Boosting in the Presence of Outliers: Adaptive Classification With Nonconvex Loss Functions

• 成果类型: Article
• 署名作者: Li, Alexander Hanbo; Bradic, Jelena
• 署名单位: University of California System; University of California San Diego
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2016.1273116
• 发表日期: 2018
• 页码: 660-674
• 关键词: logistic-regression; breakdown points; robust; Consistency; adaboost; error

摘要

This article examines the role and the efficiency of nonconvex loss functions for binary classification problems. In particular, we investigate how to design adaptive and effective boosting algorithms that are robust to the presence of outliers in the data or to the presence of errors in the observed data labels. We demonstrate that nonconvex losses play an important role for prediction accuracy because of the diminishing gradient propertiesthe ability of the losses to efficiently adapt to the outlying data. We propose a new boosting framework called ArchBoost that uses diminishing gradient property directly and leads to boosting algorithms that are provably robust. Along with the ArchBoost framework, a family of nonconvex losses is proposed, which leads to the new robust boosting algorithms, named adaptive robust boosting (ARB). Furthermore, we develop a new breakdown point analysis and a new influence function analysis that demonstrate gains in robustness. Moreover, based only on local curvatures, we establish statistical and optimization properties of the proposed ArchBoost algorithms with highly nonconvex losses. Extensive numerical and real data examples illustrate theoretical properties and reveal advantages over the existing boosting methods when data are perturbed by an adversary or otherwise.