Learning and Generalisation
Subtitle: With Applications to Neural Networks
By: by M. Vidyasagar
Series: Communications and Control Engineering; Communications and control engineering
Publisher: Springer London; Imprint; Springer
Published: 2003
Place of publication: London
Language: eng
Format: [electronic resource] :
Number of pages: 488
ISBN-13: 9781447137481; 9781849968676
Subjects: Group theory; Engineering; Computer Communication Networks; Engineering mathematics; Distribution (Probability theory); Systems theory
Description: 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.
Table of contents: title: Introduction; title: Preliminaries; title: Problem Formulations; title: Vapnik-Chervonenkis, Pseudo- and Fat-Shattering Dimensions; title: Uniform Convergence of Empirical Means; title: Learning Under a Fixed Probability Measure; title: Distribution-Free Learning; title: Learning Under an Intermediate Family of Probabilities; title: Alternate Models of Learning; title: Applications to Neural Networks; title: Applications to Control Systems; title: Some Open Problems.