Regularization Strategies and Empirical Bayesian Learning for MKL

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 $\ell2$-norm MKL and Elastic-net MKL achieve comparable accuracy to uniform kernel combination. Although uniform kernel combination might be preferable from its simplicity, $\ell2$-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.