  Multiple kernel learning (MKL), structured sparsity, and multi-task learning
have recently received considerable attention. In this paper, we show how
different MKL algorithms can be understood as applications of either
regularization on the kernel weights or block-norm-based regularization, which
is more common in structured sparsity and multi-task learning. We show that
these two regularization strategies can be systematically mapped to each other
through a concave conjugate operation. When the kernel-weight-based regularizer
is separable into components, we can naturally consider a generative
probabilistic model behind MKL. Based on this model, we propose learning
algorithms for the kernel weights through the maximization of marginal
likelihood. We show through numerical experiments that $\ell_2$-norm MKL and
Elastic-net MKL achieve comparable accuracy to uniform kernel combination.
Although uniform kernel combination might be preferable from its simplicity,
$\ell_2$-norm MKL and Elastic-net MKL can learn the usefulness of the
information sources represented as kernels. In particular, Elastic-net MKL
achieves sparsity in the kernel weights.
