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Improved Learning Rates of a Functional Lasso-type SVM with Sparse Multi-Kernel Representation
shaogao lv · Junhui Wang · Jiankun Liu · Yong Liu

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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.

Author Information

shaogao lv (Nanjing Audit University)
Junhui Wang (City University of Hong Kong)
Jiankun Liu (Institute of Information Engineering, CAS)
Yong Liu (Renmin University of China)

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