Iterative Selection Using Orthogonal Regression Techniques

• Activity Number: 191
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Bradley Turnbull*+ and Subhashis Ghosal and Hao Helen Zhang
• Companies: North Carolina State University and North Carolina State University and North Carolina State University
• Keywords: Forward Selection ; Orthogonalization ; LASSO ; High Dimensional Regression

Abstract

Variable selection techniques play a key role in analyzing high dimensional data. Recently, penalized forward selection has been introduced as a procedure, which selects sparser models than comparable methods without compromising predictive power. The motivation for this approach comes from the fact that penalization techniques like LASSO give rise to closed form expressions when used in one dimension. Hence, one can repeat such a procedure in a forward selection setting until it converges. However, when predictors are highly correlated, unnecessary duplication can occur in the selection step. We show it is possible to improve stability and computation efficiency by introducing an orthogonalization step. At each selection step, variables are screened on the basis of their correlation with variables already in the model, thus preventing unnecessary duplication. This new strategy, called the Selection Technique in Orthogonalized Regression Models (STORM), is extremely successful in further reducing the model dimension and also leads to improved predicting power. We carry out a detailed simulation study which compares STORM to existing methods and analyze a gene expression dataset.