Adaptive Kernel Function Of Sparse Gaussian Process

The arrival and continuous development of big data era have put forward higher requirements for data processing technics.Machine learning method is the main method of data processing in recent years.Gaussian process is a probabilistic non-parametric data processing machine learning method using Bayes theorem and kernel tricks.It has the advantages of nonparametric and probabilistic output.However,due to the use of kernel tricks in the Gaussian Process,a certain problem of kernel selection and construction has emerged,which still a dark art and relies on expert experience.At the same time,the Gaussian process has the disadvantage of large computational complexity,which also limits the wide application of the Gaussian process.This thesis presents an adaptive Gaussian Process kernel function construction method,AGPKC algorithm,by considering kernel as global and local two parts to realize kernel function self-selection and self-construction,then reduce the dependence on expert experience.Also,AGPKC used a sparse technique to reduce the large computation scale.Finally,its construction ability is verified by two classical real data sets in the field of Gaussian process data processing,and then the method is applied in the field of lithium-ion battery life prediction.This thesis emphasized on several aspects as follows:(1)The mathematical principle of Gaussian process fitting and prediction is studied and analyzed.For the problem of high computational complexity of Gaussian Process,a comparative study of commonly used Gaussian Process sparse methods is carried out.The selection of the current Gaussian process kernel function is still a dark art and mainly based on expert experience,and the kernel function selection method is not supported by a unified theory.This thesis systematically explores the influence of a single kernel function,hyperparameters and combined kernel functions on the prediction results.It provides a theoretical basis for the subsequent proposal of the kernel function adaptive algorithm.(2)In order to solve the problem that the Gaussian process kernel function still needs expert experience selection,a Gaussian process kernel function adaptive method is proposed: AGPKC(Adaptive Gaussian Process Kernel Search,AGPKC)kernel function adaptive Gaussian process.The method divides the kernel function into two types: global kernel function and local kernel function,respectively describing the global and local features of the data.First,it realizes the self-selection of the global kernel function by analyzing the global features of the data,and then combines the kernel functions according to the kernel functions construction rules and constructs all possible kernel functions by algorithm,and realizes the self-combination of kernel functions.After each combination,the optimal combined kernel function is selected by judging the fitting result and the complexity of the combined kernel function for the next combination and judgment,realized kernel functions self-update.(3)Two sets of classical data in the field of Gaussian process data processing are used to verify the fitting results of the combined kernel function constructed by the proposed AGPKC method with actual data,and compared with the same type of algorithm,GPSS(Gaussian Process Structure Search,GPSS)method.The verification results show that the AGPKC method can successfully construct the kernel function by learning the data,and the fitting results are good.The comparison results with GPSS method show that the fitting results and running time of the AGPKC method are better than those of the GPSS method.Applied the AGPKC method in the field of lithium-ion battery life prediction,and a newer data set in the field of lithium-ion batteries is used to test the fitting and prediction result of real-life data.The verification results show that the AGPKC kernel function adaptive algorithm proposed in this thesis can successfully construct a kernel function through the learning of data features,and the model fitting and prediction results using this kernel function is good,indicating that the algorithm has a certain application prospect.