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Register a new userFast learning rate of multiple kernel learning: Trade-off between sparsity and smoothness
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Taiji Suzuki
Publication date
2012
fields
Mathematical Statistics
and research's language is
English
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We investigate the learning rate of multiple kernel learning (MKL) with $ell_1$ and elastic-net regularizations. The elastic-net regularization is a composition of an $ell_1$-regularizer for inducing the sparsity and an $ell_2$-regularizer for controlling the smoothness. We focus on a sparse setting where the total number of kernels is large, but the number of nonzero components of the ground truth is relatively small, and show sharper convergence rates than the learning rates have ever shown for both $ell_1$ and elastic-net regularizations. Our analysis reveals some relations between the choice of a regularization function and the performance. If the ground truth is smooth, we show a faster convergence rate for the elastic-net regularization with less conditions than $ell_1$-regularization; otherwise, a faster convergence rate for the $ell_1$-regularization is shown.
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We empirically investigate the best trade-off between sparse and uniformly-weighted multiple kernel learning (MKL) using the elastic-net regularization on real and simulated datasets. We find that the best trade-off parameter depends not only on the sparsity of the true kernel-weight spectrum but also on the linear dependence among kernels and the number of samples.
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