Derivative reproducing properties for kernel methods in learning theory |
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Authors: | Ding-Xuan Zhou |
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Affiliation: | aDepartment of Mathematics, City University of Hong Kong, Kowloon, Hong Kong, China |
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Abstract: | The regularity of functions from reproducing kernel Hilbert spaces (RKHSs) is studied in the setting of learning theory. We provide a reproducing property for partial derivatives up to order s when the Mercer kernel is C2s. For such a kernel on a general domain we show that the RKHS can be embedded into the function space Cs. These observations yield a representer theorem for regularized learning algorithms involving data for function values and gradients. Examples of Hermite learning and semi-supervised learning penalized by gradients on data are considered. |
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Keywords: | Learning theory Reproducing kernel Hilbert spaces Derivative reproducing Representer theorem Hermite learning and semi-supervised learning |
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