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Decision trees have found widespread application within the machine learningcommunity due to their flexibility and interpretability. This paper is directedtowards learning decision trees from data using a Bayesian approach, which ischallenging due to the potentially enormous parameter space required to spanall tree models. Several approaches have been proposed to combat thischallenge, with one of the more successful being Markov chain Monte Carlo(MCMC) methods. The efficacy and efficiency of MCMC methods fundamentally relyon the quality of the so-called proposals, which is the focus of this paper. Inparticular, this paper investigates using a Hamiltonian Monte Carlo (HMC)approach to explore the posterior of Bayesian decision trees more efficientlyby exploiting the geometry of the likelihood within a global update scheme. Twoimplementations of the novel algorithm are developed and compared to existingmethods by testing against standard datasets in the machine learning andBayesian decision tree literature. HMC-based methods are shown to performfavourably with respect to predictive test accuracy, acceptance rate, and treecomplexity.

RJHMC-Tree for Exploration of the Bayesian Decision Tree Posterior