Contrast trees and distribution boosting.

Abstract

A method for decision tree induction is presented. Given a set of predictor variables [Formula: see text] and two outcome variables y and z associated with each x, the goal is to identify those values of x for which the respective distributions of [Formula: see text] and [Formula: see text], or selected properties of those distributions such as means or quantiles, are most different. Contrast trees provide a lack-of-fit measure for statistical models of such statistics, or for the complete conditional distribution [Formula: see text], as a function of x. They are easily interpreted and can be used as diagnostic tools to reveal and then understand the inaccuracies of models produced by any learning method. A corresponding contrast-boosting strategy is described for remedying any uncovered errors, thereby producing potentially more accurate predictions. This leads to a distribution-boosting strategy for directly estimating the full conditional distribution of y at each x under no assumptions concerning its shape, form, or parametric representation.