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Regularization

Regularization   Regularization (mathematics) – Wikipedia regularization – Google Scholar regularization – Google Search Plan of Class 4 EVGENIOU, Theodoros, et al., Regularization and statistical learning theory for data analysis EVGENIOU, Theodoros, Massimiliano PONTIL and Tomaso POGGIO, A unified framework for Regularization Networks and Support Vector Machines Evgeniou, Pontil and Poggio GIROSI, Federico, Michael JONES and Tomaso …

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Regression

Support Vector Machines for Regression   “The Support Vector method can also be applied to the case of regression, maintaining all the main features that characterise the maximal margin algorithm: a non-linear function is learned by a linear learning machine in a kernel-induced feature space while the capacity of the system is controlled by a …

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Performance

Performance   “In most of these cases, SVM generalization performance (i.e. error rates on test sets) either matches or is significantly better than that of competing methods.” Burgess (1998) “The time complexity of training SVMs scales approximately between quadratic and cubic in the number of training data points [22].” Cao (2003) “Practical experience with such …

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Parameters

SVM Parameters   C “However, it is critical here, as in any regularization scheme, that a proper value is chosen for C, the penalty factor. If it is too large, we have a high penalty for nonseparable points and we may store many support vectors and overfit. If it is too small, we may have …

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PAC Learning

PAC Learning   The paper that proposed the PAC learning framework: L. Valiant. A Theory of the Learnable. Communications of the ACM, 27(11):1134–1142, 1984. Communications of the ACM Volume 27 , Issue 11 (November 1984) Pages: 1134 – 1142 Year of Publication: 1984 Author: L. G. Valiant Links Wikipedia: Probably approximately correct learning Bibliography AIZENSTEIN, …

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nu

nu   SCH?O?LKOPF, Bernhard, et al., New Support Vector Algorithms “We describe a new class of Support Vector algorithms for regression and classification. In these algorithms, a parameter v lets one effectively control the number of Support Vectors.”

Norm

Norm   Norm (mathematics) – Wikipedia Norm — From MathWorld L1-Norm — From MathWorld L2-Norm — From MathWorld “In linear algebra, functional analysis and related areas of mathematics, a norm is a function which assigns a positive length or size to all vectors in a vector space, other than the zero vector.” Wikipedia (2006) “The norm of a mathematical object is …

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Mercer’s Condition

Mercer’s Condition   Mercer’s condition – Wikipedia “Mercer’s condition” – Google Scholar “Mercer’s condition” – Google Search Finally, what happens if one uses a kernel which does not satisfy Mercer�s condition? In general, there may exist data such that the Hessian is indefinite, and for which the quadratic programming problem will have no solution (the …

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