Learning Polynomial Functions by Feature Construction

We present a method for learning higher-order polynomial functions from examples using linear regression and feature construction. Regression is used on a set of training instances to produce a weight vector for a linear function over the feature set. If this hypothesis is imperfect, a new feature is constructed by forming the product of the two features that most effectively predict the squared error of the current hypothesis. The algorithm is then repeated. In an extension to this method, the specific pair of features to combine is selected by measuring their joint ability to predict the hypothesis' error