Abstract
•Three multi-target regression ensemble models with different architectures.•Use gene-expression programming to build each member of the ensemble.•Individuals encode a full solution to the problem, using as many genes as targets.•Competitive results compared versus 5 state-of-the-art methods over 18 datasets.
Multi-Target Regression problem comprises the prediction of multiple continuous variables given a common set of input features, unlike traditional regression tasks, where just one output target is available. There are two major challenges when addressing this problem, namely the exploration of the inter-target dependencies and the modeling of complex input–output relationships. This work proposes a Symbolic Regression method following the basis of Gene Expression Programming paradigm to solve the multi-target regression problem, and called GEPMTR. It evolves a population of individuals, where each one represents a complete solution to the problem by using a multi-genic chromosome, and encodes a mathematical function for each target variable involving the input attributes. The proposed model can estimate the inter-target dependencies by applying some genetic operators. Furthermore, three ensemble-based methods are developed to better exploit the inter-target and input–output relationships. The effectiveness of the proposals is analyzed through an extensive experimental study on 18 datasets. The codification schema and the process followed to ensure a diverse population in GEPMTR lead to obtain an effective proposal to solve the MTR problem. Furthermore, the EGEPMTR-B ensemble method obtained the best performance across all proposed models, being the best in 8 out of 11 cases, demonstrating that more sophisticated mechanisms were not needed for ensuring that GEPMTR method would properly model the existing inter-target dependencies. Finally, the experimental results also showed that the proposed approach attains competitive results compared to state-of-the-art, showing the possibilities that can bring this research line for effectively solving the MTR problem.