Regression Tree Analysis Using TARGET

Abstract

Regression trees are a popular alternative to classical regression methods. A number of approaches exist for constructing regression trees. Most of these techniques, including CART, are sequential in nature and locally optimal at each node split, so the final tree solution found may not be the best tree overall. In addition, small changes in the training data often lead to large changes in the final result due to the relative instability of these greedy tree-growing algorithms. Ensemble techniques, such as random forests, attempt to take advantage of this instability by growing a forest of trees from the data and averaging their predictions. The predictive performance is improved, but the simplicity of a single-tree solution is lost.

In earlier work, we introduced the Tree Analysis with Randomly Generated and Evolved Trees (TARGET) method for constructing classification trees via genetic algorithms. In this article, we extend the TARGET approach to regression trees. Simulated data and real world data are used to illustrate the TARGET process and compare its performance to CART, Bayesian CART, and random forests. The empirical results indicate that TARGET regression trees have better predictive performance than recursive partitioning methods, such as CART, and single-tree stochastic search methods, such as Bayesian CART. The predictive performance of TARGET is slightly worse than that of ensemble methods, such as random forests, but the TARGET solutions are far more interpretable.

Key Words:

• Bayesian CART
• CART
• Data mining
• Genetic algorithm
• Prediction
• Random forests