An Adaptive Ridge Procedure for L0 Regularization.
An Adaptive Ridge Procedure for L0 Regularization.
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DOI：
10.1371/journal.pone.0148620
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发表时间：
2016
期刊：
影响因子：
3.7
通讯作者：
Nuel G
中科院分区：
文献类型：
--
作者：
Frommlet F;Nuel G
惩罚性选择标准（如AIC或BIC）是最流行的变量选择方法之一。它们的理论性质已经被深入研究并得到很好的理解，但由于L0惩罚引起的非凸优化问题，在高维数据的情况下使用它们是困难的。在本文中，我们介绍了一个自适应岭过程（AR），迭代加权岭问题的解决，其权重更新的方式，该过程收敛到选择与L0处罚。在引入AR后，在正交线性回归的特殊情况下研究了其特定的收缩性能。基于大量的模拟的非正交的情况下，以及泊松回归的AR的性能进行了研究，并与SCAD和自适应LASSO。此外，AR的最小二乘分割的上下文中的一个有效的实现。最后，本文给出了一个应用AR分析GWAS数据的示例。
Penalized selection criteria like AIC or BIC are among the most popular methods for variable selection. Their theoretical properties have been studied intensively and are well understood, but making use of them in case of high-dimensional data is difficult due to the non-convex optimization problem induced by L0 penalties. In this paper we introduce an adaptive ridge procedure (AR), where iteratively weighted ridge problems are solved whose weights are updated in such a way that the procedure converges towards selection with L0 penalties. After introducing AR its specific shrinkage properties are studied in the particular case of orthogonal linear regression. Based on extensive simulations for the non-orthogonal case as well as for Poisson regression the performance of AR is studied and compared with SCAD and adaptive LASSO. Furthermore an efficient implementation of AR in the context of least-squares segmentation is presented. The paper ends with an illustrative example of applying AR to analyze GWAS data.