  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.
