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Study of the Density Function Corresponding with Support Vector Regression Machine

Author: LiJinWei
Tutor: PanJiBin
School: Hubei Normal University,
Course: Applied Mathematics
Keywords: Statistical Learning Theory Support Vector Regression Machine density function estimation loss function Laplace distribution Order Statistics
CLC: O174
Type: Master's thesis
Year: 2011
Downloads: 32
Quote: 0
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Abstract


Density function estimation not only is the core part of traditional statistical learn-ing, but also is an important research of statistical learning theory. This article reviews machine learning, statistical learning theory, support vector machine systematically, then density function corresponding with Support Vector Regression Machine is stud-ied by the means of Maximum Likelihood Estimation. As the extends of Laplace dist-ribution, the Maximum Likelihood Estimation of the parameter in the new density fu-sution is figured out, along with the natures related the Order Statistics also will be di-scussed. So the Laplace distribution is used more widely.The main body of this paper is divided into four chapters. Chapter One systematica-lly illustrates research background of statistical learning theory and support vector machine, It specifically pointed out that machine learning is a challenging task of pre-sent massive information, support vector machine is a novel machine learning approa-ch which developed in the frame work of statistical learning theory. Chapter Two involves in machine learning and statistical learning theory, which mainly includes the basic and the key problems of statistical learning theory. In the basic problems, mach-ine learning and the empirical risk minimization inductive principle will be introduced, among machine learning problems, it contains three basic problems.There are model recognition, regression function estimation and density function estimation, in the key problem, I mainly discussed consistency of the learning processes, VC dimension, Boundary of ability of spread and structure risk minimization principle. Chapter Three study support vector machine, mainly discussed support vector machine, kernel funct-ion and support vector regression machine, analysis of the characteristics of SVM, which involved in linearly separable, approximation linearly separable and Nonlinear separability, elaborates and analyzes mercer conditions, regression problem, linearlyε-SVRM and SVRM. In particular, the chapter points out five features and some shor-tcomings of support vector machine. Chapter Four studies an extension of Laplace di-stribution based on SVRM. On the basis of MLE means, This chapter calculates the estimators of unknown parameters of new density function, besides studies density function and digital features of relevant order statistics.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Theory of functions
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