  In this paper, we study the problem of sparse multiple kernel learning (MKL),
where the goal is to efficiently learn a combination of a fixed small number of
kernels from a large pool that could lead to a kernel classifier with a small
prediction error. We develop an efficient algorithm based on the greedy
coordinate descent algorithm, that is able to achieve a geometric convergence
rate under appropriate conditions. The convergence rate is achieved by
measuring the size of functional gradients by an empirical $\ell_2$ norm that
depends on the empirical data distribution. This is in contrast to previous
algorithms that use a functional norm to measure the size of gradients, which
is independent from the data samples. We also establish a generalization error
bound of the learned sparse kernel classifier using the technique of local
Rademacher complexity.
