A decomposable branch-and-price formulation for optimal classification trees

Abstract

Construction of Optimal Classification Trees (OCTs) using mixed-integer programs, is a promising approach as it returns a tree with minimum classification error. Yet solving integer programs to optimality is known to be computationally costly, especially as the size of the instance and the depth of the tree grow, calling for efficient solution methods. Our research presents a new, decomposable model which lends itself to efficient solution algorithms such as Branch-and-Price. We model the classification tree using a “patternbased” formulation, deciding which feature should be used to split data at each branching node of each leaf. Our results are promising, illustrating the potential of decomposition in the domain of binary OCTs.