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Operator-valued reproducing kernels and their application in approximation and statistical learning.

Aachen: Shaker, 2009, 122 S. (Zugl. München, Technische Universität München, Fakultät für Mathematik, Diss., 2009) (Berichte aus der Mathematik)
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Kernel-based methods and their underlying structure of reproducing kernel Hilbert spaces (RKHS) are widely used in many areas of applied mathematics, such as spatial statistics, machine learning and approximation theory. In this thesis, we provide an overview over RKHS of vector-valued functions and their corresponding operator-valued kernels. We show the link between conditionally positive definite operator-valued kernels and reproducing kernel Pontryagin spaces. Further on, we provide a method to construct parameterized matrix-valued kernels. Moreover, we transfer concepts for qualitative estimates in approximation and statistical learning to the vector-valued setting. To be precise, we demonstrate how stability and error estimates from approximation theory lead to estimates of covering numbers used in statistical learning.
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Publikationstyp Buch: Monographie
Typ der Hochschulschrift Dissertationsschrift
Schlagwörter Vector-valued Functions; Regularization; Reproducing Kernel Hilbert Spaces; Kernel Methods; Operator-valued Kernels; Matrix-valued Kernels; Matrix-valued Radial Basis Functions; Statistical Learning Theory; Multi-task Learning Covering Number
ISBN 978-3-8322-8492-3
Quellenangaben Band: , Heft: , Seiten: 122 S. Artikelnummer: , Supplement: ,
Reihe Berichte aus der Mathematik
Verlag Shaker
Verlagsort Aachen
Hochschule Technische Universität München
Hochschulort München
Fakultät Fakultät für Mathematik