Genetic Multivariate Polynomials: An Alternative Tool to Neural Networks

摘要

One of the basic problems of applied mathematics is to find a synthetic expression (model) which captures the essence of a system given a (necessarily) finite sample which reflects selected characteristics. When the model considers several independent variables its mathematical treatment may become burdensome or even downright impossible from a practical standpoint. This regression problem has been tackled with success using neural networks (NN). However, the "black box" characteristic of such models is frequently cited as a major drawback. We show that it is possible to find a polynomial model for an arbitrary set of data. From selected practical cases we argue that, despite the restrictions of a polynomial basis, our Genetic Multivariate Polynomials (GMP) compete with the NN approach without the mentioned limitation. We show how to treat constrained functions as unconstrained ones using GMPs.