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We study iterative methods based on Krylov subspaces for low-rank approximation under any Schatten-$p$ norm.
Some matrix-inequalities and metrization of matric space
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Norm ideals of completely continuous operators
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Krylov subspace methods for solving large unsymmetric linear systems
Yousef Saad · 1981
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On an inequality of Lieb and Thirring
Huzihiro Araki · 1990
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Some operator inequalities concerning generalized inverses
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Fast exact multiplication by the Hessian
Barak A. Pearlmutter · 1994
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Some large-scale matrix computation problems
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Nonlinear dimensionality reduction by locally linear embedding
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A global geometric framework for nonlinear dimensionality reduction
Joshua B Tenenbaum, Vin De Silva, and John C Langford · 2000
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Pinchings and norms of scaled triangular matrices
Rajendra Bhatia, William Kahan, and Ren-Cang Li · 2002
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Chebyshev polynomials
John C Mason and David C Handscomb · 2002
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Weighted low-rank approximations
Nathan Srebro and Tommi Jaakkola · 2003
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Data streams: Algorithms and applications
S. Muthukrishnan · 2005
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On a norm compression inequality for 2 × \times N partitioned block matrices
Koenraad MR Audenaert · 2008
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Fast counting of triangles in large real networks without counting: Algorithms and laws
Charalampos E Tsourakakis · 2008
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Exact matrix completion via convex optimization
Emmanuel J Candès and Benjamin Recht · 2009
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Numerical linear algebra in the streaming model
Kenneth L Clarkson and David P Woodruff · 2009
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Learning multiple layers of features from tiny images
Alex Krizhevsky, Geoffrey Hinton, et al · 2009
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Spectral algorithms
Ravi Kannan and Santosh S. Vempala · 2009
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Counting triangles in large graphs using randomized matrix trace estimation
Haim Avron · 2010
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Matrix completion with noise
Emmanuel J Candes and Yaniv Plan · 2010
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Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization
Benjamin Recht, Maryam Fazel, and Pablo A Parrilo · 2010
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Robust PCA via outlier pursuit
Huan Xu, Constantine Caramanis, and Sujay Sanghavi · 2010
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Robust principal component analysis?
Emmanuel J Candès, Xiaodong Li, Yi Ma, and John Wright · 2011
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Randomized algorithms for matrices and data
Michael W. Mahoney · 2011
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Sketching and streaming high-dimensional vectors
Jelani Jelani Osei Nelson · 2011
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Problems and conjectures in matrix and operator inequalities
Koenraad MR Audenaert and Fuad Kittaneh · 2012
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Topics in random matrix theory
Terence Tao · 2012
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Eigenvalues of a matrix in the streaming model
Alexandr Andoni and Huy L. Nguyen · 2013
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Matrix analysis
Rajendra Bhatia · 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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Krylov subspace methods: principles and analysis
Jörg Liesen and Zdenek Strakos · 2013
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Low-distortion subspace embeddings in input-sparsity time and applications to robust linear regression
Xiangrui Meng and Michael W Mahoney · 2013
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Low-distortion subspace embeddings in input-sparsity time and applications to robust linear regression
Xiangrui Meng and Michael W. Mahoney · 2013
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OSNAP: faster numerical linear algebra algorithms via sparser subspace embeddings
Jelani Nelson and Huy L. Nguyen · 2013
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Sublinear time low-rank approximation of distance matrices
Ainesh Bakshi and David Woodruff · 2018
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Quantum-inspired sublinear classical algorithms for solving low-rank linear systems
Nai-Hui Chia, Han-Hsuan Lin, and Chunhao Wang · 2018
