Solving l1 Regularization Problems With Piecewise Linear Losses
Solving l1 Regularization Problems With Piecewise Linear Losses
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DOI：
10.1198/jcgs.2010.08115
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发表时间：
2010-12-01
影响因子：
2.4
通讯作者：
Kato, Kengo
中科院分区：
文献类型：
--
作者：
Kato, Kengo
本文研究了具有一类分段线性损失函数的Pi正则化问题的计算问题。计算分段线性损失的l（1）正则化路径的问题可以形式化为参数线性规划问题。针对此类问题，我们提出了一种参数单纯形算法的有效实现方法。我们还进行了一个模拟研究，调查的行为的“断点”的正则化路径的数量时，观察的数量和解释变量的数量变化。我们的方法也适用于计算的正则化路径的分段线性损失和blockwise l（无穷大）的罚款。这篇文章在网上有补充材料。
This article is concerned with the computational aspect of Pi regularization problems with a certain class of piecewise linear loss functions. The problem of computing the l(1) regularization path for a piecewise linear loss can be formalized as a parametric linear programming problem. We propose an efficient implementation method of the parametric simplex algorithm for such a problem. We also conduct a simulation study to investigate the behavior of the number of "breakpoints" of the regularization path when both the number of observations and the number of explanatory variables vary. Our method is also applicable to the computation of the regularization path for a piecewise linear loss and the blockwise l(infinity) penalty. This article has supplementary material online.