Learning and Generalisation: With Applications to Neural Networks / Edition 2

Learning and Generalisation: With Applications to Neural Networks / Edition 2

by Mathukumalli Vidyasagar
     
 

Learning and Generalization provides a formal mathematical theory for addressing intuitive questions such as:

• How does a machine learn a new concept on the basis of examples?

• How can a neural network, after sufficient training, correctly predict the outcome of a previously unseen input?

• How much training is required to

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Overview

Learning and Generalization provides a formal mathematical theory for addressing intuitive questions such as:

• How does a machine learn a new concept on the basis of examples?

• How can a neural network, after sufficient training, correctly predict the outcome of a previously unseen input?

• How much training is required to achieve a specified level of accuracy in the prediction?

• How can one identify the dynamical behaviour of a nonlinear control system by observing its input-output behaviour over a finite interval of time?

In its successful first edition, A Theory of Learning and Generalization was the first book to treat the problem of machine learning in conjunction with the theory of empirical processes, the latter being a well-established branch of probability theory. The treatment of both topics side-by-side leads to new insights, as well as to new results in both topics.

This second edition extends and improves upon this material, covering new areas including:

• Support vector machines.

• Fat-shattering dimensions and applications to neural network learning.

• Learning with dependent samples generated by a beta-mixing process.

• Connections between system identification and learning theory.

• Probabilistic solution of 'intractable problems' in robust control and matrix theory using randomized algorithm.

Reflecting advancements in the field, solutions to some of the open problems posed in the first edition are presented, while new open problems have been added.

Learning and Generalization (second edition) is essential reading for control and system theorists, neural network researchers, theoretical computer scientists and probabilist.

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Product Details

ISBN-13:
9781849968676
Publisher:
Springer London
Publication date:
12/08/2010
Series:
Communications and Control Engineering Series
Edition description:
Softcover reprint of hardcover 2nd ed. 2002
Pages:
488
Product dimensions:
9.21(w) x 6.14(h) x 1.03(d)

Table of Contents

1. Introduction.- 2. Preliminaries.- 3. Problem Formulations.- 4. Vapnik-Chervonenkis, Pseudo- and Fat-Shattering Dimensions.- 5. Uniform Convergence of Empirical Means.- 6. Learning Under a Fixed Probability Measure.- 7. Distribution-Free Learning.- 8. Learning Under an Intermediate Family of Probabilities.- 9. Alternate Models of Learning.- 10. Applications to Neural Networks..- 11. Applications to Control Systems.- 12. Some Open Problems.

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