A Branch-and-Price approach to find optimal decision trees

In Artificial Intelligence (AI) field, decision trees have gained certain importance due to their effectiveness in solving classification and regression problems. Recently, in the literature we see finding optimal decision trees are formulated as Mixed Integer Linear Programming (MILP) models. This elegant way enables us to construct optimal decision trees with different error concerns. In our work, we find the optimal decision trees by employing the Column Generation (CG) approach. To do so, we first reformulated the previously proposed MILP model as a master MILP model. This master model is basically a partitioning problem of the rows in the given data set such that every We obtain the integer solutions by applying a Branch-and-Price search. Our approach of constructing decision trees is successfully tested in real-world benchmark datasets.