PAC-Bayesian Boundary Of GIBBS Classification Based On A Prior Of The Gaussian Process

This paper is mainly related to the knowledge of supervised learning; Gaussian process is used mainly to solve classification problems. This problem is to study the input-output mapping from the training samples, nevertheless statistical learning theory is on the basis of probability theory, and forms statistics model in accordance with the training sample; also evaluate pros and cons of statistical models in accordance with the testing sample, and is used to predict. As a part of statistical learning theory, supervised learning plays an important role for study of this paper.PAC (Probably approximately correct), and its substance is on the basis of the training sample, so that the resulting statistical model approaches real target model with high probability.In the second Chapter of this paper, we put forward the boundary of the PAC-Bayesian based on the Bayes classification according to the PAC-Bayesian theorem and analogy between the Gibbs classification and the Bayes classification. And this paper gives its relevant certificates.In the third chapter, we recommend the steps and principles of the Gaussian process classification in detail, in allusion to the Gaussian process classification. Then we build the kernel function by selecting the appropriate variables, depending on the circumstances of this thesis and the actual needs. Again, the Gaussian process classification is used for classification problems which are based on the Bayesian framework.In the forth chapter, we approach the posterior probability distribution by using the Laplace approximation method, and get the posterior probability distribution for a future observations by using Laplace approximation method. Nevertheless, we analyze the Kullback-Leibler divergence of the PAC-Bayesian theorem according to predicted the posterior probability distribution and the prior probability distribution, thus, we analyze the true error boundary and the generalization error boundary of the PAC-Bayesian theorem.In the fifth chapter, the Gaussian process classification is applied to the PAC-Bayesian framework, because there are not too many the relevant theoretical researches based on the Bayes classification, in this paper, we only discuss the PAC-Bayesian boundary based on the Gibbs classification in accordance with a prior of Gaussian process, then analyze the error boundary, and we get a preliminary illustration of test conclusions about the error boundary.