Learning the kernel matrix via predictive low-rank approximations

Efficient and accurate low-rank approximations to multiple data sources are essential in the era of big data. The scaling of kernel-based learning algorithms to large datasets is limited by the O(n) complexity associated with computation and storage of the kernel matrix, which is assumed to be available in most recent multiple kernel learning algorithms. We propose a method to learn simultaneous low-rank approximations of a set of base kernels in regression tasks. We present the mklaren algorithm, which approximates multiple kernel matrices with least angle regression in the lowdimensional feature space. The idea is based on geometrical concepts and does not assume access to full kernel matrices. The algorithm achieves linear complexity in the number of data points as well as kernels, while it accounts for the correlations between kernel matrices. When explicit feature space representation is available for kernels, we use the relation between primal and dual regression weights to gain model interpretation. Our approach outperforms contemporary kernel matrix approximation approaches when learning with multiple kernels on standard regression datasets, as well as improves selection of relevant kernels in comparison to multiple kernel learning methods.