TY  - JOUR
PB  - Hikari Ltd
JF  - Applied Mathematical Sciences
IS  - 4
SN  - 1312-885X
N2  - Approximation properties of some connectionistic models, commonly used to construct approximation schemes for optimization problems with multivariable functions as admissible solutions, are investigated. Such models are made up of linear combinations of computational units
with adjustable parameters. The relationship between model complexity (number of computational units) and approximation error is investigated using tools from Statistical Learning Theory, such as Talagrand's
inequality, fat-shattering dimension, and Rademacher's complexity. For some families of multivariable functions, estimates of the approximation accuracy of models with certain computational units are derived in dependence of the Rademacher's complexities of the families. The
estimates improve previously-available ones, which were expressed in terms of V C dimension and derived by exploiting union-bound techniques. The results are applied to approximation schemes with certain radial-basis-functions as computational units, for which it is shown that
the estimates do not exhibit the curse of dimensionality with respect to the number of variables.
ID  - eprints1749
EP  - 176
VL  - 2
A1  - Gnecco, Giorgio
A1  - Sanguineti, Marcello
UR  - http://www.m-hikari.com/ams/ams-password-2008/ams-password1-4-2008/
Y1  - 2008///
KW  - approximation error
KW  -  model complexity
KW  -  curse of dimensionality
KW  -  Rademacher's complexity
KW  -  Talagrand's inequality
KW  -  union bounds
KW  -  VC dimension.
AV  - public
TI  - Approximation Error Bounds via Rademacher's Complexity 
SP  - 153
ER  -