SMILES and FFANNS: similarity least squares and feed forward artificial neural networks

Summary form only given, as follows. Similarity least squares (SMILES) is an alternative to high-degree polynomial regression models for the analysis of nonlinear data. Local or nonparametric regression techniques prevalent in the statistics literature are special cases of the more general SMILES estimator. The method is developed as a series of statistical projections. The results are used to construct feedforward artificial neural nets (FFANNs) and prove their capability to represent vector mapping functions between two sets of vectors. A key result is how to achieve stable predictions (generalizations) for highly nonlinear data. The computing effort to train these networks scales as a polynomial in the size of the data set.<>