# Measuring the Algorithmic Convergence of Randomized Ensembles: The Regression Setting

arXiv: https://arxiv.org/abs/1908.01251 · HTML: https://mlsanity.com/paper/1908.01251/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Aug 2019.

## Built on by (most cited first, 5 of 5)

- [Why do Random Forests Work? Understanding Tree Ensembles as Self-Regularizing Adaptive Smoothers](https://mlsanity.com/paper/2402.01502/) (2024)
- [Corrected generalized cross-validation for finite ensembles of penalized estimators](https://mlsanity.com/paper/2310.01374/) (2023)
- [Extrapolated cross-validation for randomized ensembles](https://mlsanity.com/paper/2302.13511/) (2023)
- [Random Forests as Statistical Procedures: Design, Variance, and Dependence](https://mlsanity.com/paper/2602.13104/) (2026)
- [Cheap Bootstrap for Fast Uncertainty Quantification of Stochastic Gradient Descent](https://mlsanity.com/paper/2310.11065/) (2023)

## Abstract (arXiv)

When randomized ensemble methods such as bagging and random forests are implemented, a basic question arises: Is the ensemble large enough? In particular, the practitioner desires a rigorous guarantee that a given ensemble will perform nearly as well as an ideal infinite ensemble (trained on the same data). The purpose of the current paper is to develop a bootstrap method for solving this problem in the context of regression --- which complements our companion paper in the context of classification (Lopes 2019). In contrast to the classification setting, the current paper shows that theoretical guarantees for the proposed bootstrap can be established under much weaker assumptions. In addition, we illustrate the flexibility of the method by showing how it can be adapted to measure algorithmic convergence for variable selection. Lastly, we provide numerical results demonstrating that the method works well in a range of situations.