# Scalable and Efficient Hypothesis Testing with Random Forests

arXiv: https://arxiv.org/abs/1904.07830 · HTML: https://mlsanity.com/paper/1904.07830/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Apr 2019.

## Built on by (most cited first, 8 of 8)

- [Bridging Breiman's Brook: From Algorithmic Modeling to Statistical Learning](https://mlsanity.com/paper/2102.12328/) (2021)
- [Statistical Inference for Gradient Boosting Regression](https://mlsanity.com/paper/2509.23127/) (2025)
- [TrIM: Transformed Iterative Mondrian Forests for Gradient-based Dimension Reduction and High-Dimensional Regression](https://mlsanity.com/paper/2407.09964/) (2024)
- [Nonparametric IPSS: Fast, flexible feature selection with false discovery control](https://mlsanity.com/paper/2410.02208/) (2024)
- [Sequential Permutation Testing of Random Forest Variable Importance Measures](https://mlsanity.com/paper/2206.01284/) (2022)
- [AICO: Feature Significance Tests for Supervised Learning](https://mlsanity.com/paper/2506.23396/) (2025)
- [Empirical Likelihood for Random Forests and Ensembles](https://mlsanity.com/paper/2511.13934/) (2025)
- [A statistical perspective on transformers for small longitudinal cohort data](https://mlsanity.com/paper/2602.16914/) (2026)

## Abstract (arXiv)

Throughout the last decade, random forests have established themselves as among the most accurate and popular supervised learning methods. While their black-box nature has made their mathematical analysis difficult, recent work has established important statistical properties like consistency and asymptotic normality by considering subsampling in lieu of bootstrapping. Though such results open the door to traditional inference procedures, all formal methods suggested thus far place severe restrictions on the testing framework and their computational overhead precludes their practical scientific use. Here we propose a permutation-style testing approach to formally assess feature significance. We establish asymptotic validity of the test via exchangeability arguments and show that the test maintains high power with orders of magnitude fewer computations. As importantly, the procedure scales easily to big data settings where large training and testing sets may be employed without the need to construct additional models. Simulations and applications to ecological data where random forests have recently shown promise are provided.