A new approach to variable selection in least squares problems
A new approach to variable selection in least squares problems
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DOI：
10.1093/imanum/20.3.389
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发表时间：
2000-07-01
影响因子：
2.1
通讯作者：
Turlach, BA
中科院分区：
文献类型：
--
作者：
Osborne, MR;Presnell, B;Turlach, BA
Tibshiani(1996年)建议将Lasso作为变量选择技术的一个五颜六色的名称，该技术要求在解上满足L(1)界卡帕的平方和最小。对于kappa较小的值，这迫使最小化解中的零分量。因此，该界限可以用作选择参数。本文对与套索算法实现有关的计算问题作了两点贡献：(1)建立了求解kappa特定值约束问题的紧致下降法；(2)发展了一种同伦方法，其中约束界kappa成为同伦参数，以完全描述可能的选择区域。这两种算法都具有有限终止性。将改进的Gram-Schmidt正交化应用于增广设计矩阵，为算法的实现提供了有效的依据。
The title Lasso has been suggested by Tibshirani (1996) as a colourful name for a technique of variable selection which requires the minimization of a sum of squares subject to an l(1) bound kappa on the solution. This forces zero components in the minimizing solution for small values of kappa. Thus this bound can function as a selection parameter. This paper makes two contributions to computational problems associated with implementing the Lasso: (1) a compact descent method for solving the constrained problem for a particular value of kappa is formulated, and (2) a homotopy method, in which the constraint bound kappa becomes the homotopy parameter, is developed to completely describe the possible selection regimes. Both algorithms have a finite termination property. It is suggested that modified Gram-Schmidt orthogonalization applied to an augmented design matrix provides an effective basis for implementing the algorithms.