TY  - JOUR
N2  - 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. 
SN  - 0893-6080
UR  - http://www.sciencedirect.com/science/article/pii/S0893608011001560
TI  - Can Dictionary-Based Computational Models Outperform the Best Linear Ones? 
AV  - none
KW  - Dictionary-based approximation; Linear approximation; Rates of approximation; Worst-case error; Kolmogorov width; Perceptron networks
EP  -  887
N1  - Special Issue "Artificial Neural Networks: Selected Papers from ICANN 2010"
ID  - eprints1751
SP  - 881 
A1  - Gnecco, Giorgio
A1  - K?rková, V?ra
A1  - Sanguineti, Marcello
PB  - Elseviers
IS  - 8
JF  - Neural Networks 
Y1  - 2011///
VL  - 24
ER  -