Abstract
Abstract High-dimensional data analysis arises from almost all scienti c areas, evolving withdevelopment of computing skills, and has encouraged penalized estimations that playimportant roles in statistical learning. For the past years, various penalized estimationshave been developed, and the least absolute shrinkage and selection operator (LASSO)proposed by Tibshirani (1996) has shown outstanding ability, earning the rst place onthe development of penalized estimation. In this paper, we rst introduce a number ofrecent advances in high-dimensional data analysis using the LASSO. The topics includevarious statistical problems such as variable selection and grouped or structured variableselection under sparse high-dimensional linear regression models. Several unsupervisedlearning methods including inverse covariance matrix estimation are presented. In ad-dition, we address further studies on new applications which may establish a guidelineon how to use the LASSO for statistical challenges of high-dimensional data analysis.Keywords: High dimension, LASSO, penalized estimation, review.
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