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Decision tree optimization is notoriously difficult from a computational perspective but essential for the field of interpretable machine learning. Despite efforts over the past 40 years, only recently have optimization breakthroughs been made that have allowed practical algorithms to find optimal decision trees. These new techniques have the potential to trigger a paradigm shift where it is possible to construct sparse decision trees to efficiently optimize a variety of objective functions without relying on greedy splitting and pruning heuristics that often lead to suboptimal solutions. The contribution in this work is to provide a general framework for decision tree optimization that addresses the two significant open problems in the area: treatment of imbalanced data and fully optimizing over continuous variables. We present techniques that produce optimal decision trees over a variety of objectives including F-score, AUC, and partial area under the ROC convex hull. We also introduce a scalable algorithm that produces provably optimal results in the presence of continuous variables and speeds up decision tree construction by several orders of magnitude relative to the state-of-the art.
Several recent publications report advances in training optimal decision trees (ODT) using mixed-integer programs (MIP), due to algorithmic advances in integer programming and a growing interest in addressing the inherent suboptimality of heuristic a
Multi-layered representation is believed to be the key ingredient of deep neural networks especially in cognitive tasks like computer vision. While non-differentiable models such as gradient boosting decision trees (GBDTs) are the dominant methods fo
Recent research has recognized interpretability and robustness as essential properties of trustworthy classification. Curiously, a connection between robustness and interpretability was empirically observed, but the theoretical reasoning behind it re
Model selection consists in comparing several candidate models according to a metric to be optimized. The process often involves a grid search, or such, and cross-validation, which can be time consuming, as well as not providing much information abou
Learning graph generative models is a challenging task for deep learning and has wide applicability to a range of domains like chemistry, biology and social science. However current deep neural methods suffer from limited scalability: for a graph wit