Improved Learning Rates of a Functional Lasso-type SVM with Sparse Multi-Kernel Representation
Datasets and Benchmarks Track
Authors: shaogao lv, Junhui Wang, Jiankun Liu, Yong Liu

In this paper, we  provide  theoretical results of estimation bounds and excess risk upper bounds for  support vector machine (SVM) with sparse multi-kernel representation. These convergence rates for multi-kernel SVM are established by analyzing a Lasso-type regularized learning scheme within composite multi-kernel spaces. It is shown that the oracle rates of convergence of classifiers depend on the complexity of  multi-kernels, the sparsity, a Bernstein condition and the sample size, which significantly improves on previous results even for the additive or linear cases. In summary, this paper not only provides unified theoretical results for multi-kernel SVMs, but also enriches the literature on high-dimensional nonparametric classification.