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One approach to improving the running time of kernel-based machine learning methods is to build a small sketch of the input and use it in lieu of the full kernel matrix in the machine learning task of interest.
Some results on Tchebycheffian spline functions
George Kimeldorf and Grace Wahba · 1971
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Influential observations, high leverage points, and outliers in linear regression
Samprit Chatterjee and Ali S Hadi · 1986
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The elements of statistical learning
Jerome Friedman, Trevor Hastie, and Robert Tibshirani · 2001
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A generalized representer theorem
Bernhard Schölkopf, Ralf Herbrich, and Alex J Smola · 2001
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Using the Nyström method to speed up kernel machines
Christopher Williams and Matthias Seeger · 2001
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Efficient SVM training using low-rank kernel representations
Shai Fine and Katya Scheinberg · 2002
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Fast Monte-Carlo algorithms for finding low-rank approximations
Alan Frieze, Ravi Kannan, and Santosh Vempala · 2004
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Fast Monte-Carlo algorithms for matrices I: Approximating matrix multiplication
Petros Drineas, Ravi Kannan, and Michael W Mahoney · 2006
Earlier work this paper cites.
Fast Monte-Carlo algorithms for matrices II: Computing a low-rank approximation to a matrix
Petros Drineas, Ravi Kannan, and Michael W Mahoney · 2006
Cited alongside, same era.
Relative-error CUR matrix decompositions
Petros Drineas, Michael W Mahoney, and S Muthukrishnan · 2008
Cited alongside, same era.
CUR matrix decompositions for improved data analysis
Michael W Mahoney and Petros Drineas · 2009
Cited alongside, same era.
Sampling techniques for the Nyström method
Sanjiv Kumar, Mehryar Mohri, and Ameet Talwalkar · 2009
Cited alongside, same era.
Self-concordant analysis for logistic regression
Francis Bach · 2010
Cited alongside, same era.
Randomized algorithms for matrices and data
Michael W Mahoney · 2011
Cited alongside, same era.
Fast approximation of matrix coherence and statistical leverage
Petros Drineas, Malik Magdon-Ismail, Michael W Mahoney, and David P Woodruff · 2012
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User-friendly tail bounds for sums of random matrices
Joel A Tropp · 2012
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Revisiting the Nyström method for improved large-scale machine learning
Alex Gittens and Michael W Mahoney · 2013
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Sharp analysis of low-rank kernel matrix approximations
Francis Bach · 2013
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Divide and conquer kernel ridge regression
Yuchen Zhang, John Duchi, and Martin Wainwright · 2013
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Rajendra Bhatia · 2013
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Faster least squares approximation
Petros Drineas, Michael W Mahoney, S Muthukrishnan, and Tamás Sarlós · 2011
Cited alongside, same era.
Personal communication, October 2015
Francis Bach · 2015
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