A fast unified algorithm for solving group-lasso penalize learning problems
A fast unified algorithm for solving group-lasso penalize learning problems
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DOI：
10.1007/s11222-014-9498-5
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发表时间：
2015-11-01
影响因子：
2.2
通讯作者：
Zou, Hui
中科院分区：
文献类型：
--
作者：
Yang, Yi;Zou, Hui
本文研究了一类群体套索学习问题，其中目标函数是经验损失和群体套索惩罚之和。对于一类满足二次优化条件的损失函数，我们给出了一个统一的算法，称为群优下降（groupwise-majorization-descent，GMD），用于有效地计算相应的群套索惩罚学习问题的解路径. GMD允许一般的设计矩阵，而不需要预测是分组正交归一化。作为说明的例子，我们开发了具体的算法解决组套索惩罚最小二乘和几个组套索惩罚大间距分类。这些群套索模型已经在一个R软件包gglasso中实现，该软件包可从http://cran.r-project.org/web/packages/gglasso的综合R存档网络（CRAN）公开获得。在模拟和真实的数据上，gglasso始终优于现有的用于计算组套索的软件，该软件实现了经典的分组下降算法或Nesterov方法。
This paper concerns a class of group-lasso learning problems where the objective function is the sum of an empirical loss and the group-lasso penalty. For a class of loss function satisfying a quadratic majorization condition, we derive a unified algorithm called groupwise-majorization-descent (GMD) for efficiently computing the solution paths of the corresponding group-lasso penalized learning problem. GMD allows for general design matrices, without requiring the predictors to be group-wise orthonormal. As illustration examples, we develop concrete algorithms for solving the group-lasso penalized least squares and several group-lasso penalized large margin classifiers. These group-lasso models have been implemented in an R package gglasso publicly available from the Comprehensive R Archive Network (CRAN) at http://cran.r-project.org/web/packages/gglasso. On simulated and real data, gglasso consistently outperforms the existing software for computing the group-lasso that implements either the classical groupwise descent algorithm or Nesterov's method.