Mathematical Methods for Neural Network Analysis and Design PDF Download
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Author: Richard M. Golden
Publisher: MIT Press
ISBN: 9780262071741
Category : Computers
Languages : en
Pages : 452
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Book Description
For convenience, many of the proofs of the key theorems have been rewritten so that the entire book uses a relatively uniform notion.
Author: Richard M. Golden
Publisher: MIT Press
ISBN: 9780262071741
Category : Computers
Languages : en
Pages : 452
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Book Description
For convenience, many of the proofs of the key theorems have been rewritten so that the entire book uses a relatively uniform notion.
Author: J.G. Taylor
Publisher: Elsevier
ISBN: 0080887392
Category : Computers
Languages : en
Pages : 391
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Book Description
The subject of Neural Networks is being seen to be coming of age, after its initial inception 50 years ago in the seminal work of McCulloch and Pitts. It is proving to be valuable in a wide range of academic disciplines and in important applications in industrial and business tasks. The progress being made in each approach is considerable. Nevertheless, both stand in need of a theoretical framework of explanation to underpin their usage and to allow the progress being made to be put on a firmer footing. This book aims to strengthen the foundations in its presentation of mathematical approaches to neural networks. It is through these that a suitable explanatory framework is expected to be found. The approaches span a broad range, from single neuron details to numerical analysis, functional analysis and dynamical systems theory. Each of these avenues provides its own insights into the way neural networks can be understood, both for artificial ones and simplified simulations. As a whole, the publication underlines the importance of the ever-deepening mathematical understanding of neural networks.
Author: Paul Smolensky
Publisher: Psychology Press
ISBN: 1134773013
Category : Psychology
Languages : en
Pages : 890
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Book Description
Recent years have seen an explosion of new mathematical results on learning and processing in neural networks. This body of results rests on a breadth of mathematical background which even few specialists possess. In a format intermediate between a textbook and a collection of research articles, this book has been assembled to present a sample of these results, and to fill in the necessary background, in such areas as computability theory, computational complexity theory, the theory of analog computation, stochastic processes, dynamical systems, control theory, time-series analysis, Bayesian analysis, regularization theory, information theory, computational learning theory, and mathematical statistics. Mathematical models of neural networks display an amazing richness and diversity. Neural networks can be formally modeled as computational systems, as physical or dynamical systems, and as statistical analyzers. Within each of these three broad perspectives, there are a number of particular approaches. For each of 16 particular mathematical perspectives on neural networks, the contributing authors provide introductions to the background mathematics, and address questions such as: * Exactly what mathematical systems are used to model neural networks from the given perspective? * What formal questions about neural networks can then be addressed? * What are typical results that can be obtained? and * What are the outstanding open problems? A distinctive feature of this volume is that for each perspective presented in one of the contributed chapters, the first editor has provided a moderately detailed summary of the formal results and the requisite mathematical concepts. These summaries are presented in four chapters that tie together the 16 contributed chapters: three develop a coherent view of the three general perspectives -- computational, dynamical, and statistical; the other assembles these three perspectives into a unified overview of the neural networks field.
Author: Ovidiu Calin
Publisher: Springer Nature
ISBN: 3030367215
Category : Mathematics
Languages : en
Pages : 760
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Book Description
This book describes how neural networks operate from the mathematical point of view. As a result, neural networks can be interpreted both as function universal approximators and information processors. The book bridges the gap between ideas and concepts of neural networks, which are used nowadays at an intuitive level, and the precise modern mathematical language, presenting the best practices of the former and enjoying the robustness and elegance of the latter. This book can be used in a graduate course in deep learning, with the first few parts being accessible to senior undergraduates. In addition, the book will be of wide interest to machine learning researchers who are interested in a theoretical understanding of the subject.
