A coordinate-wise optimization algorithm for the Fused Lasso
A coordinate-wise optimization algorithm for the Fused Lasso
复制标题
Fused Lasso 的坐标优化算法
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
M. Schumacher
中科院分区：
文献类型：
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作者：
Holger Hofling;H. Binder;M. Schumacher
l1惩罚回归方法，如Lasso (Tibshirani 1996)，既实现了变量选择，又实现了收缩，已经非常流行。该方法的扩展是融合套索（Tibshirani and Wang 2007），它允许将外部信息合并到模型中。本文提出了一种基于坐标优化的快速求解融合套索的新算法。这类算法最近被非常成功地应用于快速解决l1惩罚问题（Friedman et al. 2007）。由于直接的坐标智能过程一般不会收敛到全局最优，我们以两种方式对其进行调整，使用最大流量算法和基于Huber惩罚的损失函数近似。在仿真研究中，我们评估了这些算法的速度，并将它们与其他标准方法进行了比较。由于基于huber惩罚的方法只是近似的，我们还对其精度进行了评价。除此之外，我们还将融合套索扩展到逻辑以及比例风险模型，并允许更灵活的惩罚结构。
L1-penalized regression methods such as the Lasso (Tibshirani 1996) that achieve both variable selection and shrinkage have been very popular. An extension of this method is the Fused Lasso (Tibshirani and Wang 2007), which allows for the incorporation of external information into the model. In this article, we develop new and fast algorithms for solving the Fused Lasso which are based on coordinate-wise optimization. This class of algorithms has recently been applied very successfully to solve L1-penalized problems very quickly (Friedman et al. 2007). As a straightforward coordinate-wise procedure does not converge to the global optimum in general, we adapt it in two ways, using maximum-flow algorithms and a Huber penalty based approximation to the loss function. In a simulation study, we evaluate the speed of these algorithms and compare them to other standard methods. As the Huber-penalty based method is only approximate, we also evaluate its accuracy. Apart from this, we also extend the Fused Lasso to logistic as well as proportional hazards models and allow for a more flexible penalty structure.