On aggregation for heavy-tailed classes
成果类型：
Article
署名作者：
Mendelson, Shahar
署名单位：
Technion Israel Institute of Technology
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-016-0720-6
发表日期：
2017
页码：
641-674
关键词：
摘要：
We introduce an alternative to the notion of 'fast rate' in Learning Theory, which coincides with the optimal error rate when the given class happens to be convex and regular in some sense. While it is well known that such a rate cannot always be attained by a learning procedure (i.e., a procedure that selects a function in the given class), we introduce an aggregation procedure that attains that rate under rather minimal assumptions-for example, that the and norms are equivalent on the linear span of the class for some , and the target random variable is square-integrable. The key components in the proof include a two-sided isomorphic estimator on distances between class members, which is based on the median-of-means; and an almost isometric lower bound of the form which holds uniformly in the class. Both results only require that the and norms are equivalent on the linear span of the class for some q > 2.