# Boulevard: Regularized Stochastic Gradient Boosted Trees and Their Limiting Distribution

arXiv: https://arxiv.org/abs/1806.09762 · HTML: https://mlsanity.com/paper/1806.09762/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jun 2018.

## Built on by (most cited first, 7 of 7)

- [Fast Interpretable Greedy-Tree Sums](https://mlsanity.com/paper/2201.11931/) (2022)
- [Bridging Breiman's Brook: From Algorithmic Modeling to Statistical Learning](https://mlsanity.com/paper/2102.12328/) (2021)
- [The Infinitesimal Jackknife and Combinations of Models](https://mlsanity.com/paper/2209.00147/) (2022)
- [Autoencoding Random Forests](https://mlsanity.com/paper/2505.21441/) (2025)
- [Statistical Inference for Explainable Boosting Machines](https://mlsanity.com/paper/2601.18857/) (2026)
- [Minimax Rates and Spectral Distillation for Tree Ensembles](https://mlsanity.com/paper/2605.11841/) (2026)
- [Conditioning Tree-Based Diffusions and Flows for Probabilistic Tabular Regression](https://mlsanity.com/paper/2607.28864/) (2026)

## Abstract (arXiv)

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.