The Experts below are selected from a list of 51030 Experts worldwide ranked by ideXlab platform
Veronica Umanita - One of the best experts on this subject based on the ideXlab platform.
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vector valued reproducing kernel Hilbert Spaces and universality
Analysis and Applications, 2010Co-Authors: C. Carmeli, E. De Vito, Alessandro Toigo, Veronica UmanitaAbstract:This paper is devoted to the study of vector valued reproducing kernel Hilbert Spaces. We focus on two aspects: vector valued feature maps and universal kernels. In particular, we characterize the structure of translation invariant kernels on abelian groups and we relate it to the universality problem.
Lorenzo Rosasco - One of the best experts on this subject based on the ideXlab platform.
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reproducing kernel Hilbert Spaces on manifolds sobolev and diffusion Spaces
Analysis and Applications, 2021Co-Authors: E. De Vito, Nicole Mucke, Lorenzo RosascoAbstract:We study reproducing kernel Hilbert Spaces (RKHS) on a Riemannian manifold. In particular, we discuss under which condition Sobolev Spaces are RKHS and characterize their reproducing kernels. Furth...
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reproducing kernel Hilbert Spaces on manifolds sobolev and diffusion Spaces
arXiv: Functional Analysis, 2019Co-Authors: E. De Vito, Nicole Mucke, Lorenzo RosascoAbstract:We study reproducing kernel Hilbert Spaces (RKHS) on a Riemannian manifold. In particular, we discuss under which condition Sobolev Spaces are RKHS and characterize their reproducing kernels. Further, we introduce and discuss a class of smoother RKHS that we call diffusion Spaces. We illustrate the general results with a number of detailed examples.
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implicit regularization of accelerated methods in Hilbert Spaces
Neural Information Processing Systems, 2019Co-Authors: Nicolo Pagliana, Lorenzo RosascoAbstract:We study learning properties of accelerated gradient descent methods for linear least-squares in Hilbert Spaces. We analyze the implicit regularization properties of Nesterov acceleration and a variant of heavy-ball in terms of corresponding learning error bounds. Our results show that acceleration can provides faster bias decay than gradient descent, but also suffers of a more unstable behavior. As a result acceleration cannot be in general expected to improve learning accuracy with respect to gradient descent, but rather to achieve the same accuracy with reduced computations. Our theoretical results are validated by numerical simulations. Our analysis is based on studying suitable polynomials induced by the accelerated dynamics and combining spectral techniques with concentration inequalities.
Alessandro Toigo - One of the best experts on this subject based on the ideXlab platform.
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vector valued reproducing kernel Hilbert Spaces and universality
Analysis and Applications, 2010Co-Authors: C. Carmeli, E. De Vito, Alessandro Toigo, Veronica UmanitaAbstract:This paper is devoted to the study of vector valued reproducing kernel Hilbert Spaces. We focus on two aspects: vector valued feature maps and universal kernels. In particular, we characterize the structure of translation invariant kernels on abelian groups and we relate it to the universality problem.
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vector valued reproducing kernel Hilbert Spaces of integrable functions and mercer theorem
Analysis and Applications, 2006Co-Authors: C. Carmeli, E. De Vito, Alessandro ToigoAbstract:We characterize the reproducing kernel Hilbert Spaces whose elements are p-integrable functions in terms of the boundedness of the integral operator whose kernel is the reproducing kernel. Moreover, for p = 2, we show that the spectral decomposition of this integral operator gives a complete description of the reproducing kernel, extending the Mercer theorem.
C. Carmeli - One of the best experts on this subject based on the ideXlab platform.
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vector valued reproducing kernel Hilbert Spaces and universality
Analysis and Applications, 2010Co-Authors: C. Carmeli, E. De Vito, Alessandro Toigo, Veronica UmanitaAbstract:This paper is devoted to the study of vector valued reproducing kernel Hilbert Spaces. We focus on two aspects: vector valued feature maps and universal kernels. In particular, we characterize the structure of translation invariant kernels on abelian groups and we relate it to the universality problem.
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vector valued reproducing kernel Hilbert Spaces of integrable functions and mercer theorem
Analysis and Applications, 2006Co-Authors: C. Carmeli, E. De Vito, Alessandro ToigoAbstract:We characterize the reproducing kernel Hilbert Spaces whose elements are p-integrable functions in terms of the boundedness of the integral operator whose kernel is the reproducing kernel. Moreover, for p = 2, we show that the spectral decomposition of this integral operator gives a complete description of the reproducing kernel, extending the Mercer theorem.
E. De Vito - One of the best experts on this subject based on the ideXlab platform.
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reproducing kernel Hilbert Spaces on manifolds sobolev and diffusion Spaces
Analysis and Applications, 2021Co-Authors: E. De Vito, Nicole Mucke, Lorenzo RosascoAbstract:We study reproducing kernel Hilbert Spaces (RKHS) on a Riemannian manifold. In particular, we discuss under which condition Sobolev Spaces are RKHS and characterize their reproducing kernels. Furth...
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reproducing kernel Hilbert Spaces on manifolds sobolev and diffusion Spaces
arXiv: Functional Analysis, 2019Co-Authors: E. De Vito, Nicole Mucke, Lorenzo RosascoAbstract:We study reproducing kernel Hilbert Spaces (RKHS) on a Riemannian manifold. In particular, we discuss under which condition Sobolev Spaces are RKHS and characterize their reproducing kernels. Further, we introduce and discuss a class of smoother RKHS that we call diffusion Spaces. We illustrate the general results with a number of detailed examples.
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vector valued reproducing kernel Hilbert Spaces and universality
Analysis and Applications, 2010Co-Authors: C. Carmeli, E. De Vito, Alessandro Toigo, Veronica UmanitaAbstract:This paper is devoted to the study of vector valued reproducing kernel Hilbert Spaces. We focus on two aspects: vector valued feature maps and universal kernels. In particular, we characterize the structure of translation invariant kernels on abelian groups and we relate it to the universality problem.
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vector valued reproducing kernel Hilbert Spaces of integrable functions and mercer theorem
Analysis and Applications, 2006Co-Authors: C. Carmeli, E. De Vito, Alessandro ToigoAbstract:We characterize the reproducing kernel Hilbert Spaces whose elements are p-integrable functions in terms of the boundedness of the integral operator whose kernel is the reproducing kernel. Moreover, for p = 2, we show that the spectral decomposition of this integral operator gives a complete description of the reproducing kernel, extending the Mercer theorem.
