This paper presents an approach to automated discovery of high-order multivariate polynomials by inductive Genetic Programming (iGP). Evolutionary search is used for learning polynomials represented as non-linear multivariate trees. Optimal search performance is pursued with balancing the statistical bias and the variance of iGP. We reduce the bias by extending the set of basis polynomials for better agreement with the examples. Possible overfitting due to the reduced bias is conteracted by a variance component, implemented as a regularizing factor of the error in an MDL fitness function. Experimental results demonstrate that regularized iGP discovers accurate, parsimonious, and predictive polynomials when trained on practical data mining tasks.
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