Time Series Multimodality Regression And Prediction Based On Gaussian Process Mixture Models

Gaussian Process(GP)is a kind of very important machine learning model,using threshold function to combine multiple Gaussian Processes into a Gaussian Process Mixture(GPM)model,this model is applicable to analyse mass and multi-model data's regression and prediction.This paper mainly studies Gaussian Process model and its improved model in the application of multimodality prediction of time series,the specific research work are as follows:(1)Classical Gaussian Process Mixture model's chaotic time series multimodality regression and predictionTraditional prediction model predict the sample as a whole,ignoring the important information of multimodality characteristics of the sample.Gaussian Process Mixture model is an effective prediction model,what unlike traditional model is that it accords to sample's multimodality characteristics to "divide and conquer" to the samples.GPM model's concrete implementation method is to classify samples according to their own characteristics,each kind of samples trained by an independent Gaussian Process model,thus simplifying the covariance matrix's calculation,describing the multimodality data exactly,improving the accuracy of prediction.Selecting two groups of chaotic time series Mackey-Glass and Rossler to verify the effectiveness of GPM model,and compared with classical prediction models such as SVM and RBF.The experimental results show that selecting suitable embedding dimension and time delay,GPM model prediction effect is better than the others.(2)Sparse Gaussian Process Mixture model's chaotic time series multimodality regression and predictionCompared with the traditional prediction models,classical Gaussian Process Mixture model has the characteristics of higher prediction accuracy and low algorithm complexity,but to large amount of samples,Sparse Gaussian Process Mixture model(Sparse-GPM)has faster computing speed than GPM model.Sparse-GPM model is improved based on GPM model,replacing each of the Gaussian Process of GPM model with Sparse Gaussian Process,it means that use a small amount of input sample(pseudo input)replacing the original input sample,simplifying the model's calculation.Using Lorenz and Chua chaotic time series to verify Sparse-GPM model,and showing the multimodality prediction method in the prediction results,and comparing this model with GPM model's two other learning methods such as LooCV-GPM model and Variational-GPM model.Sparse-GPM model has obvious effect on improving the computing speed,and showing some advantages on the anti-noise property..(3)Gaussian Process Mixture model in the application of the regression and prediction on financial time seriesFinancial time series reflect the internal rule of financial market,complex and easily influenced by the market,the particularity of financial time series determines the prediction difficult of the series.For the reason of multimodality prediction method of GPM model and Sparse-GPM model,applying the two models in the prediction of four financial data such as the RMB exchange rate,the S&P 500 Index,a stock price of Shanghai Stock Exchange and the Consumer Price Index,and compared with the prediction results of GP model,SVM model,RBF model,LooCV-GPM model,Variational-GPM model.The experiment results show that the Sparse-GPM model and the RBF model ‘s training speed are faster,the GPM mode and the SVM model are generally better than other models on the prediction precision.