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Support Vector Machine-based Probability Density Estimation

Posted on:2008-08-21Degree:MasterType:Thesis
Country:ChinaCandidate:Y HuFull Text:PDF
GTID:2208360242463976Subject:Financial mathematics and econometrics
Abstract/Summary:PDF Full Text Request
Density function estimation is the core part of Statistical learning, because if we know the density function, we may solve almost all the problem of Statistics. In the traditional ways of statistical learning, pattern recognition and regression estimation is based on the estimation of density function. So density function estimation plays significant role, whether in theoretical study or practical application.Statistical learning theory is a theory based on small sample data, which has been considered to be an important complement and development of traditional statistics. Support Vector Machines algorithms based on the foundations of statistical learning theory was presented by Vapnik and his study group in 1995. Unlike traditional methods, which minimize the empirical training error, SVM make use of the structure risk minimization principle, which may bring a good generalization performance, can also solve some practical problems with low sample size, non-linearity, high-dimension of feature space and local minimization. Because of their excellent performance SVM becomes a hot spot of machine learning theory. SVM has successful applications in many fields, such as pattern recognition, regression estimation, function approaching and so on.In this paper, first of all, Statistical Learning Theory will be introduced, the foundation of support vector machine. Then the principles of SVM are reviewed, and the application in pattern recognition, regression estimation. In this paper we focus on the application of SVM in density function estimation. Because density function estimation is ill-posed problems, so we can use regularization technology to solve this problem. In this paper, to estimate the density function, I use T methods and P methods. Specially we use W-SVM to solve density function estimation. And we take an experimental simulation, finding that simulation results is better than the way we use standard SVM.
Keywords/Search Tags:Statistical learning theory, Support Vector Machines(SVM), Density function estimation, weighted- Support Vector Machines(w-SVM)
PDF Full Text Request
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