Learning and Generalisation

The author is extremely well known and respected in this field and he provides a very comprehensive text with a broad focus covering all aspects of learning theory and it's applications.

Comprehensive; this book covers all aspects of learning theory and its applications. Other books have a narrower focus It contains applications not only to neural networks but also to control systems The author has recently been selected to receive the Hendrik W. Bode Lecture Prize awarded by the IEEE Control Systems Society Includes supplementary material: sn.pub/extras

Klappentext

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.

Zusammenfassung

Learning and Generalization provides a formal mathematical theory addressing intuitive questions of the type:

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

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

• How much training is required to achieve a given 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 time?

The second edition covers 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 algorithms.

It also contains solutions to some of the open problems posed in the first edition, while adding new open problems.

Inhalt

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.