کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6868683 | 1440032 | 2018 | 17 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A Forward and Backward Stagewise algorithm for nonconvex loss functions with adaptive Lasso
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موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
نظریه محاسباتی و ریاضیات
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: A Forward and Backward Stagewise algorithm for nonconvex loss functions with adaptive Lasso A Forward and Backward Stagewise algorithm for nonconvex loss functions with adaptive Lasso](/preview/png/6868683.png)
چکیده انگلیسی
Penalization is a popular tool for multi- and high-dimensional data. Most of the existing computational algorithms have been developed for convex loss functions. Nonconvex loss functions can sometimes generate more robust results and have important applications. Motivated by the BLasso algorithm, this study develops the Forward and Backward Stagewise (Fabs) algorithm for nonconvex loss functions with the adaptive Lasso (aLasso) penalty. It is shown that each point along the Fabs paths is a δ-approximate solution to the aLasso problem and the Fabs paths converge to the stationary points of the aLasso problem when δ goes to zero, given that the loss function has second-order derivatives bounded from above. This study exemplifies the Fabs with an application to the penalized smooth partial rank (SPR) estimation, for which there is still a lack of effective algorithm. Extensive numerical studies are conducted to demonstrate the benefit of penalized SPR estimation using Fabs, especially under high-dimensional settings. Application to the smoothed 0-1 loss in binary classification is introduced to demonstrate its capability to work with other differentiable nonconvex loss function.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computational Statistics & Data Analysis - Volume 124, August 2018, Pages 235-251
Journal: Computational Statistics & Data Analysis - Volume 124, August 2018, Pages 235-251
نویسندگان
Xingjie Shi, Yuan Huang, Jian Huang, Shuangge Ma,