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

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	Author	volume	Date Value	title	type	journal	titleUrl	doi	note	year
2000 RegularizationNetworksAndSVMs	Massimiliano Pontil Tomaso Poggio Theodorus Evgeniou			Regularization Networks and Support Vector Machines			http://cbcl.mit.edu/publications/ps/evgeniou-reviewall.pdf