Regresión Lasso

Abstract

Currently we find regression problems in many branches of science, so, as better is the model we use to select variables, better will be solved the problem. The models seek: precise predictions, stability and interpretability. Traditional methods such as stepwise regression, all subsets regression or ridge regression fail in any of the required requirements. In this text we present the LASSO method (least absolute shrinkage and selection operator), which generally improves stability and predictions. However, LASSO has some limitations that will be solved with Elastic Net. This work begins with an introduction, motivating, as in this fragment, the purpose and usefulness of this text, then, to refresh the memory will be a concise reminder of the linear model. In order to facilitate the reader’s understanding, some measures of goodness of fit will be presented. Then we present the method mentioned above, LASSO, a formulation of it as an optimization problem, and a way of solving it are presented. In order to solve the limitations of the LASSO, we present the Na¨ıve Elastic Net. Next, we introduce the LARS method, which will provide an optimal implementation of LASSO in R, we provide the reader a summary of the functions that constitute the package lars. To finalize, and to fix ideas, we will make use of two numerical examples implemented in R, in which the solutions obtained with least squares, LASSO, stepwise and Elastic Net will be compared.