[Banach] Abstract of a paper by Guohui Song, Haizhang Zhang, Fred J. Hickernell

This is an announcement for the paper "Reproducing kernel Banach spaces with the l1 norm" by Guohui Song, Haizhang Zhang, Fred J. Hickernell.

Abstract: 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.

Archive classification: stat.ML cs.LG math.FA

Submitted from: zhhaizh2@sysu.edu.cn

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1101.4388

or

http://arXiv.org/abs/1101.4388