Open Access
April 2012 Degrees of freedom in lasso problems
Ryan J. Tibshirani, Jonathan Taylor
Ann. Statist. 40(2): 1198-1232 (April 2012). DOI: 10.1214/12-AOS1003


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.


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Ryan J. Tibshirani. Jonathan Taylor. "Degrees of freedom in lasso problems." Ann. Statist. 40 (2) 1198 - 1232, April 2012.


Published: April 2012
First available in Project Euclid: 18 July 2012

zbMATH: 1274.62469
MathSciNet: MR2985948
Digital Object Identifier: 10.1214/12-AOS1003

Primary: 62J07 , 90C46

Keywords: Degrees of freedom , generalized lasso , high-dimensional , Lasso

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 2 • April 2012
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