Reproducing Kernel Banach Spaces with the l1 Norm

Details Reproducing Kernel Banach Spaces with the l1 Norm Reproducing Kernel Banach Spaces with the l1 Norm

2011-01-23

arxiv.org/abs/1101.4388v3

Statistics

Machine Learning

28 pages, an extra section was added

Scientific paper

10.1016/j.acha.2012.03.009

Targeting at sparse learning, we construct Banach spaces B of functions on an input space X with the properties that (1) B possesses an l1 norm in the sense that it is isometrically isomorphic to the Banach space of integrable functions on X with respect to the counting measure; (2) point evaluations are continuous linear functionals on B and are representable through a bilinear form with a kernel function; (3) regularized learning schemes on B satisfy the linear representer theorem. Examples of kernel functions admissible for the construction of such spaces are given.

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