The Studies On Variable Separation Algorithm And Some Multiple Response Problem

With the advent of the era of big data,there are more and more types of data.The application scenarios of the multivariate response variable problem are increasing.At present7 more and more scholars have begun to study the problem of multiple response variables and have made great progress.The reduced rank regression is an important tool in the regression of multiple response variables.When the data dimension is high7 there are dependencies other than the hypotenuse between the response variables,or there are many corresponding methods when there are outliers in the observed data.However,there is no unified framework and algorithm to solve.Multi-label classification is also a multiple response problem.Only its response variables are two categorical variables.Although there are many algorithms to solve the problem of multi-label classification,there are always different problems.This paper proposes a new framework for studying multi-label classification.Variable selection is a statistical method that has been widely studied and widely used in recent years.Many statisticians have proposed a variety of different penalty functions to get better statistical properties.Many different algorithms have been proposed for various penalty functions,and the orthogonal EM algorithm proposed in the past two years is a new one.Very innovative algorithm that can be used to solve linear models with penalties.And we try to generalize this idea to the general loss function with penalty and turn it into a variable separation algorithm.In addition,the zero-and-one inflated Poisson regression model is also proposed and studied,and a generalized EM algorithm(GEM)is proposed based on the idea of variable separation mentioned beforeThe main contents are as follows:(1)The algorithm variable separation algorithm accelerates the optimization problem with non-convex penalty functions.The OEM algorithm was reviewed from a new perspective.A new algorithm is proposed for a class of more general functions other than least squares of linear regression models.The convergence of the generated se?quence is proved and our algorithm is accelerated using the Barzilai-Borwein(BB)criterion and the Nesterov's method.The effectiveness of the method is demon?strated by simulation and real data analysis.(2)Sparse robust reduced rank regression with covariance estimation is studied.Reduced rank regression is a very important method in the linear regression model of multi?variate response variables.Many statisticians have proposed improvements to the reduced rank regression for different situations.Without a unified framework,this paper considers the modeling and estimation problems of reduced rank regression when multiple different situations occur simultaneously.Indicates the effectiveness of the new method.(3)A new framework for multi-label classification problems is studied.We consider the use of non-convex robust loss functions to reduce the impact of label misclassifica-tion.Second,we have used an additional hyperparameterization method to capture the dependencies between the labels of any loss function.Then the penalty function and the reduced rank regression method are used to deal with the problem that the dimension of the feature matrix is high.Finally,statistical simulation data and actual data analysis have obtained the effectiveness of our method.(4)Zero-and-one inflated Poisson regression model.We propose a Zero-and-one inflated Poisson regression model for zero and one simultaneous count data.Then the max?imum likelihood estimation and Bayesian estimation of the Zero-and-one inflated Poisson regression model are obtained.Moreover,a new generalized EM algorithm is proposed.Various methods were compared by simulation studies.Finally7 through an actual data analysis7 the practicality of the method is shown.