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An Example Of A Reproducing Kernel Hilbert Space
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Book Synopsis Reproducing Kernel Hilbert Spaces in Probability and Statistics by : Alain Berlinet
Download or read book Reproducing Kernel Hilbert Spaces in Probability and Statistics written by Alain Berlinet and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book covers theoretical questions including the latest extension of the formalism, and computational issues and focuses on some of the more fruitful and promising applications, including statistical signal processing, nonparametric curve estimation, random measures, limit theorems, learning theory and some applications at the fringe between Statistics and Approximation Theory. It is geared to graduate students in Statistics, Mathematics or Engineering, or to scientists with an equivalent level.
Book Synopsis An Example of a Reproducing Kernel Hilbert Space by : Edward Tutaj
Download or read book An Example of a Reproducing Kernel Hilbert Space written by Edward Tutaj and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Book Synopsis Multivariate Statistical Machine Learning Methods for Genomic Prediction by : Osval Antonio Montesinos López
Download or read book Multivariate Statistical Machine Learning Methods for Genomic Prediction written by Osval Antonio Montesinos López and published by Springer Nature. This book was released on 2022-02-14 with total page 707 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is open access under a CC BY 4.0 license This open access book brings together the latest genome base prediction models currently being used by statisticians, breeders and data scientists. It provides an accessible way to understand the theory behind each statistical learning tool, the required pre-processing, the basics of model building, how to train statistical learning methods, the basic R scripts needed to implement each statistical learning tool, and the output of each tool. To do so, for each tool the book provides background theory, some elements of the R statistical software for its implementation, the conceptual underpinnings, and at least two illustrative examples with data from real-world genomic selection experiments. Lastly, worked-out examples help readers check their own comprehension.The book will greatly appeal to readers in plant (and animal) breeding, geneticists and statisticians, as it provides in a very accessible way the necessary theory, the appropriate R code, and illustrative examples for a complete understanding of each statistical learning tool. In addition, it weighs the advantages and disadvantages of each tool.
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.
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:
Book Synopsis Kernel Mean Embedding of Distributions by : Krikamol Muandet
Download or read book Kernel Mean Embedding of Distributions written by Krikamol Muandet and published by . This book was released on 2017-06-28 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a comprehensive review of kernel mean embeddings of distributions and, in the course of doing so, discusses some challenging issues that could potentially lead to new research directions. The targeted audience includes graduate students and researchers in machine learning and statistics.
Book Synopsis Support Vector Machines by : Ingo Steinwart
Download or read book Support Vector Machines written by Ingo Steinwart and published by Springer Science & Business Media. This book was released on 2008-09-15 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: Every mathematical discipline goes through three periods of development: the naive, the formal, and the critical. David Hilbert The goal of this book is to explain the principles that made support vector machines (SVMs) a successful modeling and prediction tool for a variety of applications. We try to achieve this by presenting the basic ideas of SVMs together with the latest developments and current research questions in a uni?ed style. In a nutshell, we identify at least three reasons for the success of SVMs: their ability to learn well with only a very small number of free parameters, their robustness against several types of model violations and outliers, and last but not least their computational e?ciency compared with several other methods. Although there are several roots and precursors of SVMs, these methods gained particular momentum during the last 15 years since Vapnik (1995, 1998) published his well-known textbooks on statistical learning theory with aspecialemphasisonsupportvectormachines. Sincethen,the?eldofmachine learninghaswitnessedintenseactivityinthestudyofSVMs,whichhasspread moreandmoretootherdisciplinessuchasstatisticsandmathematics. Thusit seems fair to say that several communities are currently working on support vector machines and on related kernel-based methods. Although there are many interactions between these communities, we think that there is still roomforadditionalfruitfulinteractionandwouldbegladifthistextbookwere found helpful in stimulating further research. Many of the results presented in this book have previously been scattered in the journal literature or are still under review. As a consequence, these results have been accessible only to a relativelysmallnumberofspecialists,sometimesprobablyonlytopeoplefrom one community but not the others.
