A Primer On Reproducing Kernel Hilbert Spaces

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A Primer on Reproducing Kernel Hilbert Spaces

Author : Jonathan H. Manton
Publisher :
ISBN 13 : 9781680830927
Total Pages : 138 pages
Book Rating : 4.8/5 (39 download)

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Book Synopsis A Primer on Reproducing Kernel Hilbert Spaces by : Jonathan H. Manton

Download or read book A Primer on Reproducing Kernel Hilbert Spaces written by Jonathan H. Manton and published by . This book was released on 2015-11-20 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilbert space theory is an invaluable mathematical tool in numerous signal processing and systems theory applications. Hilbert spaces satisfying certain additional properties are known as Reproducing Kernel Hilbert Spaces (RKHSs). This primer gives a gentle and novel introduction to RKHS theory. It also presents several classical applications. It concludes by focusing on recent developments in the machine learning literature concerning embeddings of random variables. Parenthetical remarks are used to provide greater technical detail, which some readers may welcome, but they may be ignored without compromising the cohesion of the primer. Proofs are there for those wishing to gain experience at working with RKHSs; simple proofs are preferred to short, clever, but otherwise uninformative proofs. Italicised comments appearing in proofs provide intuition or orientation or both. A Primer on Reproducing Kernel Hilbert Spaces empowers readers to recognize when and how RKHS theory can profit them in their own work.

An Introduction to the Theory of Reproducing Kernel Hilbert Spaces

Author : Vern I. Paulsen
Publisher : Cambridge University Press
ISBN 13 : 1107104092
Total Pages : 193 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis An Introduction to the Theory of Reproducing Kernel Hilbert Spaces by : Vern I. Paulsen

Download or read book An Introduction to the Theory of Reproducing Kernel Hilbert Spaces written by Vern I. Paulsen and published by Cambridge University Press. This book was released on 2016-04-11 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique introduction to reproducing kernel Hilbert spaces, covering the fundamental underlying theory as well as a range of applications.

Reproducing Kernel Hilbert Spaces

Author : Howard L. Weinert
Publisher :
ISBN 13 :
Total Pages : 680 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Reproducing Kernel Hilbert Spaces by : Howard L. Weinert

Download or read book Reproducing Kernel Hilbert Spaces written by Howard L. Weinert and published by . This book was released on 1982 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Reproducing Kernel Spaces and Applications

Author : Daniel Alpay
Publisher : Birkhäuser
ISBN 13 : 3034880774
Total Pages : 355 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Reproducing Kernel Spaces and Applications by : Daniel Alpay

Download or read book Reproducing Kernel Spaces and Applications written by Daniel Alpay and published by Birkhäuser. This book was released on 2012-12-06 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notions of positive functions and of reproducing kernel Hilbert spaces play an important role in various fields of mathematics, such as stochastic processes, linear systems theory, operator theory, and the theory of analytic functions. Also they are relevant for many applications, for example to statistical learning theory and pattern recognition. The present volume contains a selection of papers which deal with different aspects of reproducing kernel Hilbert spaces. Topics considered include one complex variable theory, differential operators, the theory of self-similar systems, several complex variables, and the non-commutative case. The book is of interest to a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.

$J$ Contractive Matrix Functions, Reproducing Kernel Hilbert Spaces and Interpolation

Author : Harry Dym
Publisher : American Mathematical Soc.
ISBN 13 : 0821807226
Total Pages : 159 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis $J$ Contractive Matrix Functions, Reproducing Kernel Hilbert Spaces and Interpolation by : Harry Dym

Download or read book $J$ Contractive Matrix Functions, Reproducing Kernel Hilbert Spaces and Interpolation written by Harry Dym and published by American Mathematical Soc.. This book was released on 1989 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an introduction to the theory and applications of $J$ inner matrices. This book discusses matrix interpolation problems including two-sided tangential problems of both the Nevanlinna-Pick type and the Caratheodory-Fejer type, as well as mixtures of these.

A Primer on Hilbert Space Theory

Author : Carlo Alabiso
Publisher : Springer Nature
ISBN 13 : 3030674177
Total Pages : 343 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis A Primer on Hilbert Space Theory by : Carlo Alabiso

Download or read book A Primer on Hilbert Space Theory written by Carlo Alabiso and published by Springer Nature. This book was released on 2021-03-03 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an essential introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for providing an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, lies in the strenuous mathematics demands that even the simplest physical cases entail. Graduate courses in physics rarely offer enough time to cover the theory of Hilbert space and operators, as well as distribution theory, with sufficient mathematical rigor. Accordingly, compromises must be found between full rigor and the practical use of the instruments. Based on one of the authors’s lectures on functional analysis for graduate students in physics, the book will equip readers to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. It also includes a brief introduction to topological groups, and to other mathematical structures akin to Hilbert space. Exercises and solved problems accompany the main text, offering readers opportunities to deepen their understanding. The topics and their presentation have been chosen with the goal of quickly, yet rigorously and effectively, preparing readers for the intricacies of Hilbert space. Consequently, some topics, e.g., the Lebesgue integral, are treated in a somewhat unorthodox manner. The book is ideally suited for use in upper undergraduate and lower graduate courses, both in Physics and in Mathematics.

