Neural Network Learning: Theoretical Foundations
This important work describes recent theoretical advances in the study of artificial neural networks. It explores probabilistic models of supervised learning problems, and addresses the key statistical and computational questions. Chapters survey research on pattern classification with binary-output networks, including a discussion of the relevance of the Vapnik Chervonenkis dimension, and of estimates of the dimension for several neural network models. In addition, Anthony and Bartlett develop a model of classification by real-output networks, and demonstrate the usefulness of classification with a "large margin." The authors explain the role of scale-sensitive versions of the Vapnik Chervonenkis dimension in large margin classification, and in real prediction. Key chapters also discuss the computational complexity of neural network learning, describing a variety of hardness results, and outlining two efficient, constructive learning algorithms. The book is self-contained and accessible to researchers and graduate students in computer science, engineering, and mathematics.
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activation function algorithm for H apply approximate assume Bartlett binary bound chapter choose class F class of functions classiﬁcation Clearly close combination components computation units condition connected consider consistent constants construct convergence convex corresponding covering numbers deﬁned deﬁnition denote described erp(h estimation example fact fat-shattering dimension ﬁnite ﬁrst layer ﬁxed function class function f functions computed given gives Hence implies inequality input instance integer interval labelled learning algorithm least Lemma linear threshold lower bound mapping minimization neural networks Notes Notice obtain parameters perceptron points polynomial positive possible probability distribution problem proof proof of Theorem prove pseudo-dimension random respect restricted model result returns sample complexity sample error satisﬁes set of functions shattered shows sigmoid similar simple space subset Suppose Theorem tion uniform variables VC-dimension vector weights