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Quantum-inspired low-rank stochastic regression with logarithmic dependence on the dimension
András Gilyén, Seth Lloyd, and Ewin Tang · 2018
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Quantum singular-value decomposition of nonsparse low-rank matrices
Patrick Rebentrost, Adrian Steffens, Iman Marvian, and Seth Lloyd · 2018
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Tight query complexity lower bounds for PCA via finite sample deformed wigner law
Max Simchowitz, Ahmed El Alaoui, and Benjamin Recht · 2018
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Weighted nuclear norm minimization with application to image denoising
Shuhang Gu, Lei Zhang, Wangmeng Zuo, and Xiangchu Feng · 2014
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On sketching matrix norms and the top singular vector
Yi Li, Huy L Nguyen, and David P Woodruff · 2014
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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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Sketching as a tool for numerical linear algebra
David P. Woodruff · 2014
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Optimal query complexity for estimating the trace of a matrix
Karl Wimmer, Yi Wu, and Peng Zhang · 2014
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Toward a unified theory of sparse dimensionality reduction in euclidean space
Jean Bourgain, Sjoerd Dirksen, and Jelani Nelson · 2015
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A PTAS for lp-low rank approximation
Frank Ban, Vijay Bhattiprolu, Karl Bringmann, Pavel Kolev, Euiwoong Lee, and David P Woodruff · 2019
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Schatten norms in matrix streams: Hello sparsity, goodbye dimension
Vladimir Braverman, Robert Krauthgamer, Aditya Krishnan, and Roi Sinoff · 2019
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Regularized weighted low rank approximation
Frank Ban, David Woodruff, and Qiuyi Zhang · 2019
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An investigation into neural net optimization via Hessian eigenvalue density
Behrooz Ghorbani, Shankar Krishnan, and Ying Xiao · 2019
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Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
András Gilyén, Yuan Su, Guang Hao Low, and Nathan Wiebe · 2019
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Sample-optimal low-rank approximation of distance matrices
Piotr Indyk, Ali Vakilian, Tal Wagner, and David Woodruff · 2019
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Sublinear time numerical linear algebra for structured matrices
Xiaofei Shi and David P. Woodruff · 2019
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Querying a matrix through matrix-vector products
Xiaoming Sun, David P. Woodruff, Guang Yang, and Jialin Zhang · 2019
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Ewin Tang · 2019
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Robust and sample optimal algorithms for PSD low rank approximation
Ainesh Bakshi, Nadiia Chepurko, and David P Woodruff · 2020
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The gradient complexity of linear regression
Mark Braverman, Elad Hazan, Max Simchowitz, and Blake Woodworth · 2020
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Quantum-inspired algorithms from randomized numerical linear algebra
Nadiia Chepurko, Kenneth L Clarkson, Lior Horesh, and David P Woodruff · 2020
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Input-sparsity low rank approximation in Schatten norm
Yi Li and David P. Woodruff · 2020
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The Hessian penalty: A weak prior for unsupervised disentanglement
William Peebles, John Peebles, Jun-Yan Zhu, Alexei A. Efros, and Antonio Torralba · 2020
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Chebyshev polynomials
Theodore J Rivlin · 2020
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Vector-matrix-vector queries for solving linear algebra, statistics, and graph problems
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Average case column subset selection for entrywise l1-norm loss
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Notes 3a: Eigenvalues and sums of hermitian matrices, 2020
Terence Tao · 2020
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PyHessian: Neural networks through the lens of the Hessian, 2020
Zhewei Yao, Amir Gholami, Kurt Keutzer, and Michael Mahoney · 2020
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Learning a latent simplex in input-sparsity time
Ainesh Bakshi, Chiranjib Bhattacharyya, Ravi Kannan, David P Woodruff, and Samson Zhou · 2021
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Hutch++: Optimal stochastic trace estimation
Raphael A. Meyer, Cameron Musco, Christopher Musco, and David P. Woodruff · 2021
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Optimal L1 column subset selection and a fast PTAS for low rank approximation
Arvind V Mahankali and David P Woodruff · 2021
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Average-case communication complexity of statistical problems, 2021
Cyrus Rashtchian, David P. Woodruff, Peng Ye, and Hanlin Zhu · 2021
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