Research On Robust Regression Learning Algorithm With Noise Characteristic And Its Application

In the open environment,due to data acquisition environment,accuracy of data measurement instruments,and human factors etc.,the collected data will contain lots of uncertainties,such as noise and missing data etc.Therefore,it is very important to establish machine learning methods that consider uncertainties.This thesis mainly analyzes the complex noise characteristics of wind data,and studies how to construct robust regression methods by using the discovered noise characteristics.It includes the following four research topics:(1)Uncertainty modeling based on a hierarchical mixture of multiple distributions.By analyzing the uncertainties in the data,this thesis uses a unified uncertainty expression,namely the probability distribution function,to represent the common uncertainties,including noise,data missing and outliers etc.Considering the limitations of single distributions and mixed distributions in describing the complex uncertainties,based on the mixed distributions,this thesis proposes an uncertainty representation framework,namely hierarchical mixture of multiple distributions,to describe the complex uncertainties.(2)Robust regression modeling based on the assumption that noise obeys a mixture of Gaussians.In the open environment,the noise varies with the environment,climate,time,and application domain.So,it presents complex non-Gaussian and heteroscedastic characteristics.Considering the limitations of the robust regression models based on the specific noise distribution hypothesis,the thesis proposes two robust regression models by assuming that the noise obeys a mixture of Gaussians,or with the Bayesian heteroscedasticity hypothesis.The proposed models further improve the universality of the robust regression models.They have good performance in wind power forecasting and wind power curve modeling.(3)Robust regression modeling based on noise variability and noise correlation.In the multi-output regression task,the difference of each output leads to the difference of the corresponding noise distributions.The correlation between the outputs makes the noise distributions also have a certain correlation.This thesis proposes two noise prior distributions,namely multiple mixture of Gaussians and Bayesian heteroscedasticity prior with embedded correlation,to describe the discrepancy and correlation of noise in the regression tasks with multiple outputs.Thus,a robust functional regression model and a heteroscedastic multi-kernel regression model are developed and then applied to make multi-step ahead wind speed forecasting.(4)Generalized robust regression modeling based on mixture of asymmetric distributions.For the complex non-Gaussian and asymmetric properties of noise,mixture of Gaussians cannot fit the asymmetric noise distributions well.The thesis utilize a mixture of asymmetric Gaussian distributions and a mixture of asymmetric exponential power distributions to construct two asymmetric spline regression models.It is found that the error distribution of wind power curve modeling is complex and asymmetric.The best power curves can be obtained with the proposed two asymmetric spline regression models.The thesis mainly focuses on the analysis of noise characteristics in wind data,the construction of robust regression models based on the discovered noise characteristics,and the corresponding applications in wind energy.However,in addition to the field of wind power,the proposed robust strategies and robust models have certain applicability in other areas such as environment and finance.