Sparsity in multiple kernel learning

Abstract

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.

Published in at http://dx.doi.org/10.1214/10-AOS825 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (5)

• Consistency of the group Lasso and multiple kernel learning
• Component selection and smoothing in multivariate nonparametric regression
• Statistical performance of support vector machines
• The Dantzig selector and sparsity oracle inequalities
• Sparse recovery in convex hulls via entropy penalization

Cited by in corpus (12)

• Nonparametric sparsity and regularization
• Group Lasso for high dimensional sparse quantile regression models
• The Local Rademacher Complexity of Lp-Norm Multiple Kernel Learning
• Nonparametric Basis Pursuit via Sparse Kernel-based Learning
• A Simple Algorithm for Semi-supervised Learning with Improved Generalization Error Bound
• Learning Heteroscedastic Models by Convex Programming under Group Sparsity
• Sparse Additive Functional and Kernel CCA
• Scalable Matrix-valued Kernel Learning for High-dimensional Nonlinear Multivariate Regression and Granger Causality
• Two-step estimation of high dimensional additive models
• Fast Convergence Rate of Multiple Kernel Learning with Elastic-net Regularization
• Sparse Multiple Kernel Learning with Geometric Convergence Rate
• Fast Learning Rate of lp-MKL and its Minimax Optimality