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A tutorial on support vector regression


     The analyzed article is titled « A tutorial on support vector regression » written by Alexander J. Smola who is a professor in Carnegie Mellon University at Pittsburgh USA « machine learning department ». And Bernhard Scholkopf who is director in Max Planck Institute for Intelligent Systems in GERMANY. It is Published by Statistics and Computing in 2004 and manufactured in the NETHERLANDS. Statistics and Computing as sitted in the oficiel site, "is a bi-monthly refereed journal that publishes papers covering the interface between the statistical and computing sciences. The journal includes techniques for evaluating analytically intractable problems, such as bootstrap resampling, Markov chain Monte Carlo, sequential Monte Carlo, approximate Bayesian computation,  search and optimization methods, stochastic simulation and Monte Carlo, graphics, computer environments, statistical approaches to software errors, information retrieval, machine learning, statistics of databases and database technology, huge data sets and big data analytics, computer algebra, graphical models, image processing, tomography, inverse problems and uncertainty quantification".
     The article talks about SVM (Support Vector Machine) The authors structured their work as follows: they began by giving us an overview and idea on Support Vector (SV) machines and some examples of application then they added a small summary of techniques and algorithms currently used for The training of SV machines. We will see in the next parts the context of the article, its positioning, contributions, ad finally we will try to experiment some algorithms proposed by the authors. 

 Context of the work

     Supervised learning contains several techniques. And among them, we find SVMs which are very effective to solve the problems of discrimination and regression.
      SVM appeared in the 1990s on the basis and extension of the Vapnik-Chervonenkis (VC) theory. And thanks to their multiple effectiveness, ability to work with large data, the small number of hyper parameters, their theoretical guarantees, and good results in practice. SVM quickly integrate the world of statistics
    SVM have a broad scope of application as(information retrieval, bioinformatics  finance, computer vision, finance ...). The performance of support vector machine can be compared to that of the neural network or the Gaussian mixture model. And depending on the type of data, SVM may be similar to these even see better
   SVMs can be used to solve data classification problems, which is to decide which class belongs to a sample, or regression problems, that means to represent a set of  scattered data  by a known functions or to predict the numerical value of a variable. To solve these two problems we have to construct a function h which has  as inputs, a vector x, to which it  makes correspond an output y:      Y = h (x)


I have tooken un example of un SVM application from Wikipedea to be more explicite 
" Imagine a plane (two-dimensional space) which are distributed in two groups of points. These points are associated with a group: points (+) for y> x and points (-) for y <x we can find an obvious linear separator in this example, the line y = x. The problem is said to be linearly separable.


For more complicated problems, there is generally no linear separation. For example, imagine a plane in which the points (-) are grouped in a circle with points (+) all around no linear separator cannot properly separate groups the problem is not linearly separable. There is no separating hyper-plane.