Complete Statistical Theory of Learning
| Autor: | Vladimir Vapnik |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
0209 industrial biotechnology
Weak convergence Computer science 010102 general mathematics Hilbert space 02 engineering and technology Function (mathematics) 01 natural sciences Set (abstract data type) symbols.namesake 020901 industrial engineering & automation Control and Systems Engineering Convergence (routing) symbols Applied mathematics 0101 mathematics Electrical and Electronic Engineering Statistical theory Selection (genetic algorithm) Reproducing kernel Hilbert space |
| Zdroj: | Automation and Remote Control. 80:1949-1975 |
| ISSN: | 1608-3032 0005-1179 |
| DOI: | 10.1134/s000511791911002x |
| Popis: | Existing mathematical model of learning requires using training data find in a given subset of admissible function the function that minimizes the expected loss. In the paper this setting is called Second selection problem. Mathematical model of learning in this paper along with Second selection problem requires to solve the so-called First selection problem where using training data one first selects from wide set of function in Hilbert space an admissible subset of functions that include the desired function and second selects in this admissible subset a good approximation to the desired function. Existence of two selection problems reflects fundamental property of Hilbert space, existence of two different concepts of convergence of functions: weak convergence (that leads to solution of the First selection problem) and strong convergence (that leads to solution of the Second selection problem). In the paper we describe simultaneous solution of both selection problems for functions that belong to Reproducing Kernel Hilbert space. The solution is obtained in closed form. |
| Databáze: | OpenAIRE |
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