Book Synopsis Adaptive Learning Methods for Nonlinear System Modeling by : Danilo Comminiello
Download or read book Adaptive Learning Methods for Nonlinear System Modeling written by Danilo Comminiello and published by Butterworth-Heinemann. This book was released on 2018-06-11 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Adaptive Learning Methods for Nonlinear System Modeling presents some of the recent advances on adaptive algorithms and machine learning methods designed for nonlinear system modeling and identification. Real-life problems always entail a certain degree of nonlinearity, which makes linear models a non-optimal choice. This book mainly focuses on those methodologies for nonlinear modeling that involve any adaptive learning approaches to process data coming from an unknown nonlinear system. By learning from available data, such methods aim at estimating the nonlinearity introduced by the unknown system. In particular, the methods presented in this book are based on online learning approaches, which process the data example-by-example and allow to model even complex nonlinearities, e.g., showing time-varying and dynamic behaviors. Possible fields of applications of such algorithms includes distributed sensor networks, wireless communications, channel identification, predictive maintenance, wind prediction, network security, vehicular networks, active noise control, information forensics and security, tracking control in mobile robots, power systems, and nonlinear modeling in big data, among many others. This book serves as a crucial resource for researchers, PhD and post-graduate students working in the areas of machine learning, signal processing, adaptive filtering, nonlinear control, system identification, cooperative systems, computational intelligence. This book may be also of interest to the industry market and practitioners working with a wide variety of nonlinear systems. Presents the key trends and future perspectives in the field of nonlinear signal processing and adaptive learning. Introduces novel solutions and improvements over the state-of-the-art methods in the very exciting area of online and adaptive nonlinear identification. Helps readers understand important methods that are effective in nonlinear system modelling, suggesting the right methodology to address particular issues.
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.
Book Synopsis Dynamics of Linear Operators by : Frédéric Bayart
Download or read book Dynamics of Linear Operators written by Frédéric Bayart and published by Cambridge University Press. This book was released on 2009-06-04 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book to assemble the wide body of theory which has rapidly developed on the dynamics of linear operators. Written for researchers in operator theory, but also accessible to anyone with a reasonable background in functional analysis at the graduate level.
Book Synopsis Digital Signal Processing with Kernel Methods by : Jose Luis Rojo-Alvarez
Download or read book Digital Signal Processing with Kernel Methods written by Jose Luis Rojo-Alvarez and published by John Wiley & Sons. This book was released on 2018-02-05 with total page 665 pages. Available in PDF, EPUB and Kindle. Book excerpt: A realistic and comprehensive review of joint approaches to machine learning and signal processing algorithms, with application to communications, multimedia, and biomedical engineering systems Digital Signal Processing with Kernel Methods reviews the milestones in the mixing of classical digital signal processing models and advanced kernel machines statistical learning tools. It explains the fundamental concepts from both fields of machine learning and signal processing so that readers can quickly get up to speed in order to begin developing the concepts and application software in their own research. Digital Signal Processing with Kernel Methods provides a comprehensive overview of kernel methods in signal processing, without restriction to any application field. It also offers example applications and detailed benchmarking experiments with real and synthetic datasets throughout. Readers can find further worked examples with Matlab source code on a website developed by the authors: http://github.com/DSPKM • Presents the necessary basic ideas from both digital signal processing and machine learning concepts • Reviews the state-of-the-art in SVM algorithms for classification and detection problems in the context of signal processing • Surveys advances in kernel signal processing beyond SVM algorithms to present other highly relevant kernel methods for digital signal processing An excellent book for signal processing researchers and practitioners, Digital Signal Processing with Kernel Methods will also appeal to those involved in machine learning and pattern recognition.
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.
