheffet · 2019
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Locally private Gaussian estimation
Matthew Joseph, Janardhan Kulkarni, Jieming Mao, and Zhiwei Steven Wu · 2019
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Privately learning high-dimensional distributions
Gautam Kamath, Jerry Li, Vikrant Singhal, and Jonathan Ullman · 2019
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Differentially private algorithms for learning mixtures of separated Gaussians
Gautam Kamath, Or Sheffet, Vikrant Singhal, and Jonathan Ullman · 2019
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Mean estimation and regression under heavy-tailed distributions: A survey
Gábor Lugosi and Shahar Mendelson · 2019
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Sub-Gaussian estimators of the mean of a random vector
Gábor Lugosi and Shahar Mendelson · 2019
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Generalized resilience and robust statistics
Banghua Zhu, Jiantao Jiao, and Jacob Steinhardt · 2019
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Coinpress: Practical private mean and covariance estimation
Sourav Biswas, Yihe Dong, Gautam Kamath, and Jonathan Ullman · 2020
Closest in time.
Differentially private confidence intervals
Wenxin Du, Canyon Foot, Monica Moniot, Andrew Bray, and Adam Groce · 2020
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A primer on private statistics
Gautam Kamath and Jonathan Ullman · 2020
Closest in time.