Fast Convergence Rate of Multiple Kernel Learning with Elastic-net Regularization

Taiji Suzuki; Ryota Tomioka; Masashi Sugiyama

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arXiv · 1103.0431

Fast Convergence Rate of Multiple Kernel Learning with Elastic-net Regularization

Taiji Suzuki·Ryota Tomioka·Masashi Sugiyama

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Abstract

We investigate the learning rate of multiple kernel leaning (MKL) with elastic-net regularization, which consists 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 non-zero components of the ground truth is relatively small, and prove that elastic-net MKL achieves the minimax learning rate on the $\ell_2$-mixed-norm ball. Our bound is sharper than the convergence rates ever shown, and has a property that the smoother the truth is, the faster the convergence rate is.

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BibTeX RIS

Taiji Suzuki, Ryota Tomioka, Masashi Sugiyama. 2011-07-13. Fast Convergence Rate of Multiple Kernel Learning with Elastic-net Regularization. https://arxiv.org/abs/1103.0431

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