Shrinkage and Variable Selection by Polytopes

Petry, Sebastian and Tutz, Gerhard (07. April 2009): Shrinkage and Variable Selection by Polytopes. Department of Statistics: Technical Reports, No.53

Abstract

Constrained estimators that enforce variable selection and grouping of highly correlated data have been shown to be successful in finding sparse representations and obtaining good performance in prediction. We consider polytopes as a general class of compact and convex constraint regions. Well established procedures like LASSO (Tibshirani, 1996) or OSCAR (Bondell and Reich, 2008) are shown to be based on specific subclasses of polytopes. The general framework of polytopes can be used to investigate the geometric structure that underlies these procedures. Moreover, we propose a specifically designed class of polytopes that enforces variable selection and grouping. Simulation studies and an application illustrate the usefulness of the proposed method.

• Item Type: Paper (Technical Report)
• Keywords: Constraint Regions, Polytopes, Lasso, Elastic Net, Oscar
• Subjects: Mathematics, Computer Science and Statistics > Statistics > Technical Reports
• Dewey Classification: 600 Natural sciences and mathematics > 510 Mathematics
• Language: English