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