标题： 多核学习中的稀疏性 显示英文标题

标题： Sparsity in multiple kernel learning

摘要： 基于惩罚经验风险最小化的多核学习问题被讨论。 复杂度惩罚由经验$L_2$范数和由核诱导的再生核希尔伯特空间（RKHS）范数共同确定，正则化参数是通过数据驱动选择的。 主要关注当核的总数较大，但只需要相对较少的核来表示目标函数的情况，因此问题具有稀疏性。 目标是建立所得预测规则的额外风险的 oracle 不等式，表明该方法既能适应未知的设计分布，又能适应问题的稀疏性。 显示英文摘要

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.