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Title: Detecting and leveraging structural information with Bayesian forests Authors:  Antonio Linero - Florida State University (United States) [presenting]
Abstract: Bayesian methods based on ensembles of decision trees, such as Bayesian additive regression trees (BART) have proven to be extremely useful in a wide variety of statistical problems. We show how a-priori known structural information, such as graphical or group structures of the predictors, can be used to improve the efficiency and stability of the ensemble. This structural information is encoded through priors on the splitting proportions of BART ensembles, and can be used to encode, for example, sparsity within or between groups of predictors. We also consider the problem of detecting interactions among predictors in BART-type models. Using a clustering of trees in the ensemble, we allow the model to smoothly vary between a sparse additive model (SPAM) model and a dense model in which interactions between variables are not penalized. We illustrate the methodology proposed on a variety of simulated and real datasets.