Regularition Parameters Selection Of Beyesian Penalized Regression

Penalized regression is a vital method of coefficient estimation and variable selection in statistics,and regularization parameter plays a balanced role between loss function and a regular term in penalty regression.Therefore,the selection of regularization parameters is particularly important in fitting penalized regression model process.On the basis of studying bayesian theory and studying penalized regression,from the perspective of bayesian analysis,by finding the relationship between the various components of the penalized regression and the prior function and likelihood function in the bayesian model,Correspondingly,gives the Bayesian estimate expreesion of the regularization parameter in penalized regression.Specifically,the response variable in the penalty regression is subject to the normal distribution,and the coefficient follows a member of the exponential family.In the hypothesis,the loss function of the penalized regression is expressed as a likelihood function in the bayesian model,the regular term is expressed as a prior function in the bayesian model.The bayesian formula is used to combine the loss function with the regular term in the form of a bayesian model,thus forming a posterior distribution of the regression coefficient model.It is this process that find the relationship between the penalized regression and the bayesian model's various parts.Correspondingly,the bayesian estimate expression of the regularizatio-n parameter in the penalized regression can be obtained.This approach generalizes to the general penalized regression(ridge regression and lasso regression),gain the respective regularization parameters expression.From bayesian perspective,obtained the estimation expression of the regularization parameter contains the response variable and the regression coefficient distribution paramete-r.Therefore,this article also focuses on the bayesian estimation of the unknown parameters(position parameter and scale parameter)in the distribution.Finally,case studies,compared with the existing ridge parameter selection method(generalized cross validation method,ridge trace method)under the certain conditions of the data set,the method in this paper is lower than the generalized cross validation method in terms of the calculation complexity,compared with the ridge trace method,gives a statistic interpretation in a certain bayesian sense.