Support vector regression : propiedades y aplicaciones

Abstract

Statistical learning plays a key role in many areas of science, finance and industry. In particular, supervised learning plays a key role in the fields of statistics, data mining and artificial intelligence, intersecting with areas of engineering and other disciplines. Mathematical optimization has played a crucial role in supervised learning. Techniques from very diverse fields within mathematical optimization have been shown to be useful. Support Vector Machine (SVM) and Support Vector Regression (SVR) are ones of the main exponents as application of the mathematical optimization to supervised learning. SVM and SVR are state of the art methods for supervised learning and regression. These geometrical optimization problems can be written as convex quadratic optimization problems with linear constraints, in principle solvable by any nonlinear optimization procedure. In this work we analyze SVMs and SVRs: how the problems are obtained and expressed in a manageable way. On the one hand, we describe the techniques used by the algorithms of supports vectors dedicated to the classification, in linear and nonlinear cases. On the other hand, we focus on the theoretical development of the techniques in the field of support vector regression. We pay more attention to the nonlinear case, where the algorithm of support vector shows its full potential, using a kernel function to calculate a nonlinear approximation function. Finally we bring these theoretical procedures into practice with the help of the statistical language and environment R.