%O Special Issue "Artificial Neural Networks: Selected Papers from ICANN 2010"
%I Elseviers
%V 24
%T Can Dictionary-Based Computational Models Outperform the Best Linear Ones? 
%P 881 - 887
%R 10.1016/j.neunet.2011.05.014
%N 8
%J Neural Networks 
%A Giorgio Gnecco
%A V?ra K?rkov?
%A Marcello Sanguineti
%K Dictionary-based approximation; Linear approximation; Rates of approximation; Worst-case error; Kolmogorov width; Perceptron networks
%L eprints1751
%D 2011
%X Approximation capabilities of two types of computational models are explored: dictionary-based models (i.e., linear combinations of n -tuples of basis functions computable by units belonging to a set called ?dictionary?) and linear ones (i.e., linear combinations of n fixed basis functions). The two models are compared in terms of approximation rates, i.e., speeds of decrease of approximation errors for a growing number n of basis functions. Proofs of upper bounds on approximation rates by dictionary-based models are inspected, to show that for individual functions they do not imply estimates for dictionary-based models that do not hold also for some linear models. Instead, the possibility of getting faster approximation rates by dictionary-based models is demonstrated for worst-case errors in approximation of suitable sets of functions. For such sets, even geometric upper bounds hold.