# 2000 RegularizationNetworksAndSVMs

- (Evgeniou et al., 2000) ⇒ Theodorus Evgeniou, Massimiliano Pontil, and Tomaso Poggio. (2000). “Regularization Networks and Support Vector Machines.” In: Advances in Computational Mathematics, 13(1).

**Subject Headings:** Regularization, Radial Basis Functions, Support Vector Machines, Reproducing Kernel Hilbert Space, Structural Risk Minimization.

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### Author Keywords

regularization - Radial Basis Functions - Support Vector Machines - Reproducing Kernel Hilbert Space - Structural Risk Minimization

### 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 [math]f[/math] 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 [math]D_l ≡ \{(x_i, y_i) \in X×Y\}^l_{i=1}[/math] called the *training data*, obtained by sampling [math]l[/math] times the set [math]X × Y[/math] according to [math]P(x, y)[/math].

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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 + |