Constructing classification trees using column generation

This paper explores the use of Column Generation (CG) techniques in constructing univariate binary decision trees for classification tasks. We propose a novel Integer Linear Programming (ILP) formulation, based on paths in decision trees. We show that the associated pricing problem is NP-hard and propose a random procedure for column selection. In addition, to speed up column generation, we use a restricted parameter set via a sampling procedure using the well-known CART algorithm. Extensive numerical experiments show that our approach outperforms the state-of-the-art ILP-based algorithms in the recent literature both in computation time and solution quality. We also find better solutions that have higher training and testing accuracy than an optimized version of CART. Furthermore, our approach is capable of handling big data sets with tens of thousands of data rows, unlike other ILP-based algorithms. In addition, our approach has the advantage of being able to easily incorporate different objectives.