Covariance-Enhanced Screening for Ultra-High-Dimensional Variable Selection

• Activity Number: 346
• Type: Topic Contributed
• Date/Time: Tuesday, August 11, 2015 : 10:30 AM to 12:20 PM
• Sponsor: ENAR
• Author(s): Kevin He* and Yanming Li and Ji Zhu and Yi Li
• Companies: University of Michigan and University of Michigan and University of Michigan and University of Michigan
• Keywords: Covariance-enhanced ; Screening ; High-dimensional ; Variable Selection

Abstract

Genome-wide association studies (GWAS) and gene expression studies have become increasingly popular for studying complex human diseases. For such problems with ultra-high dimensional predictors, the commonly used variable selection approaches are infeasible to implement and their required assumption will be likely to fail. Sure independence screening (SIS) has been proposed to reduce the ultrahigh dimensionality down to a moderate scale. Despite the popularity and computational simplicity of SIS, the theoretical basis for the univariate screening relies on strong assumptions such as Partial Faithfulness Condition. In genetic studies, the marginal effects of genetic variants may be quite different from their joint effects. Marginal screening may miss important predictors that have weak marginal effects but strong joint effects. To address this concern, we proposed covariance-enhanced screening procedure which is based on a sufficient and necessary condition for the sure screening property without requiring the restrictive partial faithfulness assumption. The proposed methods are applied to Cutaneous Melanoma data.