Mathukumalli Vidyasagar

Learning and Generalisation

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 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? The 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 process, 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. The second edition extends and improves upon this material, covering new areas including: * Support vector machines (SVM's) * 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. This book is essential reading for control and system theorists, neural network researchers, theoretical computer scientists and probabilists The Communications and Control Engineering series reflects the major technological advances which have a great impact in the fields of communication and control. It reports on the research in industrial and academic institutions around the world to exploit the new possibilities which are becoming available