A New Approach to Sparsity Recovery in Linear Regression Model

• Activity Number: 498
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Haolei Weng*+
• Companies: department of Statistics, Columbia University
• Keywords: LASSO ; independent screening ; high dimension ; consistency

Abstract

In recent years, sure independent screening proved to successfully handle ultrahigh-diemensional variable selection with fast computation. Guaranteed by sure screening property, variable selection methods such as LASSO and SCAD can be further performed in low dimension to achieve model selection consistency. Here we propose a new two-step approach in the other direction. We count on independent correlation learning to pick up partial signals and then impose L1 penalty on the remaining variables to relax consistency condition of LASSO. We prove model selection consistency in ultrahigh dimension under certain regularity conditions. Also to enhance finite sample performance, an iterative version is proposed. Simulations and real data analysis show advantages of our method in certain cases.