Learning Theory An Approximation Theory Viewpoint

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.

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.

The goal of learning theory is to approximate a function from sample values. This is a general overview of the theoretical foundations, and is the first book to emphasize the approximation theory viewpoint. This emphasis provides a balanced approach, and will attract mathematicians to the problems raised.

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.