  The success of kernel-based learning methods depend on the choice of kernel.
Recently, kernel learning methods have been proposed that use data to select
the most appropriate kernel, usually by combining a set of base kernels. We
introduce a new algorithm for kernel learning that combines a {\em continuous
set of base kernels}, without the common step of discretizing the space of base
kernels. We demonstrate that our new method achieves state-of-the-art
performance across a variety of real-world datasets. Furthermore, we explicitly
demonstrate the importance of combining the right dictionary of kernels, which
is problematic for methods based on a finite set of base kernels chosen a
priori. Our method is not the first approach to work with continuously
parameterized kernels. However, we show that our method requires substantially
less computation than previous such approaches, and so is more amenable to
multiple dimensional parameterizations of base kernels, which we demonstrate.
