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Seminar Details

Date 7-10-2009
Time 15:15
Room/Location Sala conferenze DISI, 3 piano
Title Approximation bounds via Rademacher's complexity
Speaker Giorgio Gnecco
Affiliation DISI & DIST - University of Genova
Link http://www.disi.unige.it/index.php?eventsandseminars/seminars
Abstract The sup-norm error in approximation by variable-basis approximation schemes is estimated using a tool from Statistical Learning Theory, known as Rademacher's complexity. Such schemes, also called "approximation from a dictionary", take on the form of linear combinations of all n-tuples of computational units containing some parameters, to be optimized together with the coefficients of the linear combinations (e.g., perceptrons and radial or kernel computational units). For families of scalar-valued multivariable functions having certain integral representations, estimates of the approximation accuracy are derived in dependence of the Rademacher's complexities of the families. The estimates improve previously-available ones, expressed in terms of the Vapnik-Chervonenkis' dimension. For vector-valued functions, the simultaneous approximation of all the components is investigated and advantages over componentwise scalar approximation are discussed. The estimates are applied to variable-basis approximation schemes with radial basis functions.
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