# Empirical Likelihood for Random Forests and Ensembles

arXiv: https://arxiv.org/abs/2511.13934 · HTML: https://mlsanity.com/paper/2511.13934/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 42 references that are in the map.
- First posted on arXiv 17 Nov 2025.

## Builds on (most cited first, 14 of 14)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [A Random Forest Guided Tour](https://mlsanity.com/paper/1511.05741/) (2015)
- [Consistency of random forests](https://mlsanity.com/paper/1405.2881/) (2014)
- [Confidence Intervals for Random Forests: The Jackknife and the Infinitesimal Jackknife](https://mlsanity.com/paper/1311.4555/) (2013)
- [Randomization as Regularization: A Degrees of Freedom Explanation for Random Forest Success](https://mlsanity.com/paper/1911.00190/) (2019)
- [Asymptotic Distributions and Rates of Convergence for Random Forests via Generalized U-statistics](https://mlsanity.com/paper/1905.10651/) (2019)
- [Scalable and Efficient Hypothesis Testing with Random Forests](https://mlsanity.com/paper/1904.07830/) (2019)
- [Approximating high-dimensional infinite-order U-statistics: statistical and computational guarantees](https://mlsanity.com/paper/1901.01163/) (2019)
- [On Variance Estimation of Random Forests with Infinite-Order U-statistics](https://mlsanity.com/paper/2202.09008/) (2022)
- [The Infinitesimal Jackknife and Combinations of Models](https://mlsanity.com/paper/2209.00147/) (2022)
- [Optimal Nonparametric Inference with Two-Scale Distributional Nearest Neighbors](https://mlsanity.com/paper/1808.08469/) (2018)
- [Multiway empirical likelihood](https://mlsanity.com/paper/2108.04852/) (2021)
- [Jackknife Variance Estimation for H'ajek-Dominated Generalized U-Statistics](https://mlsanity.com/paper/2509.12356/) (2025)

## Abstract (arXiv)

We develop an empirical likelihood (EL) framework for random forests and related ensemble methods, providing a likelihood-based approach to quantify their statistical uncertainty. Exploiting the incomplete U-statistic structure inherent in ensemble predictions, we construct an EL statistic that is asymptotically chi-squared when subsampling induced by incompleteness is not overly sparse. Under sparser subsampling regimes, the EL statistic tends to over-cover due to loss of pivotality; we therefore propose a modified EL that restores pivotality through a simple adjustment. Our method retains key properties of EL while remaining computationally efficient. Theory for honest random forests and simulations demonstrate that modified EL achieves accurate coverage and practical reliability relative to existing inference methods.