Learning Theory: An Approximation Theory Viewpoint

by Felipe Cucker, Ding Xuan Zhou

Overview

The goal of learning theory is to approximate a function from sample values. To attain this goal learning theory draws on a variety of diverse subjects, specifically statistics, approximation theory, and algorithmics. Ideas from all these areas blended to form a subject whose many successful applications have triggered a rapid growth during the last two decades. This is the first book to give a general overview of the theoretical foundations of the subject emphasizing the approximation theory, while still giving a balanced overview. It is based on courses taught by the authors, and is reasonably self-contained so will appeal to a broad spectrum of researchers in learning theory and adjacent fields. It will also serve as an introduction for graduate students and others entering the field, who wish to see how the problems raised in learning theory relate to other disciplines.

Product Details

ISBN-13:	9780521865593
Publisher:	Cambridge University Press
Publication date:	03/29/2007
Series:	Cambridge Monographs on Applied and Computational Mathematics , #24
Pages:	238
Product dimensions:	6.30(w) x 9.09(h) x 0.67(d)

About the Author

Felipe Cucker is a Professor of Mathematics at the City University of Hong Kong.

Ding Xuan Zhou is an Associate Professor in the Department of Mathematics at the City University of Hong Kong.

Table of Contents

Preface; Foreword; 1. The framework of learning; 2. Basic hypothesis spaces; 3. Estimating the sample error; 4. Polynomial decay approximation error; 5. Estimating covering numbers; 6. Logarithmic decay approximation error; 7. On the bias-variance problem; 8. Regularization; 9. Support vector machines for classification; 10. General regularized classifiers; Bibliography; Index.

Editorial Reviews

"... an excellent monograph on the subject. A major novelty is the focus on the point of view of approximation. This distinguishes the book from the majority of previous works on learning theory, which share a prevalent statistics/computer science flavor. As to the organization and the style of presentation, I cannot imagine a better balance between clarity and conciseness than the one achieved in this book."
Marcello Sanguineti, Mathematical Reviews

From the Publisher