# A Unified Framework for Random Forest Prediction Error Estimation

arXiv: https://arxiv.org/abs/1912.07435 · HTML: https://mlsanity.com/paper/1912.07435/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Dec 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)
- [The Infinitesimal Jackknife and Combinations of Models](https://mlsanity.com/paper/2209.00147/) (2022)
- [RFpredInterval: An R Package for Prediction Intervals with Random Forests and Boosted Forests](https://mlsanity.com/paper/2106.08217/) (2021)
- [Covariance regression with random forests](https://mlsanity.com/paper/2209.08173/) (2022)
- [Local Adaptivity of Gradient Boosting in Histogram Transform Ensemble Learning](https://mlsanity.com/paper/2112.02589/) (2021)
- [Multivariate Prediction Intervals for Random Forests](https://mlsanity.com/paper/2205.02260/) (2022)
- [Targeted Learning for Variable Importance](https://mlsanity.com/paper/2411.02221/) (2024)
- [Localized Uncertainty Quantification in Random Forests via Proximities](https://mlsanity.com/paper/2509.22928/) (2025)

## Abstract (arXiv)

We introduce a unified framework for random forest prediction error estimation based on a novel estimator of the conditional prediction error distribution function. Our framework enables simple plug-in estimation of key prediction uncertainty metrics, including conditional mean squared prediction errors, conditional biases, and conditional quantiles, for random forests and many variants. Our approach is especially well-adapted for prediction interval estimation; we show via simulations that our proposed prediction intervals are competitive with, and in some settings outperform, existing methods. To establish theoretical grounding for our framework, we prove pointwise uniform consistency of a more stringent version of our estimator of the conditional prediction error distribution function. The estimators introduced here are implemented in the R package forestError.