COCOLASSO FOR HIGH-DIMENSIONAL ERROR-IN-VARIABLES REGRESSION

• 成果类型: Article
• 署名作者: Datta, Abhirup; Zou, Hui
• 署名单位: Johns Hopkins University; University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/16-AOS1527
• 发表日期: 2017
• 页码: 2400-2426
• 关键词: dantzig selector; statistical estimation; oracle properties; Lasso; regularization; RECOVERY; sparsity; larger; models; noisy

摘要

Much theoretical and applied work has been devoted to high-dimensional regression with clean data. However, we often face corrupted data in many applications where missing data and measurement errors cannot be ignored. Loh and Wainwright [Ann. Statist. 40 (2012) 1637-1664] proposed a non-convex modification of the Lasso for doing high-dimensional regression with noisy and missing data. It is generally agreed that the virtues of convexity contribute fundamentally the success and popularity of the Lasso. In light of this, we propose a new method named CoCoLasso that is convex and can handle a general class of corrupted datasets. We establish the estimation error bounds of CoCoLasso and its asymptotic sign-consistent selection property. We further elucidate how the standard cross validation techniques can be misleading in presence of measurement error and develop a novel calibrated cross-validation technique by using the basic idea in CoCoLasso. The calibrated cross-validation has its own importance. We demonstrate the superior performance of our method over the nonconvex approach by simulation studies.