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We propose a fast method with statistical guarantees for learning an exponential family density model where the natural parameter is in a reproducing kernel Hilbert space, and may be infinite-dimensional.
“Fundamentals of Statistical Exponential Families with Applications in Statistical Decision Theory”
L.. Brown · 1986
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“Fundamentals of Statistical Exponential Families with Applications in Statistical Decision Theory”
L.. Brown · 1986
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“Approximation of density functions by sequences of exponential families”
A. Barron and C-H. Sheu · 1991
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“Approximation of density functions by sequences of exponential families”
A. Barron and C-H. Sheu · 1991
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“Smoothing spline density estimation: Theory”
C. Gu and C. Qiu · 1993
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“Smoothing spline density estimation: Theory”
C. Gu and C. Qiu · 1993
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“Sparse Greedy Matrix Approximation for Machine Learning”
Alex. Smola and Bernhard Schölkopf · 2000
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“Using the Nyström method to speed up kernel machines”
Christopher Williams and Matthias Seeger · 2000
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“Sparse Greedy Matrix Approximation for Machine Learning”
Alex. Smola and Bernhard Schölkopf · 2000
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“Using the Nyström method to speed up kernel machines”
Christopher Williams and Matthias Seeger · 2000
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“A Generalized Representer Theorem”
Bernhard Schölkopf, Ralf Herbrich and Alex. Smola · 2001
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“A Generalized Representer Theorem”
Bernhard Schölkopf, Ralf Herbrich and Alex. Smola · 2001
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“Generalized inverses: theory and applications”
Adi Ben-Israel and Thomas Greville · 2003
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“Generalized inverses: theory and applications”
Adi Ben-Israel and Thomas Greville · 2003
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“Reproducing Kernel Hilbert Spaces in Probability and Statistics”
A. Berlinet and C. Thomas-Agnan · 2004
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“Reproducing Kernel Hilbert Spaces in Probability and Statistics”
A. Berlinet and C. Thomas-Agnan · 2004
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“On the Nyström method for approximating a Gram matrix for improved kernel-based learning”
Petros Drineas and Michael Mahoney · 2005
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“Estimation of non-normalized statistical models by score matching”
Aapo Hyvärinen · 2005
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“On the Nyström method for approximating a Gram matrix for improved kernel-based learning”
Petros Drineas and Michael Mahoney · 2005
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“Estimation of non-normalized statistical models by score matching”
Aapo Hyvärinen · 2005
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“Kernel methods and the exponential family”
Stephane Canu and Alex. Smola · 2006
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“Kernel methods and the exponential family”
Stephane Canu and Alex. Smola · 2006
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“Optimal rates for regularized least-squares algorithm”
A. Caponnetto and E. De · 2007
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“Random Features for Large-Scale Kernel Machines”
A. Rahimi and B. Recht · 2007
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“Optimal rates for regularized least-squares algorithm”
A. Caponnetto and E. De · 2007
Earlier work this paper cites.
“Optimal rates for regularized least-squares algorithm”
A. Caponnetto and E. De · 2007
Cited alongside, same era.
“Random Features for Large-Scale Kernel Machines”
A. Rahimi and B. Recht · 2007
Cited alongside, same era.
“Optimal rates for regularized least-squares algorithm”
A. Caponnetto and E. De · 2007
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“A Tutorial on Energy-Based Learning”
Yann LeCun, Sumit Chopra, Raia Hadsell, Marc’Aurelio Ranzato and Fu Huang · 2008
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“Support Vector Machines”
I. Steinwart and A. Christmann · 2008
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“A Tutorial on Energy-Based Learning”
Yann LeCun, Sumit Chopra, Raia Hadsell, Marc’Aurelio Ranzato and Fu Huang · 2008
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“Support Vector Machines”
“Fast Randomized Kernel Methods With Statistical Guarantees”
Ahmed El and Michael Mahoney · 2015
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“Less is More: Nyström Computational Regularization”
Alessandro Rudi, Raffaello Camoriano and Lorenzo Rosasco · 2015
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“Optimal rates for random Fourier features”
Bharath. Sriperumbudur and Zoltán Szábo · 2015
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“Gradient-free Hamiltonian Monte Carlo with Efficient Kernel Exponential Families”
Heiko Strathmann, Dino Sejdinovic, Samuel Livingstone, Zoltán Szábo and Arthur Gretton · 2015
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I. Steinwart and A. Christmann · 2008
Cited alongside, same era.
