Study On The Theory And Application Of The Exact Post-selection Inference For Lasso

The post-selection inference method is a method that can calculate the exact p-value and confidence interval of the regression coefficient of the selected variable after the variable selection model is established.This scheme can handle arbitrary selection methods as long as the selection method can be represented by a set of linear inequalities on y.The framework's conditional hypothesis test can be applied in the generalized linear model or in the sequential regression process.This paper first analyzes the basic principles,properties and geometric meanings of Lasso(Least absolute shrinkage and selection operator)methods as well as their solution methods.The performance of least squares,Ridge regression and Lasso methods was compared through simulation experiments,the sparseness of Lasso method was verified.Afterwards,this paper analyzes in detail the principles and properties of the post-selection inference method,and investigates the conditions for the application of the post-selection inference method,namely the polyhedral condition set.The Lasso method is represented by a polyhedron theorem.Then the post-selection inference method was applied to the generalized regression model and diabetes dataset for simulation experiments to verify the stability of the new method.Finally,this paper describes the basic theory of post-selection inference method applied to the sequential regression process.Detailed analysis of the post-selection inference method applied to the forward stepwise regression,the minimum angle regression,and the conditions for the establishment of the Lasso method is presented,and a key approximation of the LAR Gaussian test,namely the interval test,is described.This method is more simplified in form and calculation.Finally,post-selection inference method and interval test method are applied to simulation data and prostate cancer dataset.From the p-value and the confidence interval,this method is more accurate and effective than the traditional feature selection method.