Generative model for decision trees

Decision trees are among the most popular supervised models due to their interpretability and knowledge representation resembling human reasoning. Commonly-used decision tree induction algorithms are based on greedy top-down strategies. Although these approaches are known to be an efficient heuristic, the resulting trees are only locally optimal and tend to have overly complex structures. On the other hand, optimal decision tree algorithms attempt to create an entire decision tree at once to achieve global optimality. We place our proposal between these approaches by designing a generative model for decision trees. Our method first learns a latent decision tree space through a variational architecture using pre-trained decision tree models. Then, it adopts a genetic procedure to explore such latent space to find a compact decision tree with good predictive performance. We compare our proposal against classical tree induction methods, optimal approaches, and ensemble models. The results show that our proposal can generate accurate and shallow, i.e., interpretable, decision trees.