Non Linear Approximations using Multi-layered Perceptions and Polynomial Regressions

Many ideas in statistics can be expressed in neural network notations. They include regression models from simple linear regression to projection pursuit regression, nonparametric regression, generalized additive models and others. In this study, we simulate a multi-layered perception with single hidden layer using error-backpropagation algorithm and compare the result with polynomial regression using the similar number of variables over five different non-linear functions which are all scaled so that the standard deviation is one for a large regular grid with 2500 points on [0,1]. The empirical results obtained shows that the polynomial regression models perform better than the multi-layered perceptrons except for complicated interaction functions. 2000 Mathematics Subject Classification: 62J02, Secondary 68T05