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We consider the noisy power method algorithm, which has wide applications in machine learning and statistics, especially those related to principal component analysis (PCA) under resource (communication, memory or privacy) constraints.
The approximation of one matrix by another of lower rank
C. Eckart and G. Young · 1936
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Numerical linear algebra
L. N. Trefethen and D. Bau III · 1997
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Our data, ourselves: Privacy via distributed noise generation
C. Dwork, K. Kenthapadi, F. McSherry, I. Mironov, and M. Naor · 2006
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Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
N. Halko, P.-G. Martinsson, and J. A. Tropp · 2011
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Near-optimal algorithms for differentially private principal components
K. Chaudhuri, A. Sarwate, and K. Sinha · 2012
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Beyond worst-case analysis in private singular vector computation
M. Hardt and A. Roth · 2013
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Memory limited, streaming pca
I. Mitliagkas, C. Caramanis, and P. Jain · 2013
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Improved distributed principal component analysis
M.-F. Balcan, V. Kanchanapally, Y. Liang, and D. Woodruff · 2014
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Analyze gauss: optimal bounds for privacy-preserving principal component analysis
C. Dwork, K. Talwar, A. Thakurta, and L. Zhang · 2014
Cited alongside, same era.
The noisy power method: A meta algorithm with applications
M. Hardt and E. Price · 2014
Cited alongside, same era.
Spectral gap error bounds for improving CUR matrix decomposition and the nyström method
D. Anderson, S. Du, M. Mahoney, C. Melgaard, K. Wu, and M. Gu · 2015
Cited alongside, same era.
Optimal principal component analysis in distributed and streaming models
C. Boutsidis, D. Woodruff, and P. Zhong · 2015
Cited alongside, same era.
Subspace iteration randomization and singular value problems
M. Gu · 2015
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Fast differentially private matrix factorization
Z. Liu, Y.-X. Wang, and A. Smola · 2015
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Stronger approximate singular value decomposition via the block lanczos and power methods
C. Musco and C. Musco · 2015
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Improved Analyses of the Randomized Power Method and Block Lanczos Method
S. Wang, Z. Zhang, and T. Zhang · 2015
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Rivalry of two families of algorithms for memory-restricted streaming pca
C.-L. Li, H.-T. Lin, and C.-J. Lu · 2016
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