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Berschneider, G.* ; zu Castell, W.

The representer theorem for Pontryagnin spaces of vector-valued functions.

Vortrag: Curves and Surfaces 2010, 24-30 June 2010, Avignon. (2010)
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Given a positive de nite kernel , there is an associated reproducing kernel Hilbert space with reproducing kernel . The fact that the solution of certain penalized approximation problems, e.g. the smoothing spline problem, is given as a linear combination of \point evaluations" of the kernel  is commonly referred to as the representer theorem in machine learning. The talk will discuss the analog statement for a conditionally positive de nite, matrix-valued kernel, where the associated space turns out to be a reproducing kernel Pontryagin space of vector-valued functions
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Publication type Other: Lecture
Keywords reproducing kernel space, conditionally positive de nite kernel
Conference Title Curves and Surfaces 2010
Conference Date 24-30 June 2010
Conference Location Avignon