In this paper, we propose a new method which is a modified group lasso with least angle regression selection to improve the high dimensional linear model in explanatory data. In this approach, the data matrix becomes sparse; the column dimension increases and columns are highly correlated. We solve the problem of multicollinearity using LARS algorithm which reduces the bias and mean square error and improves the quality of the model. A high degree of multicollinearity prevents computer software packages from performing the matrix inversion required for computing the regression coefficients. Modified group lasso estimators are solved by the Least Angle Regression and Shrinkage algorithm which calculate the correlation vector, decrease the largest absolute correlation value and select best variable selection in linear regression. It is shown that the proposed method is better than Lasso, elastic net, ordinary least square, ridge regression and adaptive group lasso in various settings, particularly for large column dimension and big group sizes. Also modified group lasso with least angle regression selection is robust to parameter selection and has less variance inflation factor, less mean square error and largest determination coefficient.
A. El Sheikh, Ahmed; L. Barakat, Shaimaa; and M. Mohamed, Salah
"New Aspects on the Modified Group LASSO using the Least Angle Regression and Shrinkage Algorithm,"
Information Sciences Letters: Vol. 10
, Article 16.
Available at: https://digitalcommons.aaru.edu.jo/isl/vol10/iss3/16