“Exponential manifold by reproducing kernel Hilbert spaces”
Kenji Fukumizu · 2009
Cited alongside, same era.
“Exponential manifold by reproducing kernel Hilbert spaces”
Kenji Fukumizu · 2009
Cited alongside, same era.
“On the impact of kernel approximation on learning accuracy”
Corinna Cortes, Mehryar Mohri and Ameet Talwalkar · 2010
Cited alongside, same era.
“On the impact of kernel approximation on learning accuracy”
Corinna Cortes, Mehryar Mohri and Ameet Talwalkar · 2010
Cited alongside, same era.
“MCMC using Hamiltonian dynamics”
R.M. Neal · 2011
Cited alongside, same era.
Dougal. Sutherland and Jeff Schneider · 2015
Later among the works it cites.
“Less is More: Nyström Computational Regularization”
Alessandro Rudi, Raffaello Camoriano and Lorenzo Rosasco · 2015
Later among the works it cites.
“Gradient-free Hamiltonian Monte Carlo with Efficient Kernel Exponential Families”
Heiko Strathmann, Dino Sejdinovic, Samuel Livingstone, Zoltán Szábo and Arthur Gretton · 2015
Later among the works it cites.
“Fast Randomized Kernel Methods With Statistical Guarantees”
Ahmed El and Michael Mahoney · 2015
Later among the works it cites.
“Less is More: Nyström Computational Regularization”
Alessandro Rudi, Raffaello Camoriano and Lorenzo Rosasco · 2015
Later among the works it cites.
“Optimal rates for random Fourier features”
Bharath. Sriperumbudur and Zoltán Szábo · 2015
Later among the works it cites.
“Gradient-free Hamiltonian Monte Carlo with Efficient Kernel Exponential Families”
Heiko Strathmann, Dino Sejdinovic, Samuel Livingstone, Zoltán Szábo and Arthur Gretton · 2015
Later among the works it cites.
“On the Error of Random Fourier Features”
Dougal. Sutherland and Jeff Schneider · 2015
Later among the works it cites.
“Less is More: Nyström Computational Regularization”
Alessandro Rudi, Raffaello Camoriano and Lorenzo Rosasco · 2015
Later among the works it cites.
“Gradient-free Hamiltonian Monte Carlo with Efficient Kernel Exponential Families”
Heiko Strathmann, Dino Sejdinovic, Samuel Livingstone, Zoltán Szábo and Arthur Gretton · 2015
Later among the works it cites.
“Control functionals for Monte Carlo integration”
Chris. Oates, Mark Girolami and Nicolas Chopin · 2017
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“Generalization Properties of Learning with Random Features”
Alessandro Rudi and Lorenzo Rosasco · 2017
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“Density Estimation in Infinite Dimensional Exponential Families”
Bharath. Sriperumbudur, Kenji Fukumizu, Revant Kumar, Arthur Gretton, Aapo Hyvärinen and Revant Kumar · 2017
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“Randomized Sketches for Kernels: Fast and Optimal Non-Parametric Regression”
Yun Yang, Mert Pilanci and Martin Wainwright · 2017
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“Density Estimation in Infinite Dimensional Exponential Families”
Bharath. Sriperumbudur, Kenji Fukumizu, Revant Kumar, Arthur Gretton, Aapo Hyvärinen and Revant Kumar · 2017
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“Control functionals for Monte Carlo integration”
Chris. Oates, Mark Girolami and Nicolas Chopin · 2017
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“Generalization Properties of Learning with Random Features”
Alessandro Rudi and Lorenzo Rosasco · 2017
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“Density Estimation in Infinite Dimensional Exponential Families”
Bharath. Sriperumbudur, Kenji Fukumizu, Revant Kumar, Arthur Gretton, Aapo Hyvärinen and Revant Kumar · 2017
Closest in time.
“Randomized Sketches for Kernels: Fast and Optimal Non-Parametric Regression”
Yun Yang, Mert Pilanci and Martin Wainwright · 2017
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“Density Estimation in Infinite Dimensional Exponential Families”
Bharath. Sriperumbudur, Kenji Fukumizu, Revant Kumar, Arthur Gretton, Aapo Hyvärinen and Revant Kumar · 2017
Closest in time.