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Decision trees have been a very popular class of predictive models fordecades due to their interpretability and good performance on categoricalfeatures. However, they are not always robust and tend to overfit the data.Additionally, if allowed to grow large, they lose interpretability. In thispaper, we present a mixed integer programming formulation to construct optimaldecision trees of a prespecified size. We take the special structure ofcategorical features into account and allow combinatorial decisions (based onsubsets of values of features) at each node. Our approach can also handlenumerical features via thresholding. We show that very good accuracy can beachieved with small trees using moderately-sized training sets. Theoptimization problems we solve are tractable with modern solvers.

Optimal Generalized Decision Trees via Integer Programming