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The optimal solution of multi-kernel regularization learning. (English) Zbl 1278.68111

Multi-kernel regularization schemes provide flexibility and better learning ability in some applications. They are also crucial in the problem of learning the kernel. It was shown by Y. Ying and D.-X. Zhou [J. Mach. Learn. Res. 8, 249–276 (2007; Zbl 1222.68339)] that the union of the unit balls of reproducing kernel Hilbert spaces generated by Gaussian kernels with flexible variances is learnable. The optimization problem when the variance runs over a compact set was also discussed. In this paper the authors discuss the optimization problem when the variance runs over the set of positive numbers (which is not compact). They present some sufficient conditions for the existence of an optimal solution for the least squares regularized regression associated with Gaussians with flexible variances.

MSC:

68Q32 Computational learning theory
68T05 Learning and adaptive systems in artificial intelligence
62J02 General nonlinear regression

Citations:

Zbl 1222.68339
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References:

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