Inducing Polynomial Equations for Regression

Regression methods aim at inducing models of numeric data. While most state-of-the-art machine learning methods for regression focus on inducing piecewise regression models (regression and model trees), we investigate the predictive performance of regression models based on polynomial equations. We present Ciper, an efficient method for inducing polynomial equations and empirically evaluate its predictive performance on standard regression tasks. The evaluation shows that polynomials compare favorably to linear and piecewise regression models, induced by standard regression methods, in terms of degree of fit and complexity. The bias-variance decomposition of predictive error shows that Ciper has lower variance than methods for inducing regression trees.