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

03/02/2011

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by   Taiji Suzuki, et al.

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We investigate the learning rate of multiple kernel leaning (MKL) with elastic-net regularization, which consists of an ℓ_1-regularizer for inducing the sparsity and an ℓ_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 ℓ_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.