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The talk discusses the problem of learning functions whose range is in a Hilbert space Y. In particular, we characterize reproducing kernel Hilbert spaces of functions whose values lie in Y. In this context, we derive the form of the minimal norm interpolant to a finite set of data and apply it to study some regularization functionals which are important in learning theory. More precisely, we consider specific examples of such functionals corresponding to multiple--output regularization networks and support vector machines, both for regression and classification. Finally, we discuss some numerical simulations which illustrate some of the advantages of learning within the above function spaces.
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