Mathematical Methods for Neural Network Analysis and Design / Edition 1

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Overview

This graduate-level text teaches students how to use a small number of powerful mathematical tools for analyzing and designing a wide variety of artificial neural network (ANN)systems, including their own customized neural networks.Mathematical Methods for Neural NetworkAnalysis and Design offers an original, broad, and integrated approach that explains each tool in a manner that is independent of specific ANN systems. Although most of the methods presented are familiar, their systematic application to neural networks is new. Included are helpful chapter summaries and detailed solutions to over 100 ANN system analysis and design problems. For convenience, many of the proofs of the key theorems have been rewritten so that the entire book uses a relatively uniform notion.This text is unique in several ways. It is organized according to categories of mathematical tools — for investigating the behavior of an ANN system, for comparing (and improving) the efficiency of system computations, and for evaluating its computational goals —that correspond respectively to David Marr's implementational, algorithmic, and computational levels of description. And instead of devoting separate chapters to different types of ANN systems, it analyzes the same group of ANN systems from the perspective of different mathematical methodologies.A Bradford Book

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Editorial Reviews

Booknews
A course text for upper-division or graduate students in cognitive or computer science, econometrics, engineering, mathematics, or other fields in which neural networks appear. Assumes knowledge at the lower-division level of linear algebra and multivariate or vector calculus, upper-division calculus- based probability theory and statistics, and an overall mathematical sophistication commensurate with graduates in the fields. Explains how to analyze and design highly nonlinear artificial neural networks within a classical mathematics and electrical engineering framework. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

  • ISBN-13: 9780262071741
  • Publisher: MIT Press
  • Publication date: 12/1/1996
  • Series: Bradford Books Series
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 432
  • Product dimensions: 7.00 (w) x 10.00 (h) x 1.30 (d)

Table of Contents

Preface
Mathematical Notation
1 Introduction 1
I Implementational Level 63
2 ANN Dynamical Systems 67
3 Deterministic Nonlinear Dynamical Systems Analysis 115
4 Stochastic Nonlinear Dynamical Systems Analysis 151
II Algorithmic Level 189
5 Nonlinear Optimization Theory 193
III Computational Level 237
6 Rational Inference Measures 241
7 Expected Risk Classification and Learning Theory 283
8 Statistical Model Evaluation 313
Epilogue 351
Problem Solutions 353
References 387
Author Index 405
Subject Index 411
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