Geometria dos métodos de regressão LARS, LASSO e Elastic Net com uma aplicação em seleção genômica

Abstract

The methods of estimation and variable selection in linear models, LASSO (Least Absolute Shrinkage and Selection Operator), LARS (Least Angle Regression) and Elastic Net, are addressed using emphasis in terms of a geometric approach. The present work proposes to be an auxiliary reading to the classic articles of Tibshirani, Hastie, Efron, Zou and Johnstone, presenting in more detail some of the results cited in such articles. Such a point of view does not occur in the basic literature regarding these methods, and in this sense the work represents an original contribution to the subject. Simulations using R code (glmnet package) are developed to study the behavior of the estimators. For a data set of Sus scrofa pork, 237 genetic markers (SNPs) are analyzed using the Elastic Net method, using as response the pork pH and carcass weight.