Research On Gaussian Process For Regression And Prediction

In recent years, the model of Gaussian process(GP) has become an important methodof machine learning. It integrates the kernel based machine learning and Bayesian theorybased machine learning,and has the advantages of the above two kinds of machine learningmethods at the same time. Gaussian process model can be used for classification, also forregression. This paper mainly studies the Gaussian process model for regression prediction.The main research work is as follows:(1)Approximation and learning curve of multi-scale Gaussian process modelThe focus of our work is to conducts the research to the learning curve multi-scaleGaussian process model through the theory of GP model. First, the concept of the learningcurve is described, then according to the principle of multi-scale Gaussian processes model,a general expression for the learning curve is derived. And by approximately computing thelearning curve through averaging a number of sample set, the approximate expression ofthe learning curve is derived.Finally, the simulation calculation of the approximate learningcurve is realized in Matlab environment.(2) Study on one-point and two-point upper bounds of the learning curveUsing the research ideas of one-point upper and two-upper bounds for GP modelpresented by Williams, C.K.I. and Vivarelli, F., the formula of the one-point and two-pointupper bounds of MGP model are derived, and using Simpson formula or gradient formulaapproximately calculate two kinds of upper bounds, the calculation expression of the twokinds of upper bounds are derived. Realize the approximate curve of learning curve andone-point,two-point upper bounds simulation using Matlab.The experimental results verifythe validity of the learning curve theory of Multi-scale Gaussian processes,and through thecomparison of the results of different parameters, derive the effects of various parameterson the learning curve of Multi-scale Gaussian processes.(3) Study on prediction of Mixture of Gaussian processes modelNext, a improved GP model is studied, namely the Mixture of Gaussian processesmodel. First introduce how to use the LOOCV method decomposition model probability,then through the analysis, the decomposition results are maximization under the frameworkof EM. This paper focuses on the EM algorithm of Mixture of Gaussian processes model, gives the specific implementation steps of EM algorithm. Using a set of experimentaldata to simulate,a good result of regression is received, which verifies the validity of theimproved model.