When is there a representer theorem? Nondifferentiable regularisers and Banach spaces

DOI10.1007/s10898-019-00767-0zbMath1489.68231arXiv1804.09605OpenAlexW2963343672WikidataQ116038508 ScholiaQ116038508MaRDI QIDQ2423813

Kevin Schlegel

Publication date: 20 June 2019

Published in: Journal of Global Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.09605

zbMATH Keywords

kernel methodsregularisationrepresenter theoremregularised interpolationsemi-inner product spaces

Mathematics Subject Classification ID

General nonlinear regression (62J02) Learning and adaptive systems in artificial intelligence (68T05) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22)

Related Items (5)

Sparse regularized learning in the reproducing kernel Banach spaces with the \(\ell^1\) norm ⋮ Interpretable time series kernel analytics by pre-image estimation ⋮ On Lipschitz implicit function theorems in Banach spaces and applications ⋮ When is there a representer theorem? Reflexive Banach spaces ⋮ Generalized representer theorems in Banach spaces

Cites Work

• Regularized learning in Banach spaces as an optimization problem: representer theorems
• Functional analysis, Sobolev spaces and partial differential equations
• On a kernel-based method for pattern recognition, regression, approximation, and operator inversion
• Some results on Tchebycheffian spline functions and stochastic processes
• Asymptotic analysis of penalized likelihood and related estimators
• On the mathematical foundations of learning
• Semi-Inner-Product Spaces
• Learning Theory
• Classes of Semi-Inner-Product Spaces
• Orthogonality and Linear Functionals in Normed Linear Spaces
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