- Full Description
This book explains the principles that make support vector machines (SVMs) a successful modelling and prediction tool for a variety of applications. The authors present the basic ideas of SVMs together with the latest developments and current research questions in a unified style. They identify three reasons for the success of SVMs: their ability to learn well with only a very small number of free parameters, their robustness against several types of model violations and outliers, and their computational efficiency compared to several other methods. The book provides a unique in-depth treatment of both fundamental and recent material on SVMs that so far has been scattered in the literature. The book can thus serve as both a basis for graduate courses and an introduction for statisticians, mathematicians, and computer scientists. It further provides a valuable reference for researchers working in the field. The book covers all important topics concerning support vector machines such as: loss functions and their role in the learning process; reproducing kernel Hilbert spaces and their properties; a thorough statistical analysis that uses both traditional uniform bounds and more advanced localized techniques based on Rademacher averages and Talagrand's inequality; a detailed treatment of classification and regression; a detailed robustness analysis; and a description of some of the most recent implementation techniques. To make the book self-contained, an extensive appendix is added which provides the reader with the necessary background from statistics, probability theory, functional analysis, convex analysis, and topology.
- Table of Contents
Table of Contents
- Loss functions and their risks.
- Surrogate loss functions.
- Kernels and reproducing kernel Hilbert spaces.
- Infinite samples versions of support vector machines.
- Basic statistical analysis of SVMs.
- Advanced statistical analysis of SVMs.
- Support vector machines for classification.
- Support vector machines for regression.
- Computational aspects.
- Data mining.
- Notation and symbols.
- Author index.
- Subject index.
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