Efficient Global Approximation of Generalized Nonlinear l1-Regularized Solution Paths and Its Applications
Efficient Global Approximation of Generalized Nonlinear l1-Regularized Solution Paths and Its Applications
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DOI：
10.1198/jasa.2009.tm08287
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发表时间：
2009-12-01
影响因子：
3.7
通讯作者：
Zou, Hui
中科院分区：
文献类型：
--
作者：
Yuan, Ming;Zou, Hui
我们考虑一般l（1）-正则化的非线性解路径的有效构造。不同于现有的方法，逐步建立的解决方案的路径，通过局部线性逼近和重新校准的组合，我们提出了一个有效的整体逼近的整体解决方案的路径。与损失函数近似的二次样条，我们表明，解决方案的路径可以使用广义Lars算法计算。所提出的方法避免了高维数值优化，从而提供更快，更稳定的计算。该方法也可以很容易地扩展到更一般的正则化框架。我们用几个例子来说明这种灵活性，包括弹性网络的推广和一种有效利用核逻辑回归中所谓的“支持向量”的新方法。
We consider efficient construction of nonlinear solution paths for general l(1)-regularization. Unlike the existing methods that incrementally build the solution path through a combination of local linear approximation and recalibration, we propose an efficient global approximation to the whole solution path. With the loss function approximated by a quadratic spline, we show that the solution path can be computed using a generalized Lars algorithm. The proposed methodology avoids high-dimensional numerical optimization and thus provides faster and more stable computation. The methodology also can be easily extended to more general regularization framework. We illustrate such flexibility with several examples, including a generalization of the elastic net and a new method that effectively exploits the so-called "support vectors" in kernel logistic regression.