Twenty-?ve years have passed since the publication of the Russian version of the book Estimation of Dependencies Based on Empirical Data (EDBED for short). Twen- ?ve years is a long period of time. During these years many things have happened. Looking back, one can see how rapidly life and technology have changed, and how slow and dif?cult it is to change the theoretical foundation of the technology and its philosophy. I pursued two goals writing this Afterword: to update the technical results presented in EDBED (the easy goal) and to describe a general picture of how the new ideas developed over these years (a much more dif?cult goal). The picture which I would like to present is a very personal (and therefore very biased) account of the development of one particular branch of science, Empirical - ference Science. Such accounts usually are not included in the content of technical publications. I have followed this rule in all of my previous books. But this time I would like to violate it for the following reasons. First of all, for me EDBED is the important milestone in the development of empirical inference theory and I would like to explain why. S- ond, during these years, there were a lot of discussions between supporters of the new 1 paradigm (now it is called the VC theory ) and the old one (classical statistics).

"In 1982, Springer published the English translation of the Russian book Estimation of Dependencies Based on Empirical Data which became the foundation of the statistical theory of learning and generalization (the VC theory). A number of new principles and new technologies of learning, including SVM technology, have been developed based on this theory.The second edition of this book contains two parts:
- A reprint of the first edition which provides the classical foundation of Statistical Learning Theory
- Four new chapters describing the latest ideas in the development of statistical inference methods. They form the second part of the book entitled Empirical Inference Science
The second part of the book discusses along with new models of inference the general philosophical principles of making inferences from observations. It includes new paradigms of inference that use non-inductive methods appropriate for a complex world, in contrast to inductive methods of inference developed in the classical philosophy of science for a simple world.
The two parts of the book cover a wide spectrum of ideas related to the essence of intelligence: from the rigorous statistical foundation of learning models to broad philosophical imperatives for generalization.
The book is intended for researchers who deal with a variety of problems in empirical inference: statisticians, mathematicians, physicists, computer scientists, and philosophers. TOC:The problem of estimating dependences from empirical data.- Methods of expected-risk minimization.- Methods of parametric statistics for the pattern recognition problem.- Methods of parametric statistics for the problem of regression estimation.- Estimation of regression parameters.- A method of minimizing empirical risk for the problem of pattern recognition.- A method of minimizing empirical risk for the problem of regression estimation.- The method of structural minimization of risk.- Solution of ill-posed problems, interpretation of measurements using the method of structural risk minimization.- Estimation of functional values at given points.- Realism and instrumentalism: Classical statistics and the VC theory (1960-1980).- Falsifiability and parsimony: VC dimension and the number of entities (1980-2000).- Non-inductive methods of inference: Direct inference instead of generalization (2000- ...).- The big picture."

Realism and Instrumentalism: Classical Statistics and VC Theory (1960-1980).- Falsifiability and Parsimony: VC Dimension and the Number of Entities (1980-2000).- Noninductive Methods of Inference: Direct Inference Instead of Generalization (2000-...).- The Big Picture.