The group lasso for logistic regression
The group lasso for logistic regression
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DOI：
10.1111/j.1467-9868.2007.00627.x
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发表时间：
2008-01-01
影响因子：
5.8
通讯作者：
Buhlmann, Peter
中科院分区：
文献类型：
--
作者：
Meier, Lukas;van de Geer, Sara A.;Buhlmann, Peter
group lasso是lasso的扩展，用于在线性回归模型中对（预定义的）变量组进行变量选择。该估计具有在分组正交重参数化下不变的吸引人的性质。将群套索推广到Logistic回归模型，给出了一个有效的算法，该算法特别适用于高维问题，也可应用于广义线性模型求解相应的凸优化问题. Logistic回归的组Lasso估计被证明是统计上一致的，即使预测因子的数量远大于样本大小，但具有稀疏的真实底层结构。我们进一步使用了两阶段的过程，其目标是比组套索更稀疏的模型，从而提高了某些情况下的预测性能。此外，由于两阶段的性质，估计可以构建为分层的。该方法被用于模拟和真实的数据集的剪接位点检测的DNA序列。
The group lasso is an extension of the lasso to do variable selection on (predefined) groups of variables in linear regression models. The estimates have the attractive property of being invariant under groupwise orthogonal reparameterizations. We extend the group lasso to logistic regression models and present an efficient algorithm, that is especially suitable for high dimensional problems, which can also be applied to generalized linear models to solve the corresponding convex optimization problem. The group lasso estimator for logistic regression is shown to be statistically consistent even if the number of predictors is much larger than sample size but with sparse true underlying structure. We further use a two-stage procedure which aims for sparser models than the group lasso, leading to improved prediction performance for some cases. Moreover, owing to the two-stage nature, the estimates can be constructed to be hierarchical. The methods are used on simulated and real data sets about splice site detection in DNA sequences.