A Theory of Learning and Generalization
With Applications to Neural Networks and Control Systems
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Beschreibung
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.
A Theory of Learning and Generalization provides a formal mathematical theory for addressing intuitive questions of the type: How does a machine learn a new concept on the basis of examples? How can a neural network, after sufficient training, correctly predict the output 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? This is 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 new results in both topics. An extensive references section and open problems will help readers to develop their own work in the field.
Autor*in
Mathukumalli Vidyasagar
Themen in »A Theory of Learning and Generalization«
Fat Shattering Bounds Learning Mixing Process Theory OJ0061 UCEM control control system control theory neural networks nonlinear control probability theory robust control stochastic processes support vector machine system identification