Research Of Group Variable Selection Based On Adaptive Elastic Net With Strongly Correlated Data

As one of the most important methods of data analysis,variable selection method is favored by a majority of scholars.In recent years,the high-dimensional,strongly correlated and redundant data are widely used in natural science and biomedical science,how to choose the appropriate variable selection method is a key in present.In this thesis,we study the data of high dimension and strong correlation,and have done the following work: 1.To select the important variables and remove noise variables in the group,this paper puts forward an improved weight adaptive elastic net method(G_aenet),whose weight is based on the partial least squares regression coefficient.The theoretical proof shows that this method has adaptive grouping effect.Comparing our algorithm with other related methods,such as Lasso,and taking the relative error and the choice accuracy as the standard,numerical simulations and numerical examples are performed to show validity and efficiency of our method.2.The partial least squares regression and the traditional adaptive elastic net method can solve the high-dimensional,strongly correlated problems,but the poor explanatory and accuracy of the model are their disadvantages.So an improved variable selection method(Aenet_PLS)is presented to solve the variable selection problem for strongly correlated data in high dimensions.By taking the linear combination of coefficients derived from two methods,the estimated coefficients in regression model are finally obtained.Thus estimation model with high accuracy,good explanatory are acquired.