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 root-to-leaf paths in decision trees. The model is solved via a Column Generation based heuristic. To speed up the heuristic, we use a restricted instance data by considering a subset of decision splits, sampled from the solutions of the well-known CART algorithm. Extensive numerical experiments show that our approach is competitive with the state-of-the-art ILP-based algorithms. In particular, the proposed approach is capable of handling big data sets with tens of thousands of data rows. Moreover, for large data sets, it finds solutions competitive to CART.
@article{arxiv.1810.06684,
title = {Column generation based math-heuristic for classification trees},
author = {Murat Firat and Guillaume Crognier and Adriana F. Gabor and C. A. J. Hurkens and Yingqian Zhang},
journal= {arXiv preprint arXiv:1810.06684},
year = {2019}
}