Ridge Functions And Applications In Neural Networks

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Ridge Functions And Applications In Neural Networks

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Author : Vugar E. Ismailov
language : en
Publisher: American Mathematical Society
Release Date : 2021-12-17

Ridge Functions And Applications In Neural Networks written by Vugar E. Ismailov and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-17 with Mathematics categories.

Recent years have witnessed a growth of interest in the special functions called ridge functions. These functions appear in various fields and under various guises. They appear in partial differential equations (where they are called plane waves), in computerized tomography, and in statistics. Ridge functions are also the underpinnings of many central models in neural network theory. In this book various approximation theoretic properties of ridge functions are described. This book also describes properties of generalized ridge functions, and their relation to linear superpositions and Kolmogorov's famous superposition theorem. In the final part of the book, a single and two hidden layer neural networks are discussed. The results obtained in this part are based on properties of ordinary and generalized ridge functions. Novel aspects of the universal approximation property of feedforward neural networks are revealed. This book will be of interest to advanced graduate students and researchers working in functional analysis, approximation theory, and the theory of real functions, and will be of particular interest to those wishing to learn more about neural network theory and applications and other areas where ridge functions are used.

Ridge Functions

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Author : Allan Pinkus
language : en
Publisher: Cambridge University Press
Release Date : 2015-08-07

Ridge Functions written by Allan Pinkus and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-07 with Computers categories.

Presents the state of the art in the theory of ridge functions, providing a solid theoretical foundation.

Neural Network Applications In Control

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Author : George William Irwin
language : en
Publisher: IET
Release Date : 1995

Neural Network Applications In Control written by George William Irwin and has been published by IET this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Computers categories.

The aim is to present an introduction to, and an overview of, the present state of neural network research and development, with an emphasis on control systems application studies. The book is useful to a range of levels of reader. The earlier chapters introduce the more popular networks and the fundamental control principles, these are followed by a series of application studies, most of which are industrially based, and the book concludes with a consideration of some recent research.

Theory Of Ridge Regression Estimation With Applications

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Author : A. K. Md. Ehsanes Saleh
language : en
Publisher: John Wiley & Sons
Release Date : 2019-02-12

Theory Of Ridge Regression Estimation With Applications written by A. K. Md. Ehsanes Saleh and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-12 with Mathematics categories.

A guide to the systematic analytical results for ridge, LASSO, preliminary test, and Stein-type estimators with applications Theory of Ridge Regression Estimation with Applications offers a comprehensive guide to the theory and methods of estimation. Ridge regression and LASSO are at the center of all penalty estimators in a range of standard models that are used in many applied statistical analyses. Written by noted experts in the field, the book contains a thorough introduction to penalty and shrinkage estimation and explores the role that ridge, LASSO, and logistic regression play in the computer intensive area of neural network and big data analysis. Designed to be accessible, the book presents detailed coverage of the basic terminology related to various models such as the location and simple linear models, normal and rank theory-based ridge, LASSO, preliminary test and Stein-type estimators. The authors also include problem sets to enhance learning. This book is a volume in the Wiley Series in Probability and Statistics series that provides essential and invaluable reading for all statisticians. This important resource: Offers theoretical coverage and computer-intensive applications of the procedures presented Contains solutions and alternate methods for prediction accuracy and selecting model procedures Presents the first book to focus on ridge regression and unifies past research with current methodology Uses R throughout the text and includes a companion website containing convenient data sets Written for graduate students, practitioners, and researchers in various fields of science, Theory of Ridge Regression Estimation with Applications is an authoritative guide to the theory and methodology of statistical estimation.

Neural Networks And Computing Learning Algorithms And Applications

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Author : Tommy Wai-shing Chow
language : en
Publisher: World Scientific
Release Date : 2007-08-13

Neural Networks And Computing Learning Algorithms And Applications written by Tommy Wai-shing Chow and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-13 with Computers categories.

This book covers neural networks with special emphasis on advanced learning methodologies and applications. It includes practical issues of weight initializations, stalling of learning, and escape from a local minima, which have not been covered by many existing books in this area. Additionally, the book highlights the important feature selection problem, which baffles many neural networks practitioners because of the difficulties handling large datasets. It also contains several interesting IT, engineering and bioinformatics applications./a

Explorations In The Mathematics Of Data Science

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Author : Simon Foucart
language : en
Publisher: Springer Nature
Release Date : 2024-09-12

Explorations In The Mathematics Of Data Science written by Simon Foucart and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-12 with Mathematics categories.

This edited volume reports on the recent activities of the new Center for Approximation and Mathematical Data Analytics (CAMDA) at Texas A&M University. Chapters are based on talks from CAMDA’s inaugural conference – held in May 2023 – and its seminar series, as well as work performed by members of the Center. They showcase the interdisciplinary nature of data science, emphasizing its mathematical and theoretical foundations, especially those rooted in approximation theory.

Recent Advances In Harmonic Analysis And Applications

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Author : Dmitriy Bilyk
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-10-16

Recent Advances In Harmonic Analysis And Applications written by Dmitriy Bilyk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-16 with Mathematics categories.

