Statistical Learning Theory

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.

• Preface xxiIntroduction: The Problem of induction and  Statistical inference 1I Theory of learning and generation1 Two Approches to the learnig problem 19Appendix to chapter 1: Methods for solving III-posed problems 512  Estimation of the probability Measure and problem of learning 593 Conditions for Consistency of Empirical Risk Minimization Principal 794 Bounds on the Risk for indicator Loss Functions 121Appendix to Chapter 4: Lower Bounds on the Risk of the ERM Principle 1695 Bounds on the Risk for Real-valued loss functions 1836 The structural Risk Minimization Principle 219Appendix to chapter 6: Estimating Functions on the basis of indirect measurements 2717 stochastic III-posed problems 2938 Estimating the values of Function at given points 339II Support Vector Estimation of Functions9 Perceptions and their Generalizations 37510 The Support Vector Method for Estimating Indicator functions 40111 The Support Vector Method for Estimating Real-Valued functions 44312 SV Machines for pattern Recognition 49313 SV Machines for Function Approximations, Regression Estimation, and Signal Processing 521III Statistical Foundation of Learning Theory14 Necessary and Sufficient Conditions for Uniform Convergence of Frequencies to their Probabilities  57115 Necessary and Sufficient Conditions for Uniform Convergence of Means to their Expectations 59716 Necessary and Sufficient Conditions for Uniform One-sided Convergence of Means to their Expectations 629Comments and Bibliographical Remarks 681References 723Index 733