Statistical Learning Theory

by Vladimir N. Vapnik

Overview

A comprehensive look at learning and generalization theory. The statistical theory of learning and generalization concerns the problem of choosing desired functions on the basis of empirical data. Highly applicable to a variety of computer science and robotics fields, this book offers lucid coverage of the theory as a whole. Presenting a method for determining the necessary and sufficient conditions for consistency of learning process, the author covers function estimates from small data pools, applying these estimations to real-life problems, and much more.

Product Details

ISBN-13:	9780471030034
Publisher:	Wiley
Publication date:	09/30/1998
Series:	Adaptive and Cognitive Dynamic Systems: Signal Processing, Learning, Communications and Control , #2
Pages:	768
Product dimensions:	6.40(w) x 9.50(h) x 1.40(d)

About the Author

Vladimir Naumovich Vapnik is one of the main developers of the Vapnik-Chervonenkis theory of statistical learning, and the co-inventor of the support vector machine method, and support vector clustering algorithm.

Table of Contents

Preface xxi

Introduction: The Problem of induction and  Statistical inference 1

I Theory of learning and generation

1 Two Approches to the learnig problem 19

Appendix to Chapter 1: Methods for solving III-posed problems 51

2  Estimation of the probability Measure and problem of learning 59

3 Conditions for Consistency of Empirical Risk Minimization Principal 79

4 Bounds on the Risk for indicator Loss Functions 121

Appendix to Chapter 4: Lower Bounds on the Risk of the ERM Principle 169

5 Bounds on the Risk for Real-valued loss functions 183

6 The structural Risk Minimization Principle 219

Appendix to chapter 6: Estimating Functions on the basis of indirect measurements 271

7 stochastic III-posed problems 293

8 Estimating the values of Function at given points 339

II Support Vector Estimation of Functions

9 Perceptions and their Generalizations 375

10 The Support Vector Method for Estimating Indicator functions 401

11 The Support Vector Method for Estimating Real-Valued functions 443

12 SV Machines for pattern Recognition 493

13 SV Machines for Function Approximations, Regression Estimation, and Signal Processing 521

III Statistical Foundation of Learning Theory

14 Necessary and Sufficient Conditions for Uniform Convergence of Frequencies to their Probabilities  571

15 Necessary and Sufficient Conditions for Uniform Convergence of Means to their Expectations 597

16 Necessary and Sufficient Conditions for Uniform One-sided Convergence of Means to their Expectations 629

Comments and Bibliographical Remarks 681

References 723

Index 733

Editorial Reviews

Devoted to the theory that explores ways of estimating functional dependency from a given collection of data, a problem that engages several important topics of classical statistics: discriminant analysis, regression analysis, and the density estimation problem. Considers a new paradigm, the learning paradigm, which has been developed over the past 30 years. The first two parts comprise a textbook for a graduate course on the subject for students in statistics, mathematics, engineering, physics, or computer science; the third part is at a higher level of sophistication and could be used in a special course on empirical processes for Ph.D. students in mathematics and statistics. Annotation c. by Book News, Inc., Portland, Or.

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