Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 57, Issue 1, Pages 549-558Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2010.2090198
Keywords
Approximation schemes; convex hulls; infinite-dimensional optimization; upper and lower bounds; variation with respect to a set; L-1-norm
Funding
- Italian Ministry for University and Research
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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 G(K) 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 G(K)-variation norms of functions having certain integral representations are given, in terms of the L-1-norms of the weighting functions in such representations. Families of functions for which the two norms are equal are described.
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