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Fast Learning Rate of Multiple Kernel Learning: Trade-Off between Sparsity and Smoothness

2 March 2012
Taiji Suzuki
Masashi Sugiyama
ArXiv (abs)PDFHTML
Abstract

We investigate the learning rate of multiple kernel leaning (MKL) with ℓ1\ell_1ℓ1​ and elastic-net regularizations. The elastic-net regularization is a composition of an ℓ1\ell_1ℓ1​-regularizer for inducing the sparsity and an ℓ2\ell_2ℓ2​-regularizer for controlling the smoothness. We focus on a sparse setting where the total number of kernels is large but the number of non-zero components of the ground truth is relatively small, and show sharper convergence rates than the learning rates ever shown for both ℓ1\ell_1ℓ1​ and elastic-net regularizations. Our analysis shows there appears a trade-off between the sparsity and the smoothness when it comes to selecting which of ℓ1\ell_1ℓ1​ and elastic-net regularizations to use; if the ground truth is smooth, the elastic-net regularization is preferred, otherwise the ℓ1\ell_1ℓ1​ regularization is preferred.

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