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Learning the kernel function via regularization. (English) Zbl 1222.68265
Summary: We study the problem of finding an optimal kernel from a prescribed convex set of kernels \(K\) for learning a real-valued function by regularization. We establish for a wide variety of regularization functionals that this leads to a convex optimization problem and, for square loss regularization, we characterize the solution of this problem. We show that, although \(K\) may be an uncountable set, the optimal kernel is always obtained as a convex combination of at most \(m+2\) basic kernels, where \(m\) is the number of data examples. In particular, our results apply to learning the optimal radial kernel or the optimal dot product kernel.

MSC:
68T05 Learning and adaptive systems in artificial intelligence
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