We investigate the learning rate of multiple kernel leaning (MKL) with and elastic-net regularizations. The elastic-net regularization is a composition of an -regularizer for inducing the sparsity and an -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 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 and elastic-net regularizations to use; if the ground truth is smooth, the elastic-net regularization is preferred, otherwise the regularization is preferred.
View on arXiv