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Abstract:
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Bayesian regression tree models are competitive with leading machine learning algorithms yet retain an elegant fully Bayesian formulation that enables uncertainty quantification. The ability of these models to capture distributional information make them incredibly useful for many modern statistical applications where investigating the question of interest requires more than point predictions. Yet one key limitation of these models are the variable split rules, which are typically chosen according to the number of unique predictor values or a dense grid of candidate values. This may limit the model's ability adapt to local sources of variation, and simply increasing the grid density introduces an expensive computational burden. We introduce a novel adaptive strategy, allowing more efficient modeling of patterns of local variation. We demonstrate the usefulness of these new ideas on an image analysis study investigating beach visitor counts in San Diego.
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