Interaction Detection with Bayesian Decision Tree Ensembles

Methods based on Bayesian decision tree ensembles have proven valuable in constructing high-quality predictions, and are particularly attractive in certain settings because they encourage low-order interaction effects. Despite adapting to the presence of low-order interactions for prediction purpose, we show that Bayesian decision tree ensembles are generally anti-conservative for the purpose of conducting interaction detection. We address this problem by introducing Dirichlet process forests (DP-Forests), which leverage the presence of low-order interactions by clustering the trees so that trees within the same cluster focus on detecting a specific interaction. We show on both simulated and benchmark data that DP-Forests perform well relative to existing interaction detection techniques for detecting low-order interactions, attaining very low false-positive and false-negative rates while maintaining the same performance for prediction using a comparable computational budget.