Author :Karl-G. Grosse-Erdmann Publisher :Springer Science & Business Media ISBN 13 :1447121708 Total Pages :391 pages Book Rating :4.4/5 (471 download)
Book Synopsis Linear Chaos by : Karl-G. Grosse-Erdmann
Download or read book Linear Chaos written by Karl-G. Grosse-Erdmann and published by Springer Science & Business Media. This book was released on 2011-08-24 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is commonly believed that chaos is linked to non-linearity, however many (even quite natural) linear dynamical systems exhibit chaotic behavior. The study of these systems is a young and remarkably active field of research, which has seen many landmark results over the past two decades. Linear dynamics lies at the crossroads of several areas of mathematics including operator theory, complex analysis, ergodic theory and partial differential equations. At the same time its basic ideas can be easily understood by a wide audience. Written by two renowned specialists, Linear Chaos provides a welcome introduction to this theory. Split into two parts, part I presents a self-contained introduction to the dynamics of linear operators, while part II covers selected, largely independent topics from linear dynamics. More than 350 exercises and many illustrations are included, and each chapter contains a further ‘Sources and Comments’ section. The only prerequisites are a familiarity with metric spaces, the basic theory of Hilbert and Banach spaces and fundamentals of complex analysis. More advanced tools, only needed occasionally, are provided in two appendices. A self-contained exposition, this book will be suitable for self-study and will appeal to advanced undergraduate or beginning graduate students. It will also be of use to researchers in other areas of mathematics such as partial differential equations, dynamical systems and ergodic theory.
Download or read book Operator Theory written by Daniel Alpay and published by Springer. This book was released on 2015-07-21 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A one-sentence definition of operator theory could be: The study of (linear) continuous operations between topological vector spaces, these being in general (but not exclusively) Fréchet, Banach, or Hilbert spaces (or their duals). Operator theory is thus a very wide field, with numerous facets, both applied and theoretical. There are deep connections with complex analysis, functional analysis, mathematical physics, and electrical engineering, to name a few. Fascinating new applications and directions regularly appear, such as operator spaces, free probability, and applications to Clifford analysis. In our choice of the sections, we tried to reflect this diversity. This is a dynamic ongoing project, and more sections are planned, to complete the picture. We hope you enjoy the reading, and profit from this endeavor.
Book Synopsis Advanced Linear Modeling by : Ronald Christensen
Download or read book Advanced Linear Modeling written by Ronald Christensen and published by Springer Nature. This book was released on 2019-12-20 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces several topics related to linear model theory, including: multivariate linear models, discriminant analysis, principal components, factor analysis, time series in both the frequency and time domains, and spatial data analysis. This second edition adds new material on nonparametric regression, response surface maximization, and longitudinal models. The book provides a unified approach to these disparate subjects and serves as a self-contained companion volume to the author's Plane Answers to Complex Questions: The Theory of Linear Models. Ronald Christensen is Professor of Statistics at the University of New Mexico. He is well known for his work on the theory and application of linear models having linear structure.
Book Synopsis Advances in Domain Adaptation Theory by : Ievgen Redko
Download or read book Advances in Domain Adaptation Theory written by Ievgen Redko and published by Elsevier. This book was released on 2019-08-23 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in Domain Adaptation Theory gives current, state-of-the-art results on transfer learning, with a particular focus placed on domain adaptation from a theoretical point-of-view. The book begins with a brief overview of the most popular concepts used to provide generalization guarantees, including sections on Vapnik-Chervonenkis (VC), Rademacher, PAC-Bayesian, Robustness and Stability based bounds. In addition, the book explains domain adaptation problem and describes the four major families of theoretical results that exist in the literature, including the Divergence based bounds. Next, PAC-Bayesian bounds are discussed, including the original PAC-Bayesian bounds for domain adaptation and their updated version. Additional sections present generalization guarantees based on the robustness and stability properties of the learning algorithm. Gives an overview of current results on transfer learning Focuses on the adaptation of the field from a theoretical point-of-view Describes four major families of theoretical results in the literature Summarizes existing results on adaptation in the field Provides tips for future research
