The Study Of Statistical Learning Theory In Chance Space

1970s, Vapnik V N proposed statistical learning theory to solve the learning problemsunder small samples, provided great convenience for us to better solve the problems ofmachine learning. Since the proposed system of statistical learning theory is based on theprobability space as we all know it, but there are a lot of regulars of the probability of theprobability space, such as the probability is non-negative function which can be set to meetthe additive. But in real life the problems we encountered are mostly presented on non-probability space, in order to apply the methods of statistical learning theory to practical lifeand production, we have the necessary to extend statistical learning theory to non-probabilistic space.In2002, Liu based on the random fuzzy theory to propose the concept of the chancemeasure, chance space, mixed variables and related concepts, build chance space theory onthe basis of probability theory and credibility theory.This paper is based on the related properties of chance measure on the chance space, toextend the key theorem of statistical learning theory,etc. on the chance space, so there is acomprehensive discussion about the knowledge of statistical learning theory on the chancespace. The paper is mainly organized as follows:Chapter Two: Preliminaries.Necessary definitions about the probability space, thecredibility space, the chance space,etc.Chapter Three: The key theorem of learning theory on the chance space. First, define theconcepts of learning theory on the chance space. Second, use some properties of the chancemeasure to prove the key theorem of learning theory on the chance space.Chapter Four: Rate of convergence of the learning process and structure riskminimization principle on the chance space.