SPARSITY IN MULTIPLE KERNEL LEARNING

• 成果类型: Article
• 署名作者: Koltchinskii, Vladimir; Yuan, Ming
• 署名单位: University System of Georgia; Georgia Institute of Technology; University System of Georgia; Georgia Institute of Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/10-AOS825
• 发表日期: 2010
• 页码: 3660-3695
• 关键词: dantzig selector; Lasso

摘要

The problem of multiple kernel learning based on penalized empirical risk minimization is discussed. The complexity penalty is determined jointly by the empirical L-2 norms and the reproducing kernel Hilbert space (RKHS) norms induced by the kernels with a data-driven choice of regularization parameters. The main focus is on the case when the total number of kernels is large, but only a relatively small number of them is needed to represent the target function, so that the problem is sparse. The goal is to establish oracle inequalities for the excess risk of the resulting prediction rule showing that the method is adaptive both to the unknown design distribution and to the sparsity of the problem.