Gnecco, Giorgio and Sanguineti, Marcello
*On a Variational Norm Tailored to Variable-Basis Approximation Schemes.*
IEEE Transactions on Information Theory, 57 (1).
pp. 549-558.
ISSN 0018-9448
(2011)

## Abstract

A variational norm associated with sets of computational units and used in function approximation, learning from data, and infinite-dimensional optimization is investigated. For sets Gk obtained by varying a vector y of parameters in a fixed-structure computational unit K(-,y) (e.g., the set of Gaussians with free centers and widths), upper and lower bounds on the GK -variation norms of functions having certain integral representations are given, in terms of the £1-norms of the weighting functions in such representations. Families of functions for which the two norms are equal are described.

Item Type: | Article |
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Identification Number: | 10.1109/TIT.2010.2090198 |

Uncontrolled Keywords: | ${cal L}_1$-norm, Approximation schemes, convex hulls, infinite-dimensional optimization, upper and lower bounds, variation with respect to a set |

Subjects: | Q Science > QA Mathematics > QA75 Electronic computers. Computer science |

Research Area: | Computer Science and Applications |

Depositing User: | Giorgio Gnecco |

Date Deposited: | 13 Sep 2013 11:34 |

Last Modified: | 16 Sep 2013 12:03 |

URI: | http://eprints.imtlucca.it/id/eprint/1719 |

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