DEGREES OF FREEDOM IN LASSO PROBLEMS

• 成果类型: Article
• 署名作者: Tibshirani, Ryan J.; Taylor, Jonathan
• 署名单位: Carnegie Mellon University; Stanford University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/12-AOS1003
• 发表日期: 2012
• 页码: 1198-1232
• 关键词: least angle regression; variable selection; path

摘要

We derive the degrees of freedom of the lasso fit, placing no assumptions on the predictor matrix X. Like the well-known result of Zou, Hastie and Tibshirani [Ann. Statist. 35 (2007) 2173-2192], which gives the degrees of freedom of the lasso fit when X has full column rank, we express our result in terms of the active set of a lasso solution. We extend this result to cover the degrees of freedom of the generalized lasso fit for an arbitrary predictor matrix X (and an arbitrary penalty matrix D). Though our focus is degrees of freedom, we establish some intermediate results on the lasso and generalized lasso that may be interesting on their own.