Recent Advances in Harmonic Analysis and Applications features selected contributions from the AMS conference which took place at Georgia Southern University, Statesboro in 2011 in honor of Professor Konstantin Oskolkov's 65th birthday. The contributions are based on two special sessions, namely "Harmonic Analysis and Applications" and "Sparse Data Representations and Applications." Topics covered range from Banach space geometry to classical harmonic analysis and partial differential equations. Survey and expository articles by leading experts in their corresponding fields are included, and the volume also features selected high quality papers exploring new results and trends in Muckenhoupt-Sawyer theory, orthogonal polynomials, trigonometric series, approximation theory, Bellman functions and applications in differential equations. Graduate students and researchers in analysis will be particularly interested in the articles which emphasize remarkable connections between analysis and analytic number theory. The readers will learn about recent mathematical developments and directions for future work in the unexpected and surprising interaction between abstract problems in additive number theory and experimentally discovered optical phenomena in physics. This book will be useful for number theorists, harmonic analysts, algorithmists in multi-dimensional signal processing and experts in physics and partial differential equations.

Multilayer Neural Networks

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Author : Maciej Krawczak
language : en
Publisher: Springer
Release Date : 2013-04-17

Multilayer Neural Networks written by Maciej Krawczak and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Technology & Engineering categories.

The primary purpose of this book is to show that a multilayer neural network can be considered as a multistage system, and then that the learning of this class of neural networks can be treated as a special sort of the optimal control problem. In this way, the optimal control problem methodology, like dynamic programming, with modifications, can yield a new class of learning algorithms for multilayer neural networks. Another purpose of this book is to show that the generalized net theory can be successfully used as a new description of multilayer neural networks. Several generalized net descriptions of neural networks functioning processes are considered, namely: the simulation process of networks, a system of neural networks and the learning algorithms developed in this book. The generalized net approach to modelling of real systems may be used successfully for the description of a variety of technological and intellectual problems, it can be used not only for representing the parallel functioning of homogenous objects, but also for modelling non-homogenous systems, for example systems which consist of a different kind of subsystems. The use of the generalized nets methodology shows a new way to describe functioning of discrete dynamic systems.

Bimonoidal Categories E N Monoidal Categories And Algebraic K Theory

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Author : Niles Johnson
language : en
Publisher: American Mathematical Society
Release Date : 2024-10-23

Bimonoidal Categories E N Monoidal Categories And Algebraic K Theory written by Niles Johnson and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-23 with Mathematics categories.

Bimonoidal categories are categorical analogues of rings without additive inverses. They have been actively studied in category theory, homotopy theory, and algebraic $K$-theory since around 1970. There is an abundance of new applications and questions of bimonoidal categories in mathematics and other sciences. The three books published by the AMS in the Mathematical Surveys and Monographs series under the title Bimonoidal Categories, $E_n$-Monoidal Categories, and Algebraic $K$-Theory (Volume I: Symmetric Bimonoidal Categories and Monoidal Bicategories, Volume II: Braided Bimonoidal Categories with Applications, and Volume III: From Categories to Structured Ring Spectra?this book) provide a unified treatment of bimonoidal and higher ring-like categories, their connection with algebraic $K$-theory and homotopy theory, and applications to quantum groups and topological quantum computation. With ample background material, extensive coverage, detailed presentation of both well-known and new theorems, and a list of open questions, this work is a user-friendly resource for beginners and experts alike. Part 1 of this book is a detailed study of enriched monoidal categories, pointed diagram categories, and enriched multicategories. Using this machinery, Part 2 discusses the rich interconnection between the higher ring-like categories, homotopy theory, and algebraic $K$-theory. Starting with a chapter on homotopy theory background, the first half of Part 2 constructs the Segal $K$-theory functor and the Elmendorf-Mandell $K$-theory multifunctor from permutative categories to symmetric spectra. For the latter, the detailed treatment here includes identification and correction of some subtle errors concerning its extended domain. The second half applies the $K$-theory multifunctor to small ring, bipermutative, braided ring, and $E_n$-monoidal categories to obtain, respectively, strict ring, $E_{infty}$-, $E_2$-, and $E_n$-symmetric spectra.

Iwasawa Theory And Its Perspective Volume 2

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Author : Tadashi Ochiai
language : en
Publisher: American Mathematical Society
Release Date : 2024-04-25

Iwasawa Theory And Its Perspective Volume 2 written by Tadashi Ochiai and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-25 with Mathematics categories.

Iwasawa theory began in the late 1950s with a series of papers by Kenkichi Iwasawa on ideal class groups in the cyclotomic tower of number fields and their relation to $p$-adic $L$-functions. The theory was later generalized by putting it in the context of elliptic curves and modular forms. The main motivation for writing this book was the need for a total perspective of Iwasawa theory that includes the new trends of generalized Iwasawa theory. Another motivation is to update the classical theory for class groups, taking into account the changed point of view on Iwasawa theory. The goal of this second part of the three-part publication is to explain various aspects of the cyclotomic Iwasawa theory of $p$-adic Galois representations.