A Primer On Reproducing Kernel Hilbert Spaces
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| Author | : Paresh Chandra Deka |
| Publisher | : CRC Press |
| Total Pages | : 258 |
| Release | : 2019-10-28 |
| Genre | : Computers |
| ISBN | : 042983666X |
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
| Author | : Jonathan H. Manton |
| Publisher | : |
| Total Pages | : 126 |
| Release | : 2015 |
| Genre | : Hilbert space |
| ISBN | : 9781680830934 |
Reproducing kernel Hilbert spaces are elucidated without assuming prior familiarity with Hilbert spaces. Compared with extant pedagogic material, greater care is placed on motivating the definition of reproducing kernel Hilbert spaces and explaining when and why these spaces are efficacious. The novel viewpoint is that reproducing kernel Hilbert space theory studies extrinsic geometry, associating with each geometric configuration a canonical overdetermined coordinate system. This coordinate system varies continuously with changing geometric configurations, making it well-suited for studying problems whose solutions also vary continuously with changing geometry. This primer can also serve as an introduction to infinite-dimensional linear algebra because reproducing kernel Hilbert spaces have more properties in common with Euclidean spaces than do more general Hilbert spaces.
| Author | : Bernhard Schölkopf |
| Publisher | : MIT Press |
| Total Pages | : 428 |
| Release | : 2004 |
| Genre | : Computers |
| ISBN | : 9780262195096 |
A detailed overview of current research in kernel methods and their application to computational biology.
| Author | : Marc Peter Deisenroth |
| Publisher | : Cambridge University Press |
| Total Pages | : 392 |
| Release | : 2020-04-23 |
| Genre | : Computers |
| ISBN | : 1108569323 |
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.
| Author | : Alain Berlinet |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 369 |
| Release | : 2011-06-28 |
| Genre | : Business & Economics |
| ISBN | : 1441990968 |
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.
| Author | : Marcus Noack |
| Publisher | : CRC Press |
| Total Pages | : 575 |
| Release | : 2023-12-14 |
| Genre | : Business & Economics |
| ISBN | : 1003821286 |
Autonomous Experimentation is poised to revolutionize scientific experiments at advanced experimental facilities. Whereas previously, human experimenters were burdened with the laborious task of overseeing each measurement, recent advances in mathematics, machine learning and algorithms have alleviated this burden by enabling automated and intelligent decision-making, minimizing the need for human interference. Illustrating theoretical foundations and incorporating practitioners’ first-hand experiences, this book is a practical guide to successful Autonomous Experimentation. Despite the field’s growing potential, there exists numerous myths and misconceptions surrounding Autonomous Experimentation. Combining insights from theorists, machine-learning engineers and applied scientists, this book aims to lay the foundation for future research and widespread adoption within the scientific community. This book is particularly useful for members of the scientific community looking to improve their research methods but also contains additional insights for students and industry professionals interested in the future of the field.
| Author | : Andreas Kirsch |
| Publisher | : Springer Nature |
| Total Pages | : 412 |
| Release | : 2021-02-15 |
| Genre | : Mathematics |
| ISBN | : 3030633438 |
This graduate-level textbook introduces the reader to the area of inverse problems, vital to many fields including geophysical exploration, system identification, nondestructive testing, and ultrasonic tomography. It aims to expose the basic notions and difficulties encountered with ill-posed problems, analyzing basic properties of regularization methods for ill-posed problems via several simple analytical and numerical examples. The book also presents three special nonlinear inverse problems in detail: the inverse spectral problem, the inverse problem of electrical impedance tomography (EIT), and the inverse scattering problem. The corresponding direct problems are studied with respect to existence, uniqueness, and continuous dependence on parameters. Ultimately, the text discusses theoretical results as well as numerical procedures for the inverse problems, including many exercises and illustrations to complement coursework in mathematics and engineering. This updated text includes a new chapter on the theory of nonlinear inverse problems in response to the field’s growing popularity, as well as a new section on the interior transmission eigenvalue problem which complements the Sturm-Liouville problem and which has received great attention since the previous edition was published.
| Author | : Rodney A. Kennedy |
| Publisher | : Cambridge University Press |
| Total Pages | : 439 |
| Release | : 2013-03-07 |
| Genre | : Mathematics |
| ISBN | : 1107010039 |
An accessible introduction to Hilbert spaces, combining the theory with applications of Hilbert methods in signal processing.
| Author | : Vern I. Paulsen |
| Publisher | : Cambridge University Press |
| Total Pages | : 193 |
| Release | : 2016-04-11 |
| Genre | : Mathematics |
| ISBN | : 1107104092 |
A unique introduction to reproducing kernel Hilbert spaces, covering the fundamental underlying theory as well as a range of applications.
| Author | : Alexandru Aleman |
| Publisher | : Springer |
| Total Pages | : 283 |
| Release | : 2019-05-30 |
| Genre | : Mathematics |
| ISBN | : 3030146405 |
This book contains both expository articles and original research in the areas of function theory and operator theory. The contributions include extended versions of some of the lectures by invited speakers at the conference in honor of the memory of Serguei Shimorin at the Mittag-Leffler Institute in the summer of 2018. The book is intended for all researchers in the fields of function theory, operator theory and complex analysis in one or several variables. The expository articles reflecting the current status of several well-established and very dynamical areas of research will be accessible and useful to advanced graduate students and young researchers in pure and applied mathematics, and also to engineers and physicists using complex analysis methods in their investigations.
