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We provide optimal lower bounds for two well-known parameter estimation (also known as statistical estimation) tasks in high dimensions with approximate differential privacy.
Condition numbers of gaussian random matrices
Zizhong Chen and Jack J. Dongarra · 2005
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Calibrating noise to sensitivity in private data analysis
Cynthia Dwork, Frank McSherry, Kobbi Nissim, and Adam D. Smith · 2006
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On the geometry of differential privacy
Moritz Hardt and Kunal Talwar · 2010
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The price of privately releasing contingency tables and the spectra of random matrices with correlated rows
Shiva Prasad Kasiviswanathan, Mark Rudelson, Adam D. Smith, and Jonathan R. Ullman · 2010
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The geometry of differential privacy: the sparse and approximate cases
Aleksandar Nikolov, Kunal Talwar, and Li Zhang · 2013
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Privacy and statistical risk: Formalisms and minimax bounds
Rina Foygel Barber and John C. Duchi · 2014
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Fingerprinting codes and the price of approximate differential privacy
Mark Bun, Jonathan R. Ullman, and Salil P. Vadhan · 2014
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Preventing false discovery in interactive data analysis is hard
Moritz Hardt and Jonathan R. Ullman · 2014
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Efficient algorithms for privately releasing marginals via convex relaxations
Cynthia Dwork, Aleksandar Nikolov, and Kunal Talwar · 2015
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Robust traceability from trace amounts
Cynthia Dwork, Adam D. Smith, Thomas Steinke, Jonathan R. Ullman, and Salil P. Vadhan · 2015
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Interactive fingerprinting codes and the hardness of preventing false discovery
Thomas Steinke and Jonathan R. Ullman · 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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Between pure and approximate differential privacy
Thomas Steinke and Jonathan R. Ullman · 2016
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Statistical query lower bounds for robust estimation of high-dimensional gaussians and gaussian mixtures
Ilias Diakonikolas, Daniel Kane, and Alistair Stewart · 2017
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Tight lower bounds for differentially private selection
Thomas Steinke and Jonathan R. Ullman · 2017
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Finite sample differentially private confidence intervals
Vishesh Karwa and Salil Vadhan · 2018
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Deterministic o(1)-approximation algorithms to 1-center clustering with outliers
Shyam Narayanan · 2018
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High-Dimensional Probability: An Introduction with Applications in Data Science
Roman Vershynin · 2018
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Differentially private covariance estimation
Kareem Amin, Travis Dick, Alex Kulesza, Andres Munoz, and Sergei Vassilvitskii · 2019
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Private stochastic convex optimization with optimal rates
Raef Bassily, Vitaly Feldman, Kunal Talwar, and Abhradeep Guha Thakurta · 2019
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Make up your mind: The price of online queries in differential privacy
Mark Bun, Thomas Steinke, and Jonathan R. Ullman · 2019
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Privately learning high-dimensional distributions
Gautam Kamath, Jerry Li, Vikrant Singhal, and Jonathan Ullman · 2019
Differentially private covariance revisited
Wei Dong, Yuting Liang, and Ke Yi · 2022
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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 · 2022
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New lower bounds for private estimation and a generalized fingerprinting lemma
Gautam Kamath, Argyris Mouzakis, and Vikrant Singhal · 2022
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A private and computationally-efficient estimator for unbounded gaussians
Gautam Kamath, Argyris Mouzakis, Vikrant Singhal, Thomas Steinke, and Jonathan Ullman · 2022
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Private robust estimation by stabilizing convex relaxations
Pravesh K Kothari, Pasin Manurangsi, and Ameya Velingker · 2022
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Differential privacy and robust statistics in high dimensions
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Private mean estimation of heavy-tailed distributions
Gautam Kamath, Vikrant Singhal, and Jonathan Ullman · 2020
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A primer on private statistics
Gautam Kamath and Jonathan Ullman · 2020
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On the sample complexity of privately learning unbounded high-dimensional gaussians
Ishaq Aden-Ali, Hassan Ashtiani, and Gautam Kamath · 2021
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Covariance-aware private mean estimation without private covariance estimation
Gavin Brown, Marco Gaboardi, Adam D. Smith, Jonathan R. Ullman, and Lydia Zakynthinou · 2021
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Private hypothesis selection
Mark Bun, Gautam Kamath, Thomas Steinke, and Zhiwei Steven Wu · 2021
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Instance-optimal mean estimation under differential privacy
Ziyue Huang, Yuting Liang, and Ke Yi · 2021
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Xiyang Liu, Weihao Kong, and Sewoong Oh · 2022
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Tight and robust private mean estimation with few users
Shyam Narayanan, Vahab Mirrokni, and Hossein Esfandiari · 2022
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Friendlycore: Practical differentially private aggregation
Eliad Tsfadia, Edith Cohen, Haim Kaplan, Yishay Mansour, and Uri Stemmer · 2022
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Privately estimating a Gaussian: Efficient, robust and optimal
Daniel Alabi, Pravesh K Kothari, Pranay Tankala, Prayaag Venkat, and Fred Zhang · 2023
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Fast, sample-efficient, affine-invariant private mean and covariance estimation for subgaussian distributions
Gavin Brown, Samuel Hopkins, and Adam Smith · 2023
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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 · 2023
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Score attack: A lower bound technique for optimal differentially private learning
T. Tony Cai, Yichen Wang, and Linjun Zhang · 2023
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A pretty fast algorithm for adaptive private mean estimation
John Duchi, Saminul Haque, and Rohith Kuditipudi · 2023
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Robustness implies privacy in statistical estimation
Samuel B. Hopkins, Gautam Kamath, Mahbod Majid, and Shyam Narayanan · 2023
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Naty Peter, Eliad Tsfadia, and Jonathan R. Ullman · 2023
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