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Activity Number: 236 - SLDS Student Paper Awards
Type: Topic Contributed
Date/Time: Monday, July 30, 2018 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistical Learning and Data Science
Abstract #328487 Presentation
Title: Variable Selection for Highly Correlated Predictors
Author(s): Fei Xue* and Annie Qu
Companies: University of Illinois at Urbana-Champaign and University of Illinois at Urbana-Champaign
Keywords: irrepresentable condition; Lasso; model selection consistency; partial correlation; SCAD

Penalty-based variable selection methods are powerful in selecting relevant covariates and estimating coefficients simultaneously. However, variable selection could fail to be consistent when covariates are highly correlated. The partial correlation approach has been adopted to solve the problem with correlated covariates. Nevertheless, the restrictive range of partial correlation is not effective for capturing signal strength for relevant covariates. In this paper, we propose a new Semi-standard PArtial Covariance (SPAC) which is able to reduce correlation effects from other predictors while incorporating the magnitude of coefficients. The proposed SPAC variable selection facilitates choosing covariates which have direct association with the response variable, via utilizing dependency among covariates. We show that the proposed method with the Lasso penalty (SPAC-Lasso) enjoys strong sign consistency in both finite-dimensional and high-dimensional settings under regularity conditions. Simulation studies and the 'HapMap' gene data application demonstrate that the proposed method outperforms the traditional Lasso, adaptive Lasso, SCAD, and Peter-Clark-simple (PC-simple) methods.

Authors who are presenting talks have a * after their name.

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