Adaptive regularization using the entire solution surface

• 成果类型: Article
• 署名作者: Wu, S.; Shen, X.; Geyer, C. J.
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asp038
• 发表日期: 2009
• 页码: 513527
• 关键词: Support vector machines; variable selection; REGRESSION SHRINKAGE; path

摘要

Several sparseness penalties have been suggested for delivery of good predictive performance in automatic variable selection within the framework of regularization. All assume that the true model is sparse. We propose a penalty, a convex combination of the L-1- and L-infinity-norms, that adapts to a variety of situations including sparseness and nonsparseness, grouping and nongrouping. The proposed penalty performs grouping and adaptive regularization. In addition, we introduce a novel homotopy algorithm utilizing subgradients for developing regularization solution surfaces involving multiple regularizers. This permits efficient computation and adaptive tuning. Numerical experiments are conducted using simulation. In simulated and real examples, the proposed penalty compares well against popular alternatives.