This paper presents k-NN as an approximator for time series prediction problems. The main advantage of this approximator is its simplicity. Despite the simplicity, k-NN can be used to perform input selection for nonlinear models and it also provides accurate approximations. Three model structure selection methods are presented: Leave-one-out, Bootstrap and Bootstrap 632. We will show that both ...

This paper describes an on-line fault detection scheme for a class of nonlinear dynamic systems with modelling uncertainty and inaccessible states. Only the inputs and outputs of the system can be measured. The faults are assumed to be functions of the state, instead of the output, and the input of the system. A nonlinear on-line approximator using dynamic recurrent neural network (DRNN) is uti...

We describe generalizations of the universal approximation theorem for neural networks to maps invariant or equivariant with respect linear representations groups. Our goal is establish network-like computational models that are both invariant/equivariant and provably complete in sense their ability approximate any continuous map. contribution three-fold. First, general case compact groups we p...

A time series is a realization or sample function from a certain stochastic process. The main goals of the analysis of time series are forecasting, modeling and characterizing. Conventional time series models i.e. autoregressive (AR), moving average (MA), hybrid AR and MA (ARMA) models, assume that the time series is stationary. The other methods to model time series are soft computing techniqu...

Whatever non-linear universal approximator, easy and fast to tune, robust enough and inherently parallel is of great interest for adaptive control as a additional way of identifying and controlling non-linear processes. Among them, fuzzy models present a singular Janus-faced: On one hand, they are knowledge-based software environments constructed from a collection of linguistic IF-THEN rules, a...

We present a method of training a differentiable function approximator for a regression task using negative examples. We effect this training using negative learning rates. We also show how this method can be used to perform direct policy learning in a reinforcement learning setting. 1 Regression and Learning Rates The goal of regression analyses is to find a regression function, a function tha...

The role of width of Gaussians in two types of computational models is investigated: Gaussian radial-basis-functions (RBFs) where both widths and centers vary and Gaussian kernel networks which have fixed widths but varying centers. The effect of width on functional equivalence, universal approximation property, and form of norms in reproducing kernel Hilbert spaces (RKHS) is explored. It is pr...

For a fast evaluation of fuzzy rule based systems (FRBS's) some special fuzzy hardware is available, but in most of the realized applications only standard hardware or specific non fuzzy ASICs are used. In this paper we discuss some of the reasons of this gap and give hints for a fast realization of FRBS's especially on digital standard processors. For the realiza tion a fast algorithm with an ...

Let X be a space and F a family of 0, 1-valued functions on X. Vapnik and Chervonenkis showed that if F is “simple” (finite VC dimension), then for every probability measure μ on X and ε > 0 there is a finite set S such that for all f ∈ F , ∑ x∈S f(x)/|S| = [ ∫ f(x)dμ(x)]± ε. Think of S as a “universal ε-approximator” for integration in F . S can actually be obtained w.h.p. just by sampling a f...

Recently, various experiments to apply reinforcement learning method to the self-learning intelligent control of continuous dynamic system have been reported in the machine learning related research community. The reports have produced mixed results of some successes and some failures, and show that the success of reinforcement learning method in application to the intelligent control of contin...