Universal Approximation by Ridge Computational Models and Neural Networks: A Survey

Abstract

Computational models made up of linear combinations of ridge basis functions, widely used in machine learning and artificial intelligence, are considered. For such models, the literature on the so-called "universal approximation property" is surveyed. Different approaches, proof techniques, and tools are examined.

Optimization based on quasi-Monte Carlo sampling to design state estimators for non-linear systems

“…The family A corresponds to the so-called RCM [33,34], in which the one-variable 'mother function' ', often called computational unit, is composed with the inner product on R m . So, the ridge construction 'shrinks' the m-dimensional vector z into a onedimensional variable via the inner product.…”

“…Ridge computational models, called in the neural-network community perceptron networks [33,34], have been successfully applied in a variety of areas, such as timeseries forecasting, system identification, data mining, financial and business 968…”

“…Theoretical investigations have shown that RCMs can achieve surprisingly good performances (see [5,[25][26][27]30,31,33,34] and the references therein). In the following, for positive integers and j ¼ 1, .…”

“…As a fixed structure for the estimator, we choose families of functions dependent on a vector of parameters to be optimized. Among the possible choices of such functions, we rely on ridge computational models (RCMs) [33,34], which include the so-called 'perceptron neural networks' [16] and have powerful approximating properties (see, e.g. [5,[25][26][27]30,31,33,34] and the references therein).…”

A Modified Approximate Internal Model-based Neural Control for the Typical Industrial Processes

“…to the desired accuracy [16]. A Neural Network Nonlinear Autoregressive Moving Average (NARMA) model, i.e.…”