A Statistical Learning Method Based On Mixture Distribution Regression Model

Statistical regression is one of the important methods in task learning.Traditional regression models are established under the assumption of normality.However,the Gaussian regression models are insufficient when the noises deviate from the normal distribution.Moreover,the statistical inference of Gaussian regression is sensitive to outliers.The finite mixture model based on mixture distributions can alleviate the problem caused by misspecification of distribution to some extent.For example,the mixture of Gaussians(Mo G)has been proposed for the purposes of regression,clustering,denoising,segmentation,recognition,learning and prediction.In order to enhance the robustness,the mixture of T-distributions(Mo T)has been developed,and extensively studied from various perspectives.The T-distribution is a kind of heavytailed distribution,which can adaptively reduce the influence of outliers to achieve desired robust inference.In this paper,we proposed a statistical learning method based on mixture distribution regression model.The main work of this article includes:The chapter 1 mainly describes the mixture distribution and its existing research,non-linear classification model,non-linear regression model,and multi-task regression model for multi-tasking.And the existing research and shortcomings of mixture distribution applied in the nonlinear regression models.Finally,the related research on Alzheimer’s disease classification based on multi-modal data is introduced.Chapter 2 introduces a non-linear classification model based on the kernel method,and uses a mixed Gaussian distribution to model noise and outliers.The 70 sample data for Alzheimer’s disease have the characteristics of multi-modality,which is combined with the idea of kernel method,and a mixed kernel containing multiple modal information is obtained by linearly combining the data of each modality.The mixed kernel is then processed using a robust non-linear classification model based on mixture of Gaussians.The experimental results show that the model can not only handle multi-modal data well,but also has a good recognition of noise.Chapters 3 deal with non-linear regression problems.We propose a robust nonlinear regression modal based on mixtures of T-distributions.The model can adaptively reduce the effects of complex noises and accurately learn the nonlinear structure of targets.By introducing latent variables,the model is expressed into a hierarchical structure,which helps explain the advantage of flexibility compared to the traditional Gaussian based learning model.We develop a two-stage efficient estimation procedure to obtain penalized likelihood estimator of the parameters combined an EM algorithm with Lagrange multiplier method.Chapters 4 extends the single-task regression model to multi-task model using task learning method.In the multi-task regression model,we can learn the parameters of multiple tasks together to achieve the effect of information sharing.By adding penalties to the task,the performance of the model can be improved to a certain extent.In both simulation and real data,experimental results can verify the performance of the proposed model.In summary,the mixture model is very useful in practical applications.Simulation and real data analysis show that classification and regression models based on mixture distributions have more stable effects on complex noise.Generalizing a single task to multiple tasks can effectively use information among similar tasks.