Methods Of Variable Selection Based On Lasso And Its Application In Bayesian Networks

The problem of regression is a very important kind problem in statistics.Least square is an classic method to solve it.But,there are many disadvantages when we use it such as weak interpretation,complex calculation,large prediction variance and so on.This article gives a solution to its disadvantages which is called variable selection method Lasso.We put forward many kinds of methods to selection variables based on Lasso and some properties of them.The simulation of random data gets their coefficient paths.By the Compare the index we can get the difference between different selection methods.Bayesian network can reflect the relationship between variables to some extent and the method of variable selection can produce covariance matrix of variables.So,we combine Bayesian network with variable and get its applications.The first part of the article gives the history of variable selection method Lasso.With the development of era,statisticians found its disadvantages by application in practice and new methods was invented based on it.The method of least square is given by practical example in the second part.We give the method which is called bridge regression and Lasso is got when takes a special value.Because the method above is not progressive,Zou put forward the method of adaptive Lasso by weighting the .By the wide use of variable select method,we can find that some variables enter and exit the model at the same time.Based on the characteristics above,Yuan put out the method to select group variables.We get some new methods by combining the adaptive Lasso with group variables select method such as weighted adaptive group Lasso,unweighted adaptive group Lasso and so on.The progressive and convergent properties of are also proved.In bridge regression,we can get Lasso and ridge regression when the parameter is equal to 1 and 2.In order to combine the advantages of both methods to one kind of method,Zou and Hastie got elastic net by applying them to the same model creatively,we prove its property of group effect.Because there are some special demands in practice,we introduce another variable selection methods such as fused Lasso,SQRT Lasso and so on.Then,the simulation and contrast is given.Lasso is widely used in Bayesian networks.The third chapter produces inverse covariance matrix of variable by variable select method and get variables' Bayesian network.So,we get the relationship between variables.