Preconditioning for feature selection and regression in high-dimensional problems'

• 成果类型: Article
• 署名作者: Paul, Debashis; Bair, Eric; Hastie, Trevor; Tibshirani, Robert
• 署名单位: University of California System; University of California Davis; Stanford University; Stanford University; Stanford University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053607000000578
• 发表日期: 2008
• 页码: 1595-1618
• 关键词: lasso

摘要

We consider regression problems where the number of predictors greatly exceeds the number of observations. We propose a method for variable selection that first estimates the regression function, yielding a preconditioned response variable. The primary method used for this initial regression is supervised principal components. Then we apply a standard procedure such as forward stepwise selection or the LASSO to the preconditioned response variable. In a number of simulated and real data examples, this two-step procedure outperforms forward stepwise selection or the usual LASSO (applied directly to the raw outcome). We also show that under a certain Gaussian latent variable model, application of the LASSO to the preconditioned response variable is consistent as the number of predictors and observations increases. Moreover, when the observational noise is rather large, the suggested procedure can give a more accurate estimate than LASSO. We illustrate our method on some real problems, including survival analysis with microarray data.