Support Vector Machines (SVM) is a new machine learning approach based on Statistical Learning Theory (Vapnik-Chervonenkis or VC-theory). VCtheory has a solid mathematical background for the dependencies estimation and predictive learning from finite data sets. SVM is based on the Structural Risk Minimisation principle, aiming to minimise both the empirical risk and the complexity of the model,...

The support vector machine (SVM) algorithm (Cortes and Vapnik, 1995) is probably the most widely used kernel learning algorithm. It achieves relatively robust pattern recognition performance using well-established concepts in optimization theory. Despite this mathematical classicism, the implementation of efficient SVM solvers has diverged from the classical methods of numerical optimization. T...

We narrow the width of the confidence intervals introduced by Vapnik for the risk function in Support Vector Machine learning [12]. We obtain this improvement by introducing both a theoretical framework for statistical inference of functions and a concept class complexity index, the detail, that is dual to the Vapnik-Chervonenkis dimension [4]. Detail of a class and maximum number of mislabelle...

Over the last ten years, estimation and learning methods utilizing positive definite kernels have become rather popular, particularly in machine learning. Since these methods have a stronger mathematical slant than earlier machine learning methods (e.g., neural networks), there is also significant interest in the statistical and mathematical community for these methods. The present review aims ...

This paper proposes a theoretical analysis of Genetic Programming (GP) from the perspective of statistical learning theory, a well grounded mathematical toolbox for machine learning. By computing the Vapnik-Chervonenkis dimension of the family of programs that can be inferred by a specific setting of GP, it is proved that a parsimonious fitness ensures universal consistency. This means that the...