Statistical Learning Theory

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