Abstract: In recent years there has been growing attention to interpretable machine learning models which can give explanatory insights on their behavior. Thanks to their interpretability, decision trees have been intensively studied for classification tasks, and due to the remarkable advances in mixed-integer programming (MIP), various approaches have been proposed to formulate the problem of training an Optimal Classification Tree (OCT) as a MIP model. We present a novel mixed-integer quadratic formulation for the OCT problem, which exploits the generalization capabilities of Support Vector Machines for binary classification. Our model, denoted as Maximum Margin Optimal Classification Tree (MARGOT), encompasses the use of maximum margin multivariate hyperplanes nested in a binary tree structure. To enhance the interpretability of our approach, we analyse two alternative versions of MARGOT, which include feature selection constraints inducing local sparsity of the hyperplanes.

Abstract: The fields of machine learning and statistics have invested great efforts into designing algorithms, models, and approaches that better predict future observations. Larger and richer data have also been shown to improve predictive power. This is especially true in the world of human behavioral big data, as is evident from recent advances in behavioral prediction technology. Large internet platforms that collect behavioral big data predict user behavior for their internal commercial purposes as well as for third parties, such as advertisers, insurers, security forces, and political consulting firms, who utilize the predictions for user-level personalization, targeting, and other decision-making. While machine learning algorithmic and data efforts are directed at improving predicted values, the internet platforms can minimize prediction error by «pushing» users' actions towards their predicted values using behavior modification techniques.