Distillation Decision Tree

Black-box machine learning models are criticized as lacking interpretability, although they tend to have good prediction accuracy. Knowledge Distillation (KD) is an emerging tool to interpret the black-box model by distilling its knowledge into a transparent model. With well-known advantages in interpretation, decision tree is a competitive candidate of the transparent model. However, theoretical or empirical understanding for the decision tree generated from KD process is limited. In this paper, we name this kind of decision tree the distillation decision tree (DDT) and lay the theoretical foundations for tree structure stability which determines the validity of DDT's interpretation. We prove that the structure of DDT can achieve stable (convergence) under some mild assumptions. Meanwhile, we develop algorithms for stabilizing the induction of DDT, propose parallel strategies for improving algorithm's computational efficiency, and introduce a marginal principal component analysis method for overcoming the curse of dimensionality in sampling. Simulated and real data studies justify our theoretical results, validate the efficacy of algorithms, and demonstrate that DDT can strike a good balance between model's prediction accuracy and interpretability.