Non local Radial Basis Functions for Forecasting and Density Estimation

AhtractThis paper discusses the rationale for employing alternative basis functions to the ubiquitous Gaussian in Radial Basis Function networks. In particular we concentrate upon employing unbounded basis functions (though the network as a whole remains bounded), and non positive definite basis functions. The use of unbounded and nonpositive basis functions, though counterintuitive in application domains such as classification and time series forecasting, have a good theoretical motivation from the domains of functional interpolation and kernel based density estimation. The use of non Gaussian Radial Basis Function networks is demonstrated on real world data.