Description
Book SynopsisThis book is devoted to the statistical theory of learning and generalization, that is, the problem of choosing the desired function on the basis of empirical data. The author will present the whole picture of learning and generalization theory. Learning theory has applications in many fields, such as psychology, education and computer science.
Table of ContentsPreface 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
