Seminar Details
Date 
7102009 
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 supnorm error in approximation by variablebasis 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 ntuples 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 scalarvalued 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 previouslyavailable ones, expressed in terms of the VapnikChervonenkis' dimension. For vectorvalued functions, the simultaneous approximation of all the components is investigated and advantages over componentwise scalar approximation are discussed. The estimates are applied to variablebasis approximation schemes with radial basis functions. 


