Estimation of Dependences Based on Empirical DataSpringer New York, 1982 - 399 sivua 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). |
Sisältö
The Problem of Estimating Dependences from | 1 |
The Problem of Interpreting Results of Indirect Experiments | 8 |
Appendix to Chapter 1 Methods for Solving Illposed | 20 |
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algorithms approximation belonging bound Chapter class of densities class of functions complete sample compute consider construct convergence of frequencies decision rules F(x defined Denote density P(x determined deviation empirical data empirical risk equality equivalence classes estimating dependences expected risk ɛ-net fulfilled function F(x hyperplane Iemp(x ill-posed problems indicator functions inequality Laplace distribution least-squares method lemma loss function mathematical expectation matrix method of minimizing method of structural metric minimize the functional minimizes the empirical minimizing the expected normal distribution number of elements obtain operator equation parametric statistics pattern recognition points polynomial probability density problem of estimating quantity random variable regression estimation right-hand side sample X1 solution solving splines structural minimization structural risk minimization sufficient Theorem training sequence unbiased estimator uniform convergence utilize valid variance vector x₁ Xemp y₁
Kirjaluettelon tiedot
| Otsikko | Estimation of Dependences Based on Empirical Data Springer Series in Statistics, ISSN 0172-7397 |
| Kirjoittaja | V. Vapnik |
| Painos | kuvitettu |
| Kustantaja | Springer New York, 1982 |
| Alkuperäisteoksen sijainti | Michiganin yliopisto |
| Digitoitu | 3. helmikuu 2010 |
| ISBN | 0387907335, 9780387907338 |
| Pituus | 399 sivua |
| Vie sitaatti | BiBTeX EndNote RefMan |