Bayesian Regression Trees for High-Dimensional Prediction and Variable Selection
提出一种贝叶斯回归树方法，通过稀疏诱导的狄利克雷超先验适应高维稀疏预测变量，能给出每个预测变量的后验包含概率，在模拟和真实数据上优于其他树集成方法。
Decision tree ensembles are an extremely popular tool for obtaining high-quality predictions in nonparametric regression problems. Unmodified, however, many commonly used decision tree ensemble methods do not adapt to sparsity in the regime in which the number of predictors is larger than the number of observations. A recent stream of research concerns the construction of decision tree ensembles that are motivated by a generative probabilistic model, the most influential method being the Bayesian additive regression trees (BART) framework. In this article, we take a Bayesian point of view on this problem and show how to construct priors on decision tree ensembles that are capable of adapting to sparsity in the predictors by placing a sparsity-inducing Dirichlet hyperprior on the splitting proportions of the regression tree prior. We characterize the asymptotic distribution of the number of predictors included in the model and show how this prior can be easily incorporated into existing Markov chain Monte Carlo schemes. We demonstrate that our approach yields useful posterior inclusion probabilities for each predictor and illustrate the usefulness of our approach relative to other decision tree ensemble approaches on both simulated and real datasets. Supplementary materials for this article are available online.