Optimal Generalized Decision Trees via Integer Programming
This work addresses the trade-off between accuracy and interpretability in decision trees for machine learning practitioners, though it is incremental as it builds on existing optimization methods.
The authors tackled the problem of constructing robust and interpretable decision trees by developing a mixed integer programming formulation that builds optimal trees of a prespecified size, achieving very good accuracy with small trees on moderately-sized training sets.
Decision trees have been a very popular class of predictive models for decades due to their interpretability and good performance on categorical features. However, they are not always robust and tend to overfit the data. Additionally, if allowed to grow large, they lose interpretability. In this paper, we present a mixed integer programming formulation to construct optimal decision trees of a prespecified size. We take the special structure of categorical features into account and allow combinatorial decisions (based on subsets of values of features) at each node. Our approach can also handle numerical features via thresholding. We show that very good accuracy can be achieved with small trees using moderately-sized training sets. The optimization problems we solve are tractable with modern solvers.