Regularization-based model tree for multi-output regression

Multi-output regression refers to the simultaneous prediction of several real-valued output variables to improve generalization performance by exploiting output relatedness. We propose a multi-output model tree that utilizes a regularization-based method to exploit the output relatedness when estimating linear models at leaf nodes. The proposed method can explain nonlinear input-output relation and provides easy interpretation of its mechanism based on input space partitioning and models at leaf nodes. The models exploit output relatedness by selecting common input variables to explain related output variables. We also present a computationally efficient two-stage splitting procedure that decreases the number of model estimations by analyzing residuals. We verify the effectiveness of the proposed method in a simulation study and demonstrate that it outperforms existing methods on several benchmark datasets. Furthermore, we apply the proposed method to real industry data as a case study to predict tensile qualities of plates.