Learning without concentration for general loss functions

• 成果类型: Article
• 署名作者: Mendelson, Shahar
• 署名单位: Technion Israel Institute of Technology; Australian National University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-017-0784-y
• 发表日期: 2018
• 页码: 459-502
• 关键词: rates

摘要

We study the performance of empirical risk minimization in prediction and estimation problems that are carried out in a convex class and relative to a sufficiently smooth convex loss function. The framework is based on the small-ball method and thus is suited for heavy-tailed problems. Moreover, among its outcomes is that a well-chosen loss, calibrated to fit the noise level of the problem, negates some of the ill-effects of outliers and boosts the confidence level-leading to a gaussian like behaviour even when the target random variable is heavy-tailed.