Author: Robert A. Dunne
Publisher: John Wiley & Sons
ISBN: 0470148144
Category : Mathematics
Languages : en
Pages : 289
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Book Description
An accessible and up-to-date treatment featuring the connection between neural networks and statistics A Statistical Approach to Neural Networks for Pattern Recognition presents a statistical treatment of the Multilayer Perceptron (MLP), which is the most widely used of the neural network models. This book aims to answer questions that arise when statisticians are first confronted with this type of model, such as: How robust is the model to outliers? Could the model be made more robust? Which points will have a high leverage? What are good starting values for the fitting algorithm? Thorough answers to these questions and many more are included, as well as worked examples and selected problems for the reader. Discussions on the use of MLP models with spatial and spectral data are also included. Further treatment of highly important principal aspects of the MLP are provided, such as the robustness of the model in the event of outlying or atypical data; the influence and sensitivity curves of the MLP; why the MLP is a fairly robust model; and modifications to make the MLP more robust. The author also provides clarification of several misconceptions that are prevalent in existing neural network literature. Throughout the book, the MLP model is extended in several directions to show that a statistical modeling approach can make valuable contributions, and further exploration for fitting MLP models is made possible via the R and S-PLUS® codes that are available on the book's related Web site. A Statistical Approach to Neural Networks for Pattern Recognition successfully connects logistic regression and linear discriminant analysis, thus making it a critical reference and self-study guide for students and professionals alike in the fields of mathematics, statistics, computer science, and electrical engineering.
Author: Michel J.A.M. van Putten
Publisher: Springer Nature
ISBN: 3662611848
Category : Science
Languages : en
Pages : 259
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Book Description
This book treats essentials from neurophysiology (Hodgkin–Huxley equations, synaptic transmission, prototype networks of neurons) and related mathematical concepts (dimensionality reductions, equilibria, bifurcations, limit cycles and phase plane analysis). This is subsequently applied in a clinical context, focusing on EEG generation, ischaemia, epilepsy and neurostimulation. The book is based on a graduate course taught by clinicians and mathematicians at the Institute of Technical Medicine at the University of Twente. Throughout the text, the author presents examples of neurological disorders in relation to applied mathematics to assist in disclosing various fundamental properties of the clinical reality at hand. Exercises are provided at the end of each chapter; answers are included. Basic knowledge of calculus, linear algebra, differential equations and familiarity with MATLAB or Python is assumed. Also, students should have some understanding of essentials of (clinical) neurophysiology, although most concepts are summarized in the first chapters. The audience includes advanced undergraduate or graduate students in Biomedical Engineering, Technical Medicine and Biology. Applied mathematicians may find pleasure in learning about the neurophysiology and clinic essentials applications. In addition, clinicians with an interest in dynamics of neural networks may find this book useful, too.
Author: Alexander I. Galushkin
Publisher: Springer Science & Business Media
ISBN: 3540481257
Category : Technology & Engineering
Languages : en
Pages : 396
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Book Description
This book, written by a leader in neural network theory in Russia, uses mathematical methods in combination with complexity theory, nonlinear dynamics and optimization. It details more than 40 years of Soviet and Russian neural network research and presents a systematized methodology of neural networks synthesis. The theory is expansive: covering not just traditional topics such as network architecture but also neural continua in function spaces as well.
Author: Marc Peter Deisenroth
Publisher: Cambridge University Press
ISBN: 1108569323
Category : Computers
Languages : en
Pages : 392
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Book Description
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: Daniel A. Roberts
Publisher: Cambridge University Press
ISBN: 1316519333
Category : Computers
Languages : en
Pages : 473
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Book Description
This volume develops an effective theory approach to understanding deep neural networks of practical relevance.
Author: Ronald T. Kneusel
Publisher: No Starch Press
ISBN: 1718501900
Category : Computers
Languages : en
Pages : 346
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Book Description
Math for Deep Learning provides the essential math you need to understand deep learning discussions, explore more complex implementations, and better use the deep learning toolkits. With Math for Deep Learning, you'll learn the essential mathematics used by and as a background for deep learning. You’ll work through Python examples to learn key deep learning related topics in probability, statistics, linear algebra, differential calculus, and matrix calculus as well as how to implement data flow in a neural network, backpropagation, and gradient descent. You’ll also use Python to work through the mathematics that underlies those algorithms and even build a fully-functional neural network. In addition you’ll find coverage of gradient descent including variations commonly used by the deep learning community: SGD, Adam, RMSprop, and Adagrad/Adadelta.
