Estimation of Dependences Based on Empirical Data

1. Front Matter

   Pages i-xviii

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2. The Problem of Estimating Dependences from Empirical Data

   • Vladimir Vapnik

   Pages 1-26

3. Methods of Expected-Risk Minimization

   • Vladimir Vapnik

   Pages 27-44

4. Methods of Parametric Statistics for the Pattern Recognition Problem

   • Vladimir Vapnik

   Pages 45-80

5. Methods of Parametric Statistics for the Problem of Regression Estimation

   • Vladimir Vapnik

   Pages 81-108

6. Estimation of Regression Parameters

   • Vladimir Vapnik

   Pages 109-138

7. A Method of Minimizing Empirical Risk for the Problem of Pattern Recognition

   • Vladimir Vapnik

   Pages 139-180

8. A Method of Minimizing Empirical Risk for the Problem of Regression Estimation

   • Vladimir Vapnik

   Pages 181-231

9. The Method of Structural Minimization of Risk

   • Vladimir Vapnik

   Pages 232-266

10. Solution of Ill-posed Problems. Interpretation of Measurements Using the Method of Structural Risk Minimization

    • Vladimir Vapnik

    Pages 267-311

11. Estimation of Functional Values at Given Points

    • Vladimir Vapnik

    Pages 312-350

12. Realism and Instrumentalism: Classical Statistics and VC Theory (1960–1980)

    • Vladimir Vapnik

    Pages 411-424

13. Falsifiability and Parsimony: VC Dimension and the Number of Entities (1980–2000)

    • Vladimir Vapnik

    Pages 425-457

14. Noninductive Methods of Inference: Direct Inference Instead of Generalization (2000–…)

    • Vladimir Vapnik

    Pages 459-478

15. The Big Picture

    • Vladimir Vapnik

    Pages 479-497

16. Back Matter

    Pages 499-505

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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).

• Schätzung
• development
• philosophy
• statistics
• technology
• time

• NEC Labs America, Princeton, USA

  Vladimir Vapnik

Policies and ethics