# 2000 RegularizationNetworksAndSVMs

## Quotes

### Abstract

Regularization Networks and Support Vector Machines are techniques for solving certain problems of learning from examples – in particular, the regression problem of approximating a multivariate function from sparse data. Radial Basis Functions, for example, are a special case of both regularization and Support Vector Machines. We review both formulations in the context of Vapnik's theory of statistical learning which provides a general foundation for the learning problem, combining functional analysis and statistics. The emphasis is on regression: classification is treated as a special case.

### 1. Introduction

... Vapnik’s theory characterizes and formalizes these concepts in terms of the capacity of a set of functions and capacity control depending on the training data: for instance, for a small training set the capacity of the function space in which $f$ is sought has to be small whereas it can increase with a larger training set.

### 2. Overview of statistical learning theory

... We are provided with examples of this probabilistic relationship, that is with a data set $D_l ≡ \{(x_i, y_i) \in X×Y\}^l_{i=1}$ called the training data, obtained by sampling $l$ times the set $X × Y$ according to $P(x, y)$.,

volumeDate ValuetitletypejournaltitleUrldoinoteyear
2000 RegularizationNetworksAndSVMsRegularization Networks and Support Vector MachinesAdvances in Computational Mathematicshttp://cbcl.mit.edu/publications/ps/evgeniou-reviewall.pdf2000
 Author Theodorus Evgeniou +, Massimiliano Pontil + and Tomaso Poggio + journal Advances in Computational Mathematics + title Regularization Networks and Support Vector Machines + titleUrl http://cbcl.mit.edu/publications/ps/evgeniou-reviewall.pdf + year 2000 +