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In the absence of explicit regularization, Kernel "Ridgeless" Regression with nonlinear kernels has the potential to fit the training data perfectly.
Generalized cross-validation as a method for choosing a good ridge parameter
Gene H. Golub, Michael Heath, and Grace Wahba · 1979
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On the limit of the largest eigenvalue of the large dimensional sample covariance matrix
Yong-Quan Yin, Zhi-Dong Bai, and Pathak R Krishnaiah · 1988
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The origins of kriging
Noel Cressie · 1990
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Spline models for observational data , volume 59
Grace Wahba · 1990
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Learning with kernels , volume 4
Alex J Smola and Bernhard Schölkopf · 1998
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Statistical learning theory. 1998 , volume 3
Vladimir Vapnik · 1998
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Regularization networks and support vector machines
Theodoros Evgeniou, Massimiliano Pontil, and Tomaso Poggio · 2000
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Rademacher and gaussian complexities: Risk bounds and structural results
Peter L Bartlett and Shahar Mendelson · 2002
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Best choices for regularization parameters in learning theory: on the bias-variance problem
Felipe Cucker and Steve Smale · 2002
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Limiting spectral distribution of large dimensional random matrices
Arup Bose, Sourav Chatterjee, and Sreela Gangopadhyay · 2003
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A few notes on statistical learning theory
Shahar Mendelson · 2003
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Kernel methods for pattern analysis
John Shawe-Taylor and Nello Cristianini · 2004
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Model selection for regularized least-squares algorithm in learning theory
Ernesto De Vito, Andrea Caponnetto, and Lorenzo Rosasco · 2005
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Exponential convergence rates in classification
Vladimir Koltchinskii and Olexandra Beznosova · 2005
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A distribution-free theory of nonparametric regression
László Györfi, Michael Kohler, Adam Krzyzak, and Harro Walk · 2006
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Optimal rates for the regularized least-squares algorithm
Andrea Caponnetto and Ernesto De Vito · 2007
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Kernels for vector-valued functions: A review
Mauricio A Alvarez, Lorenzo Rosasco, and Neil D Lawrence · 2012
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Concentration inequalities: A nonasymptotic theory of independence
Stéphane Boucheron, Gábor Lugosi, and Pascal Massart · 2013
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Kernel ridge regression
Vladimir Vovk · 2013
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In search of the real inductive bias: On the role of implicit regularization in deep learning
Behnam Neyshabur, Ryota Tomioka, and Nathan Srebro · 2014
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Understanding deep learning requires rethinking generalization
Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals · 2016
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On early stopping in gradient descent learning
Yuan Yao, Lorenzo Rosasco, and Andrea Caponnetto · 2007
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The spectrum of kernel random matrices
Noureddine El Karoui · 2010
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Mnist handwritten digit database
Yann LeCun, Corinna Cortes, and CJ Burges · 2010
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Scikit-learn: Machine learning in Python
F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay · 2011
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Overfitting or perfect fitting? risk bounds for classification and regression rules that interpolate
Mikhail Belkin, Daniel Hsu, and Partha Mitra
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To understand deep learning we need to understand kernel learning
Mikhail Belkin, Siyuan Ma, and Soumik Mandal
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Suriya Gunasekar, Blake E Woodworth, Srinadh Bhojanapalli, Behnam Neyshabur, and Nati Srebro · 2017
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Algorithmic regularization in over-parameterized matrix recovery
Yuanzhi Li, Tengyu Ma, and Hongyang Zhang · 2017
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Approximation beats concentration? an approximation view on inference with smooth radial kernels
Mikhail Belkin · 2018
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Xialiang Dou and Tengyuan Liang · 2019
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