Decision tree learning is a popular approach for classification and regression in machine learning and statistics, and Bayesian formulations---which introduce a prior distribution over decision trees, and formulate learning as posterior inference given data---have been shown to produce competitive performance. Unlike classic decision tree learning algorithms like ID3, C4.5 and CART, which work in a top-down manner, existing Bayesian algorithms produce an approximation to the posterior distribution by evolving a complete tree (or collection thereof) iteratively via local Monte Carlo modifications to the structure of the tree, e.g., using Markov chain Monte Carlo (MCMC). We present a sequential Monte Carlo (SMC) algorithm that instead works in a top-down manner, mimicking the behavior and speed of classic algorithms. We demonstrate empirically that our approach delivers accuracy comparable to the most popular MCMC method, but operates more than an order of magnitude faster, and thus represents a better computation-accuracy tradeoff.
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