Complexities of convex combinations and bounding the generalization error in classification

• 成果类型: Article
• 署名作者: Koltchinskii, V; Panchenko, D
• 署名单位: University of New Mexico; Massachusetts Institute of Technology (MIT)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053605000000228
• 发表日期: 2005
• 页码: 1455-1496
• 关键词: margin distributions; Consistency; CONVERGENCE

摘要

We introduce and study several measures of complexity of functions from the convex hull of a given base class. These complexity measures take into account the sparsity of the weights of a convex combination as well as certain clustering properties of the base functions involved in it. We prove new upper confidence bounds on the generalization error of ensemble (voting) classification algorithms that utilize the new complexity measures along with the empirical distributions of classification margins, providing a better explanation of generalization performance of large margin classification methods.