Department of Communications, Computer, and System Sciences (DIST), University of Genoa, Via Opera Pia 13, 16145 Genova, Italy.
Neural Netw. 2011 Oct;24(8):881-7. doi: 10.1016/j.neunet.2011.05.014. Epub 2011 Jun 12.
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.
基于字典的模型（即，由属于称为“字典”的集合的单元可计算的 n 元组的线性组合）和线性模型（即，n 个固定基函数的线性组合）。根据逼近率（即，随着基函数数量 n 的增加，逼近误差的减小速度）对这两种模型进行了比较。检查了基于字典的模型逼近率的上界证明，以表明对于个别函数，它们并不意味着对于某些线性模型不成立的基于字典的模型的估计。相反，对于合适的函数集的逼近中的最坏情况误差，证明了基于字典的模型可以获得更快的逼近率的可能性。对于这样的集合，甚至可以保持几何上的上界。
