An overview of variable selection procedures using regularization paths in high-dimensional Gaussian linear regression
Etude de comparaison de procédures de sélection de variable dans la régression gaussienne en grande dimension
Résumé
The size of the data sets is increasing, providing a large number of variables to describe a phenomenon. Assuming that the relationship between the active variables and the response variable is linear, the high-dimensional Gaussian linear regression provides a relevant framework to identify active variables related to the response variable. Many methods exist, and in this article, we focus on methods based on regularization paths. We perform a comparison study by considering different simulation settings and evaluate the performance of the methods.
Our results show that the ability to discriminate between active and inactive variables is important and difficult when the data are not normally distributed and there is a dependency structure between variables. We observe that LARS combined with Elastic-net often gives the best performances. Finally, even if no method is optimal, it was possible to group the methods into groups according to their performance and the characteristics of the dataset.
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