Feature Ranking for Multi-target Regression with Tree Ensemble Methods

In this work, we address the task of feature ranking for multi-target regression (MTR). The task of MTR concerns problems where there are multiple continuous dependent variables and the goal is to learn a model for predicting all of the targets simultaneously. This task is receiving an increasing attention from the research community. However, performing feature ranking in the context of MTR has not been studied. Here, we propose three feature ranking methods for MTR: Symbolic, Genie3 and Random Forest. These methods are then coupled with three types of ensemble methods: Bagging, Random Forest, and Extremely Randomized Trees. All of the ensemble methods use predictive clustering trees (PCTs) as base predictive models. PCTs are a generalization of decision trees capable of MTR. In total, we consider eight different ensemble-ranking pairs. We extensively evaluate these pairs on 26 benchmark MTR datasets. The results reveal that all of the methods produce relevant feature rankings and that the best performing method is Genie3 ranking used with Random Forests of PCTs.