Reproducing Kernel Spaces and Applications

Author : Daniel Alpay
Publisher : Birkhauser
ISBN 13 : 9780817600686
Total Pages : 344 pages
Book Rating : 4.6/5 (6 download)

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Book Synopsis Reproducing Kernel Spaces and Applications by : Daniel Alpay

Download or read book Reproducing Kernel Spaces and Applications written by Daniel Alpay and published by Birkhauser. This book was released on 2003-01 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notions of positive functions and of reproducing kernel Hilbert spaces play an important role in various fields of mathematics, such as stochastic processes, linear systems theory, operator theory, and the theory of analytic functions. Also they are relevant for many applications, for example to statistical learning theory and pattern recognition. The present volume contains a selection of papers which deal with different aspects of reproducing kernel Hilbert spaces. Topics considered include one complex variable theory, differential operators, the theory of self-similar systems, several complex variables, and the non-commutative case. The book is of interest to a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.

Generalized Mercer Kernels and Reproducing Kernel Banach Spaces

Author : Yuesheng Xu
Publisher : American Mathematical Soc.
ISBN 13 : 1470435500
Total Pages : 122 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Generalized Mercer Kernels and Reproducing Kernel Banach Spaces by : Yuesheng Xu

Download or read book Generalized Mercer Kernels and Reproducing Kernel Banach Spaces written by Yuesheng Xu and published by American Mathematical Soc.. This book was released on 2019-04-10 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article studies constructions of reproducing kernel Banach spaces (RKBSs) which may be viewed as a generalization of reproducing kernel Hilbert spaces (RKHSs). A key point is to endow Banach spaces with reproducing kernels such that machine learning in RKBSs can be well-posed and of easy implementation. First the authors verify many advanced properties of the general RKBSs such as density, continuity, separability, implicit representation, imbedding, compactness, representer theorem for learning methods, oracle inequality, and universal approximation. Then, they develop a new concept of generalized Mercer kernels to construct p-norm RKBSs for 1≤p≤∞ .

A Primer on Machine Learning Applications in Civil Engineering

Author : Paresh Chandra Deka
Publisher : CRC Press
ISBN 13 : 0429836651
Total Pages : 201 pages
Book Rating : 4.4/5 (298 download)

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Book Synopsis A Primer on Machine Learning Applications in Civil Engineering by : Paresh Chandra Deka

Download or read book A Primer on Machine Learning Applications in Civil Engineering written by Paresh Chandra Deka and published by CRC Press. This book was released on 2019-10-28 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Machine learning has undergone rapid growth in diversification and practicality, and the repertoire of techniques has evolved and expanded. The aim of this book is to provide a broad overview of the available machine-learning techniques that can be utilized for solving civil engineering problems. The fundamentals of both theoretical and practical aspects are discussed in the domains of water resources/hydrological modeling, geotechnical engineering, construction engineering and management, and coastal/marine engineering. Complex civil engineering problems such as drought forecasting, river flow forecasting, modeling evaporation, estimation of dew point temperature, modeling compressive strength of concrete, ground water level forecasting, and significant wave height forecasting are also included. Features Exclusive information on machine learning and data analytics applications with respect to civil engineering Includes many machine learning techniques in numerous civil engineering disciplines Provides ideas on how and where to apply machine learning techniques for problem solving Covers water resources and hydrological modeling, geotechnical engineering, construction engineering and management, coastal and marine engineering, and geographical information systems Includes MATLAB® exercises

Reproducing Kernel Hilbert Spaces with Applications to Control Theory, Univariate and Bivariate Spline Density Estimation

Author : Robert Maurice Kuhn
Publisher :
ISBN 13 :
Total Pages : 456 pages
Book Rating : 4.:/5 (89 download)

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Book Synopsis Reproducing Kernel Hilbert Spaces with Applications to Control Theory, Univariate and Bivariate Spline Density Estimation by : Robert Maurice Kuhn

Download or read book Reproducing Kernel Hilbert Spaces with Applications to Control Theory, Univariate and Bivariate Spline Density Estimation written by Robert Maurice Kuhn and published by . This book was released on 1975 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Kernel Methods in Computational Biology

Author : Bernhard Schölkopf
Publisher : MIT Press
ISBN 13 : 9780262195096
Total Pages : 428 pages
Book Rating : 4.1/5 (95 download)

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Book Synopsis Kernel Methods in Computational Biology by : Bernhard Schölkopf

Download or read book Kernel Methods in Computational Biology written by Bernhard Schölkopf and published by MIT Press. This book was released on 2004 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: A detailed overview of current research in kernel methods and their application to computational biology.

