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We study matrix sketching methods for regularized variants of linear regression, low rank approximation, and canonical correlation analysis.
Maximum properties and inequalities for the eigenvalues of completely continuous operators
Ky Fan · 1951
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Numerical methods for computing angles between linear subspaces
A. Björck and G.H. Golub · 1973
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Some inequalities for the eigenvalues of the product of positive semidefinite hermitian matrices
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Topics in Matrix Analysis
R.A. Horn and C.R. Johnson · 1994
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Relative perturbation techniques for singular value problems
S. Eisenstat and I. Ipsen · 1995
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The canonical correlations of matrix pairs and their numerical computation
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Rank, trace-norm and max-norm
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Sampling algorithms for ℓ 2 \ell_{2} regression and applications
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Left unitarily invariant norms on matrices
Masumi Domon, Takashi Sano, and Tomohide Toba · 2006
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R 1 {}_{\mbox{1}} -PCA: rotational invariant L 1 {}_{\mbox{1}} -norm principal component analysis for robust subspace factorization
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Improved approximation algorithms for large matrices via random projections
T. Sarlós · 2006
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Faster least squares approximation, Technical Report, arXiv:0710.1435, 2007
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Randomized algorithms for matrices and data
Michael W. Mahoney · 2011
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Improved analysis of the subsampled randomized hadamard transform
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Improved matrix algorithms via the Subsampled Randomized Hadamard Transform
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Fast approximation of matrix coherence and statistical leverage
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Eigenvalues of a matrix in the streaming model
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Unifying nuclear norm and bilinear factorization approaches for low-rank matrix decomposition
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Low rank approximation and regression in input sparsity time
Matrix estimation by universal singular value thresholding
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Fast randomized kernel methods with statistical guarantees
Ahmed El Alaoui and Michael W Mahoney · 2014
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Randomized sketches of convex programs with sharp guarantees
Mert Pilanci and Martin J. Wainwright · 2014
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M. Udell, C. Horn, R. Zadeh, and S. Boyd · 2014
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Sketching as a tool for numerical linear algebra
David P. Woodruff · 2014
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Toward a unified theory of sparse dimensionality reduction in euclidean space
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Kenneth L Clarkson and David P Woodruff · 2013
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Matrix Analysis (Second Edition)
R. A. Horn and C. R. Johnson · 2013
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The Elements of Statistical Learning
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Fast relative-error approximation algorithm for ridge regression
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Optimal approximate matrix product in terms of stable rank
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Competing with the Empirical Risk Minimizer in a Single Pass
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Un-regularizing: approximate proximal point and faster stochastic algorithms for empirical risk minimization
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Randomized sketches for kernels: Fast and optimal non-parametric regression
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Faster kernel ridge regression using sketching and preconditioning
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