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We study theoretical properties of a broad class of regularized algorithms with vector-valued output.
Vector Measures
Joe Diestel and J.J. Uhl · 1977
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Linear Operators in Hilbert Spaces
Joachim Weidmann · 1980
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Norm inequalities equivalent to heinz inequality
Jun Ichi Fujii, Masatoshi Fujii, Takayuki Furuta, and Ritsuo Nakamoto · 1993
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On converse and saturation results for Tikhonov regularization of linear ill-posed problems
Andreas Neubauer · 1997
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Applied Functional Analysis
Jean-Pierre Aubin · 2000
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Regularization of Inverse Problems
Heinz Werner Engl, Martin Hanke, and A. Neubauer · 2000
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Real Analysis and Probability
R.M. Dudley · 2002
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Saturation of regularization methods for linear ill-posed problems in hilbert spaces
Peter Mathé · 2004
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Shannon sampling and function reconstruction from point values
Steve Smale and Ding-Xuan Zhou · 2004
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Shannon sampling II: Connections to learning theory
Steve Smale and Ding-Xuan Zhou · 2005
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Vector valued reproducing kernel Hilbert spaces of integrable functions and Mercer theorem
Claudio Carmeli, Ernesto De Vito, and Alessandro Toigo · 2006
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Discretization error analysis for tikhonov regularization
Ernesto De Vito, Lorenzo Rosasco, and Andrea Caponnetto · 2006
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On regularization algorithms in learning theory
Frank Bauer, Sergei Pereverzev, and Lorenzo Rosasco · 2007
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Learning theory estimates via integral operators and their approximations
Steve Smale and Ding-Xuan Zhou · 2007
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On early stopping in gradient descent learning
Yuan Yao, Lorenzo Rosasco, and Andrea Caponnetto · 2007
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Universal multi-task kernels
Andrea Caponnetto, Charles A. Micchelli, Massimiliano Pontil, and Yiming Ying · 2008
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Support Vector Machines
Ingo Steinwart and Andreas Christmann · 2008
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Hilbert space embeddings of conditional distributions with applications to dynamical systems
Le Song, Jonathan Huang, Alex Smola, and Kenji Fukumizu · 2009
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Optimal rates for regularized least squares regression
Ingo Steinwart, Don R Hush, Clint Scovel, et al · 2009
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Cross-validation based adaptation for regularization operators in learning theory
Andrea Caponnetto and Yuan Yao · 2010
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Vector valued reproducing kernel Hilbert spaces and universality
Claudio Carmeli, Ernesto De Vito, Alessandro Toigo, and Veronica Umanitá · 2010
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Optimal distributed learning with multi-pass stochastic gradient methods
Junhong Lin and Volkan Cevher · 2018
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Beating SGD saturation with tail-averaging and minibatching
Nicole Mücke, Gergely Neu, and Lorenzo Rosasco · 2019
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Kernel instrumental variable regression
Rahul Singh, Maneesh Sahani, and Arthur Gretton · 2019
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A general framework for consistent structured prediction with implicit loss embeddings
Carlo Ciliberto, Lorenzo Rosasco, and Alessandro Rudi · 2020
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Sobolev norm learning rates for regularized least-squares algorithms
Simon Fischer and Ingo Steinwart · 2020
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Optimal convergence for distributed learning with stochastic gradient methods and spectral algorithms
Junhong Lin and Volkan Cevher · 2020
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Reproducing Kernel Hilbert Spaces in Probability and Statistics
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Global saturation of regularization methods for inverse ill-posed problems
Terry Herdman, Ruben D Spies, and Karina G Temperini · 2011
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Universality, characteristic kernels and RKHS embedding of measures
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Multi-output learning via spectral filtering
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Mercer’s theorem on general domains: On the interaction between measures, kernels, and RKHSs
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A consistent regularization approach for structured prediction
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Nonparametric approximation of conditional expectation operators
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Learning dynamical systems via Koopman operator regression in reproducing kernel Hilbert spaces
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Optimal rates for regularized conditional mean embedding learning
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Koopman operator learning: Sharp spectral rates and spurious eigenvalues
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