Learning the kernel via convex optimization

The performance of a kernel-based learning algorithm depends very much on the choice of the kernel. Recently, much attention has been paid to the problem of learning the kernel itself from given training examples. The main emphasis has been on formulating the problem as a tractable convex optimization problem. Only for a few very special cases such as support vector machines are explicit convex formulations known. In this paper, we show that, in a wide variety of kernel-based learning algorithms, the kernel learning problem can be formulated as a convex optimization problem which interior-point methods can solve globally and efficiently. The kernel learning method is illustrated with a regression problem that arises in petroleum engineering.