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We consider the noise complexity of differentially private mechanisms in the setting where the user asks $d$ linear queries $f\colon\Rn\to\Re$ non-adaptively.
Perturbation bounds in connection with the singular value decomposition
P.Å. Wedin · 1972
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Approximation of the sphere by polytopes having few vertices
I. Barany and Z. Furedi · 1988
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Isotropic position and inertia ellipsoids and zonoids of the unit ball of a normed n n -dimensional space
V.D. Milman and A. Pajor · 1989
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A random polynomial time algorithm for approximating the volume of convex bodies
Martin E. Dyer, Alan M. Frieze, and Ravi Kannan · 1991
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Geometric Algorithms and Combinatorial Optimization (Algorithms and Combinatorics)
Martin Grötschel, Laszlo Lovász, and Alexander Schrijver · 1994
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Random walks and an o * {}^{\mbox{*}} (n 5 {}^{\mbox{5}} ) volume algorithm for convex bodies
Ravi Kannan, László Lovász, and Miklós Simonovits · 1997
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Random spaces generated by vertices of the cube
Apostolos Giannopoulos and Marianna Hartzoulaki · 2002
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Revealing information while preserving privacy
Irit Dinur and Kobbi Nissim · 2003
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Notes on isotropic convex bodies
Apostolos Giannopoulos · 2003
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Convex Optimization
Stephen Boyd and Lieven Vandenberghe · 2004
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Practical privacy: the sulq framework
Avrim Blum, Cynthia Dwork, Frank McSherry, and Kobbi Nissim · 2005
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Smallest singular value of random matrices and geometry of random polytopes
A. E. Litvak, A. Pajor, M. Rudelson, and Tomczak-Jaegermann N · 2005
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Geometric random walks: a survey
Santosh Vempala · 2005
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Our data, ourselves: Privacy via distributed noise generation
Cynthia Dwork, Krishnaram Kenthapadi, Frank McSherry, Ilya Mironov, and Moni Naor · 2006
Cited alongside, same era.
Calibrating noise to sensitivity in private data analysis
Cynthia Dwork, Frank McSherry, Kobbi Nissim, and Adam Smith · 2006
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On convex perturbations with a bounded isotropic constant
Bo’az Klartag · 2006
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Privacy, accuracy, and consistency too: a holistic solution to contingency table release
Boaz Barak, Kamalika Chaudhuri, Cynthia Dwork, Satyen Kale, Frank McSherry, and Kunal Talwar · 2007
Privacy-preserving logistic regression
Kamalika Chaudhuri and Claire Monteleoni · 2008
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Differential privacy: A survey of results
Cynthia Dwork · 2008
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New efficient attacks on statistical disclosure control mechanisms
Cynthia Dwork and Sergey Yekhanin · 2008
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What can we learn privately?
Shiva Prasad Kasiviswanathan, Homin K. Lee, Kobbi Nissim, Sofya Raskhodnikova, and Adam Smith · 2008
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A decentralized algorithm for spectral analysis
David Kempe and Frank McSherry · 2008
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Private coresets
D. Feldman, A. Fiat, H. Kaplan, and K. Nissim · 2009
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Universally utility-maximizing privacy mechanisms
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Cited alongside, same era.
The price of privacy and the limits of LP decoding
Cynthia Dwork, Frank McSherry, and Kunal Talwar · 2007
Cited alongside, same era.
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
Cited alongside, same era.
The boundary between privacy and utility in data publishing
Vibhor Rastogi, Dan Suciu, and Sungho Hong · 2007
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A learning theory approach to non-interactive database privacy
Avrim Blum, Katrina Ligett, and Aaron Roth · 2008
Cited alongside, same era.
Arpita Ghosh, Tim Roughgarden, and Mukund Sundararajan · 2009
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On the hyperplane conjecture for random convex sets
Bo’az Klartag and Gady Kozma · 2009
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The price of privately releasing contingency tables and the spectra of random matrices with correlated rows
Shiva Kasiviswanathan, Mark Rudelson, and Adam Smith · 2009
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Differentially private recommender systems: building privacy into the net
Frank McSherry and Ilya Mironov · 2009
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Differentially private approximation algorithms
Anupam Gupta, Katrina Ligett, Frank McSherry, Aaron Roth, and Kunal Talwar · 2010
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