Feature ranking for multi-target regression

In this work, we address the task of feature ranking for multi-target regression (MTR). The task of MTR concerns problems with multiple continuous dependent/target variables, where the goal is to learn a model for predicting all of them simultaneously. This task is receiving an increasing attention from the research community, but performing feature ranking in the context of MTR has not been studied thus far. Here, we study two groups of feature ranking scores for MTR: scores (Symbolic, Genie3 and Random Forest score) based on ensembles (bagging, random forests, extra trees) of predictive clustering trees, and a score derived as an extension of the RReliefF method. We also propose a generic data-transformation approach to MTR feature ranking and thus have two versions of each score. For both groups of feature ranking scores, we analyze their theoretical computational complexity. For the extension of the RReliefF method, we additionally derive some theoretical properties of the scores. Next, we extensively evaluate the scores on 24 benchmark MTR datasets, in terms of the quality of the ranking and the computational complexity of producing it. The results identify the parameters that influence the quality of the rankings, reveal that both groups of methods produce relevant feature rankings, and show that the Symbolic and Genie3 score, coupled with random forest ensembles, yield the best rankings.