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2005 JMLR JMLR 2005

Frames, Reproducing Kernels, Regularization and Learning

Abstract

This work deals with a method for building a reproducing kernel Hilbert space (RKHS) from a Hilbert space with frame elements having special properties. Conditions on existence and a method of construction are given. Then, these RKHS are used within the framework of regularization theory for function approximation. Implications on semiparametric estimation are discussed and a multiscale scheme of regularization is also proposed. Results on toy and real-world approximation problems illustrate the effectiveness of such methods. [abs] [ pdf ][ bib ] © JMLR 2005. (edit, beta)

🌱 Topic Pioneer — Functional Analysis
🌉 Interdisciplinary Bridge — Machine Learning and Mathematics & Optimization
🧭 Keyword Pioneer — function approximation
🐝 Cross-Pollinator — Artificial Intelligence, Computer Science, Computer Vision, Data Science & Analytics, Deep Learning, Healthcare & Medicine, Knowledge & Reasoning, Machine Learning, Mathematics & Optimization, Reinforcement Learning, Robotics, Security & Privacy
📈 Trend Setter — Theory
🐣 Hot Topic Early Bird — function approximation

Authors

Alain Rakotomamonjy , Stéphane Canu

Topics

Machine Learning > Optimization & Theory > Learning Theory Machine Learning > Optimization & Theory > Theory Mathematics & Optimization > Mathematics > Functional Analysis Machine Learning > Core Methods > Kernel Methods

Keywords

function approximation reproducing kernel hilbert space semiparametric estimation regularization theory frame theory kernel methods
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