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We study the canonical statistical task of computing the principal component from $n$ i.i.d.~data in $d$ dimensions under $(\varepsilon,\delta)$-differential privacy.
Simplified neuron model as a principal component analyzer
Erkki Oja · 1982
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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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Differential privacy and robust statistics
Cynthia Dwork and Jing Lei · 2009
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Privacy integrated queries: an extensible platform for privacy-preserving data analysis
Frank D McSherry · 2009
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Differential privacy for clinical trial data: Preliminary evaluations
Duy Vu and Aleksandra Slavkovic · 2009
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Principal component analysis with contaminated data: The high dimensional case
Huan Xu, Constantine Caramanis, and Shie Mannor · 2010
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Beating randomized response on incoherent matrices
Moritz Hardt and Aaron Roth · 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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User-friendly tail bounds for sums of random matrices
Joel A Tropp · 2012
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Minimax rates of estimation for sparse pca in high dimensions
Vincent Vu and Jing Lei · 2012
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A near-optimal algorithm for differentially-private principal components
Kamalika Chaudhuri, Anand D Sarwate, and Kaushik Sinha · 2013
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Beyond worst-case analysis in private singular vector computation
Moritz Hardt and Aaron Roth · 2013
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On differentially private low rank approximation
Michael Kapralov and Kunal Talwar · 2013
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Differential privacy: an exploration of the privacy-utility landscape
Darakhshan J Mir · 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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Private empirical risk minimization: Efficient algorithms and tight error bounds
Raef Bassily, Adam Smith, and Abhradeep Thakurta · 2014
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Robust and private bayesian inference
Christos Dimitrakakis, Blaine Nelson, Aikaterini Mitrokotsa, and Benjamin IP Rubinstein · 2014
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The algorithmic foundations of differential privacy
Cynthia Dwork and Aaron Roth · 2014
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Analyze gauss: optimal bounds for privacy-preserving principal component analysis
Cynthia Dwork, Kunal Talwar, Abhradeep Thakurta, and Li Zhang · 2014
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Rappor: Randomized aggregatable privacy-preserving ordinal response
Úlfar Erlingsson, Vasyl Pihur, and Aleksandra Korolova · 2014
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The noisy power method: A meta algorithm with applications
Moritz Hardt and Eric Price · 2014
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The composition theorem for differential privacy
Peter Kairouz, Sewoong Oh, and Pramod Viswanath · 2015
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High dimensional statistics
Phillippe Rigollet and Jan-Christian Hütter · 2015
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Privacy for free: Posterior sampling and stochastic gradient monte carlo
Yu-Xiang Wang, Stephen Fienberg, and Alex Smola · 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
Cited alongside, same era.
An improved gap-dependency analysis of the noisy power method
Maria-Florina Balcan, Simon Shaolei Du, Yining Wang, and Adams Wei Yu · 2016
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Building a rappor with the unknown: Privacy-preserving learning of associations and data dictionaries
Giulia Fanti, Vasyl Pihur, and Úlfar Erlingsson · 2016
Cited alongside, same era.
On the theory and practice of privacy-preserving bayesian data analysis
James Foulds, Joseph Geumlek, Max Welling, and Kamalika Chaudhuri · 2016
Cited alongside, same era.
Coinpress: Practical private mean and covariance estimation
Sourav Biswas, Yihe Dong, Gautam Kamath, and Jonathan Ullman · 2020
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Private stochastic convex optimization: optimal rates in linear time
Vitaly Feldman, Tomer Koren, and Kunal Talwar · 2020
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Robust sub-gaussian principal component analysis and width-independent schatten packing
Arun Jambulapati, Jerry Li, and Kevin Tian · 2020
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Private mean estimation of heavy-tailed distributions
Gautam Kamath, Vikrant Singhal, and Jonathan Ullman · 2020
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Robust meta-learning for mixed linear regression with small batches
Weihao Kong, Raghav Somani, Sham Kakade, and Sewoong Oh · 2020
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Streaming pca: Matching matrix bernstein and near-optimal finite sample guarantees for oja’s algorithm
Prateek Jain, Chi Jin, Sham M Kakade, Praneeth Netrapalli, and Aaron Sidford · 2016
Cited alongside, same era.
Differential privacy without sensitivity
Kentaro Minami, HItomi Arai, Issei Sato, and Hiroshi Nakagawa · 2016
Cited alongside, same era.
Finite sample differentially private confidence intervals
Vishesh Karwa and Salil Vadhan · 2017
Cited alongside, same era.
Privacy loss in apple’s implementation of differential privacy on macos 10.12
Jun Tang, Aleksandra Korolova, Xiaolong Bai, Xueqiang Wang, and Xiaofeng Wang · 2017
Cited alongside, same era.
The us census bureau adopts differential privacy
John M Abowd · 2018
Cited alongside, same era.
Minimax optimal procedures for locally private estimation
John C Duchi, Michael I Jordan, and Martin J Wainwright · 2018
Cited alongside, same era.
Calibrating noise to variance in adaptive data analysis
Vitaly Feldman and Thomas Steinke · 2018
Cited alongside, same era.
Optimal private median estimation under minimal distributional assumptions
Christos Tzamos, Emmanouil-Vasileios Vlatakis-Gkaragkounis, and Ilias Zadik · 2020
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On differentially private stochastic convex optimization with heavy-tailed data
Di Wang, Hanshen Xiao, Srinivas Devadas, and Jinhui Xu · 2020
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Differentially private assouad, fano, and le cam
Jayadev Acharya, Ziteng Sun, and Huanyu Zhang · 2021
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Differentially private learning with adaptive clipping
Galen Andrew, Om Thakkar, Brendan McMahan, and Swaroop Ramaswamy · 2021
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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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Unbiased statistical estimation and valid confidence intervals under differential privacy
Christian Covington, Xi He, James Honaker, and Gautam Kamath · 2021
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Wei Dong and Ke Yi · 2021
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Tight and robust private mean estimation with few users
Hossein Esfandiari, Vahab Mirrokni, and Shyam Narayanan · 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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High dimensional differentially private stochastic optimization with heavy-tailed data
Lijie Hu, Shuo Ni, Hanshen Xiao, and Di Wang · 2021
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Improved rates for differentially private stochastic convex optimization with heavy-tailed data
Gautam Kamath, Xingtu Liu, and Huanyu Zhang · 2021
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A private and computationally-efficient estimator for unbounded gaussians
Gautam Kamath, Argyris Mouzakis, Vikrant Singhal, Thomas Steinke, and Jonathan Ullman · 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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Janardhan Kulkarni, Yin Tat Lee, and Daogao Liu · 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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Hiding among the clones: A simple and nearly optimal analysis of privacy amplification by shuffling
Vitaly Feldman, Audra McMillan, and Kunal Talwar · 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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On robustness and local differential privacy
Mengchu Li, Thomas B Berrett, and Yi Yu · 2022
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