# Learning and Generalisation

## With Applications to Neural Networks

Part of the Communications and Control Engineering book series (CCE)

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Part of the Communications and Control Engineering book series (CCE)

*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.

Computer Control Theory Robust Control Stochastic Processes Support Vector Machine Support Vector Machines System Identif UCEM algorithm algorithms artificial intelligence learning machine learning matrix theory reading

- DOI https://doi.org/10.1007/978-1-4471-3748-1
- Copyright Information Springer-Verlag London 2003
- Publisher Name Springer, London
- eBook Packages Springer Book Archive
- Print ISBN 978-1-84996-867-6
- Online ISBN 978-1-4471-3748-1
- Series Print ISSN 0178-5354
- Buy this book on publisher's site