Mathematics for Machine Learning

Author : Marc Peter Deisenroth
Publisher : Cambridge University Press
ISBN 13 : 1108569323
Total Pages : 392 pages
Book Rating : 4.1/5 (85 download)

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Book Synopsis Mathematics for Machine Learning by : Marc Peter Deisenroth

Download or read book Mathematics for Machine Learning written by Marc Peter Deisenroth and published by Cambridge University Press. This book was released on 2020-04-23 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.

Methods and Applications of Autonomous Experimentation

Author : Marcus Noack
Publisher : CRC Press
ISBN 13 : 100382126X
Total Pages : 445 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Methods and Applications of Autonomous Experimentation by : Marcus Noack

Download or read book Methods and Applications of Autonomous Experimentation written by Marcus Noack and published by CRC Press. This book was released on 2023-12-14 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: · Provides a holistic and practical guide to autonomous experimentation · Combines insights from theorists, machine-learning engineers and applied scientists to dispel common myths and misconceptions surrounding autonomous experimentation. · Incorporates practitioners’ first-hand experience

Pick Interpolation and Hilbert Function Spaces

Author : Jim Agler
Publisher : American Mathematical Society
ISBN 13 : 1470468557
Total Pages : 330 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Pick Interpolation and Hilbert Function Spaces by : Jim Agler

Download or read book Pick Interpolation and Hilbert Function Spaces written by Jim Agler and published by American Mathematical Society. This book was released on 2023-02-22 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book first rigorously develops the theory of reproducing kernel Hilbert spaces. The authors then discuss the Pick problem of finding the function of smallest $H^infty$ norm that has specified values at a finite number of points in the disk. Their viewpoint is to consider $H^infty$ as the multiplier algebra of the Hardy space and to use Hilbert space techniques to solve the problem. This approach generalizes to a wide collection of spaces. The authors then consider the interpolation problem in the space of bounded analytic functions on the bidisk and give a complete description of the solution. They then consider very general interpolation problems. The book includes developments of all the theory that is needed, including operator model theory, the Arveson extension theorem, and the hereditary functional calculus.

Integral Transforms, Reproducing Kernels and Their Applications

Author : Saburou Saitoh
Publisher : CRC Press
ISBN 13 : 1000115240
Total Pages : 289 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Integral Transforms, Reproducing Kernels and Their Applications by : Saburou Saitoh

Download or read book Integral Transforms, Reproducing Kernels and Their Applications written by Saburou Saitoh and published by CRC Press. This book was released on 2020-11-25 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general theories contained in the text will give rise to new ideas and methods for the natural inversion formulas for general linear mappings in the framework of Hilbert spaces containing the natural solutions for Fredholm integral equations of the first kind.

Nonlinear Numerical Analysis in the Reproducing Kernel Space

Author : Minggen Cui
Publisher :
ISBN 13 :
Total Pages : 248 pages
Book Rating : 4.3/5 (97 download)

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Book Synopsis Nonlinear Numerical Analysis in the Reproducing Kernel Space by : Minggen Cui

Download or read book Nonlinear Numerical Analysis in the Reproducing Kernel Space written by Minggen Cui and published by . This book was released on 2009 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the application of reproducing kernel has been explored in different fields in the past twenty to thirty years and the relevant researches are active in the recent five years, there is still not a book on the application of reproducing kernel. This book attempts to introduce to the readers engaged in mathematical application these solutions, especially the constructing theory of the reproducing kernel space that the authors originally created and gradually improved. Reproducing kernel space is a special Hilbert space. the authors have been engaged in the constructing theory research of the reproducing kernel space since 1980's, and worked out a series of specific structural methods for reproducing kernel space and reproducing kernel functions.

A Primer on Hilbert Space Operators

Author : Piotr Sołtan
Publisher : Birkhäuser
ISBN 13 : 9783319920603
Total Pages : 200 pages
Book Rating : 4.9/5 (26 download)

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Book Synopsis A Primer on Hilbert Space Operators by : Piotr Sołtan

Download or read book A Primer on Hilbert Space Operators written by Piotr Sołtan and published by Birkhäuser. This book was released on 2018-09-17 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book concisely presents the fundamental aspects of the theory of operators on Hilbert spaces. The topics covered include functional calculus and spectral theorems, compact operators, trace class and Hilbert-Schmidt operators, self-adjoint extensions of symmetric operators, and one-parameter groups of operators. The exposition of the material on unbounded operators is based on a novel tool, called the z-transform, which provides a way to encode full information about unbounded operators in bounded ones, hence making many technical aspects of the theory less involved.