Interpretable cost-sensitive regression through one-step boosting

In most practical prediction problems, such as regression and classification, the different types of prediction errors are not equally costly in the decision-making process. Although there exist numerous real-world cost-sensitive regression problems, ranging from loan charge-off forecasting to house price predictions, the literature on cost-sensitive learning mainly focuses on classification and only a few solutions are proposed for regression problems. These regressions are typically characterized by an asymmetric cost structure, where over- and underpredictions of a similar magnitude face vastly different costs. In this paper, we present a one-step boosting method (OSB) for cost-sensitive regression. The proposed methodology leverages a secondary learner to incorporate cost-sensitivity into an already trained cost-insensitive regression model. The secondary learner is defined as a linear function of certain variables deemed interesting for cost-sensitivity. These variables do not necessarily need to be the same as in the already trained model. An efficient optimization algorithm is achieved through iteratively reweighted least squares using the asymmetric cost function. The obtained results become interpretable through bootstrapping, enabling decision makers to distinguish important variables for cost-sensitivity as well as facilitating statistical inference. Applying different cost functions and various initial cost-insensitive learning methods on several public datasets consistently yields a significant reduction in the average misprediction cost, illustrating the excellent performance of our approach.