Sure Independence Screening for Ultra-High Dimensional Feature Space

• Activity Number: 276
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2007 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Jinchi Lv*+ and Jianqing Fan
• Companies: Princeton University and Princeton University
• Keywords: Variable selection ; dimensionality reduction ; SIS ; Dantzig selector ; SCAD ; adaptive Lasso

Abstract

Variable selection is fundamental to high-dimensional statistical modeling. In a seminal paper, Candes and Tao (2007) propose a minimum l_1 estimator, the Dantzig selector, and show that it mimics the ideal risk within a logarithmic factor log p. Their procedure and result are challenged when dimension p is ultra high. In this paper we introduce the concept of sure screening and propose a fast method, Sure Independence Screening (SIS) to reduce high dimensionality to a relatively large scale, say below sample size. An appealing special case of SIS is the componentwise regression. In a fairly general asymptotic framework, SIS is shown to possess the sure screening property for even exponentially growing dimension. With ultra-high dimension reduced accurately to below sample size, variable selection can be accomplished by some refined lower-dimensional methods that have oracle properties.