Trees with Soft Nodes: A New Approach to the Construction of Prediction Trees from Data

A prediction tree is a structure of the type illustrated in Figure 14.1. The tree is shown “upside down,” with the root at the top and the branches pointing downwards to the leaves. The graph shows how a prediction is made about a dependent variable (the name of a color, in the case of the figure), given the values of certain independent variables called predictors (the z’s). The prediction may take the form of a classification: if z1 < 4.8, then the observation is green; or of a probability distribution: if z1 < 4.8, then the observation is green with probability 0.60, black with probability 0.4, and red with probability 0. The figure also shows that each node of the tree induces a partition of the predictor space, hence the name of “recursive partition” often used to denote algorithms of tree construction from data.