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This paper examines a novel gradient boosting framework for regression. Weregularize gradient boosted trees by introducing subsampling and employ amodified shrinkage algorithm so that at every boosting stage the estimate isgiven by an average of trees. The resulting algorithm, titled Boulevard, isshown to converge as the number of trees grows. We also demonstrate a centrallimit theorem for this limit, allowing a characterization of uncertainty forpredictions. A simulation study and real world examples provide support forboth the predictive accuracy of the model and its limiting behavior.

Boulevard: Regularized Stochastic Gradient Boosted Trees and Their Limiting Distribution