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In this paper, we study what price one has to pay to release {\em differentially private low-rank factorization} of a matrix.
The approximation of one matrix by another of lower rank
Carl Eckart and Gale Young · 1936
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Stanley L. Warner · 1965
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William B Johnson and Joram Lindenstrauss · 1984
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Christos H Papadimitriou, Hisao Tamaki, Prabhakar Raghavan, and Santosh Vempala · 1998
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Latent semantic indexing: A probabilistic analysis
Christos H Papadimitriou, Hisao Tamaki, Prabhakar Raghavan, and Santosh Vempala · 1998
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Dimitris Achlioptas, Amos Fiat, Anna R Karlin, and Frank McSherry · 2001
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Spectral partitioning of random graphs
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Yongming Qu, George Ostrouchov, Nagiza Samatova, and Al Geist · 2002
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Irit Dinur and Kobbi Nissim · 2003
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Alexandre Evfimievski, Johannes Gehrke, and Ramakrishnan Srikant · 2003
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Petros Drineas, Alan Frieze, Ravi Kannan, Santosh Vempala, and V Vinay · 2004
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Alan Frieze, Ravi Kannan, and Santosh Vempala · 2004
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John Shawe-Taylor and Nello Cristianini · 2004
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Dimitris Achlioptas and Frank McSherry · 2005
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Zheng-Jian Bai, Raymond H Chan, and Franklin T Luk · 2005
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Practical privacy: the sulq framework
Avrim Blum, Cynthia Dwork, Frank McSherry, and Kobbi Nissim · 2005
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Approximating a gram matrix for improved kernel-based learning
Petros Drineas and Michael W Mahoney · 2005
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Ravindran Kannan, Hadi Salmasian, and Santosh Vempala · 2005
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Shanmugavelayutham Muthukrishnan · 2005
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The random projection method
Santosh S Vempala · 2005
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Maria-Florina Balcan, Avrim Blum, and Santosh Vempala · 2006
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Fast monte carlo algorithms for matrices ii: Computing a low-rank approximation to a matrix
Petros Drineas, Ravi Kannan, and Michael W Mahoney · 2006
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Our Data, Ourselves: Privacy Via Distributed Noise Generation
Cynthia Dwork, Krishnaram Kenthapadi, Frank McSherry, Ilya Mironov, and Moni Naor · 2006
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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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Matrix approximation and projective clustering via volume sampling
Amit Deshpande, Luis Rademacher, Santosh Vempala, and Grant Wang · 2006
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Amit Deshpande and Santosh Vempala · 2006
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Privacy via pseudorandom sketches
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Nir Ailon and Bernard Chazelle · 2006
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Tamas Sarlos · 2006
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Fast computation of low-rank matrix approximations
Dimitris Achlioptas and Frank McSherry · 2007
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Avrim Blum, Katrina Ligett, and Aaron Roth · 2013
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Low rank approximation and regression in input sparsity time
Kenneth L Clarkson and David P Woodruff · 2013
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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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Beyond worst-case analysis in private singular vector computation
Moritz Hardt and Aaron Roth · 2013
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Low-rank matrix completion using alternating minimization
Prateek Jain, Praneeth Netrapalli, and Sujay Sanghavi · 2013
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On differentially private low rank approximation
Michael Kapralov and Kunal Talwar · 2013
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Sampling from large matrices: An approach through geometric functional analysis
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Low-rank approximation of generic p \ \backslash timesq \ \backslash times2 arrays and diverging components in the candecomp/parafac model
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(nearly) optimal algorithms for private online learning in full-information and bandit settings
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Turnstile streaming algorithms might as well be linear sketches
Yi Li, Huy L. Nguyen, and David P. Woodruff · 2014
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Differentially private linear algebra in the streaming model
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Dimensionality reduction for k-means clustering and low rank approximation
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Wishart mechanism for differentially private principal components analysis
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