基于迭代光滑L_(1/2)算法的变量选择

Iterative smooth L_(1/2) algorithm for variable selection

变量选择是统计学中重要的问题之一,而利用正则化方法来进行变量选择是近年来研究的热点.采用一种迭代光滑L_(1/2)算法,通过增加参数稀疏化阈值条件,使其中绝对值较小的回归参数稀疏为0,从而实现变量选择的功能.将该算法与Lasso(least absolute shrinkage and selection operator),自适应Lasso以及L_(1/2)正则化方法进行比较,数值模拟结果表明该算法同样具有良好的变量选择和预测能力,最后将该算法应用到实际的前列腺数据分析.

Variable selection is one of the most important problems in statistics, and regularization method for variable selection has attracted a great attention in recent years. In this paper, an iterative smooth L1/2 algorithm is proposed, which sets the small regression parameters in magnitude to zero by a given threshold value for variable selection. A series of numerical simulations are conducted for comparing the iterative smooth L1/~ algorithm with Lasso （least absolute shrinkage and selection operator）, adaptive Lasso, and L1/2 regularization. Numerical results show that the iterative smooth L1/2 algorithm also has a good ability for variable selection and prediction. Finally, the proposed algorithm is applied to the real prostate cancer data analysis.