# Aleatoric and Epistemic Uncertainty with Random Forests

arXiv: https://arxiv.org/abs/2001.00893 · HTML: https://mlsanity.com/paper/2001.00893/

## Key facts

- Cited by 43 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jan 2020.

## Built on by (most cited first, 30 of 43)

- [DEUP: Direct Epistemic Uncertainty Prediction](https://mlsanity.com/paper/2102.08501/) (2021)
- [Pitfalls of Epistemic Uncertainty Quantification through Loss Minimisation](https://mlsanity.com/paper/2203.06102/) (2022)
- [Is the Volume of a Credal Set a Good Measure for Epistemic Uncertainty?](https://mlsanity.com/paper/2306.09586/) (2023)
- [Explaining Predictive Uncertainty with Information Theoretic Shapley Values](https://mlsanity.com/paper/2306.05724/) (2023)
- [Conformalized Credal Set Predictors](https://mlsanity.com/paper/2402.10723/) (2024)
- [Explainability through uncertainty: Trustworthy decision-making with neural networks](https://mlsanity.com/paper/2403.10168/) (2024)
- [Evidential Deep Learning: Enhancing Predictive Uncertainty Estimation for Earth System Science Applications](https://mlsanity.com/paper/2309.13207/) (2023)
- [Integral Imprecise Probability Metrics](https://mlsanity.com/paper/2505.16156/) (2025)
- [Dense Uncertainty Estimation](https://mlsanity.com/paper/2110.06427/) (2021)
- [Uncertainty quantification for probabilistic machine learning in earth observation using conformal prediction](https://mlsanity.com/paper/2401.06421/) (2024)
- [On the Calibration of Probabilistic Classifier Sets](https://mlsanity.com/paper/2205.10082/) (2022)
- [Uncertainty-Aware Mixed-Variable Machine Learning for Materials Design](https://mlsanity.com/paper/2207.04994/) (2022)
- [Model-agnostic variable importance for predictive uncertainty: an entropy-based approach](https://mlsanity.com/paper/2310.12842/) (2023)
- [Active learning for imbalanced data under cold start](https://mlsanity.com/paper/2107.07724/) (2021)
- [GOSH: Task Scheduling Using Deep Surrogate Models in Fog Computing Environments](https://mlsanity.com/paper/2112.08916/) (2021)
- [Bayesian Deep Learning with Multilevel Trace-class Neural Networks](https://mlsanity.com/paper/2203.12961/) (2022)
- [Reducing Aleatoric and Epistemic Uncertainty through Multi-modal Data Acquisition](https://mlsanity.com/paper/2501.18268/) (2025)
- [Uncertainty-Aware Boosted Ensembling in Multi-Modal Settings](https://mlsanity.com/paper/2104.10715/) (2021)
- [Robustness quantification: a new method for assessing the reliability of the predictions of a classifier](https://mlsanity.com/paper/2503.22418/) (2025)
- [Towards Clear Expectations for Uncertainty Estimation](https://mlsanity.com/paper/2207.13341/) (2022)
- [Predicting small molecules solubilities on endpoint devices using deep ensemble neural networks](https://mlsanity.com/paper/2307.05318/) (2023)
- [Enhancing Trustworthiness in ML-Based Network Intrusion Detection with Uncertainty Quantification](https://mlsanity.com/paper/2310.10655/) (2023)
- [Robust Explanations Through Uncertainty Decomposition: A Path to Trustworthier AI](https://mlsanity.com/paper/2507.12913/) (2025)
- [Deep Ensembles for Epistemic Uncertainty: A Frequentist Perspective](https://mlsanity.com/paper/2510.22063/) (2025)
- [Robustness and uncertainty: two complementary aspects of the reliability of the predictions of a classifier](https://mlsanity.com/paper/2512.15492/) (2025)
- [Detecting and Mitigating Test-time Failure Risks via Model-agnostic Uncertainty Learning](https://mlsanity.com/paper/2109.04432/) (2021)
- [Prompting the Unknown: Understanding Response Uncertainty in Large Language Models](https://mlsanity.com/paper/2407.14845/) (2024)
- [Exploring the Impact of Explainable AI and Cognitive Capabilities on Users' Decisions](https://mlsanity.com/paper/2505.01192/) (2025)
- [Scalable Bayesian Monte Carlo: fast uncertainty estimation beyond deep ensembles](https://mlsanity.com/paper/2505.13585/) (2025)
- [DoublyAware: Dual Planning and Policy Awareness for Temporal Difference Learning in Humanoid Locomotion](https://mlsanity.com/paper/2506.12095/) (2025)

## Abstract (arXiv)

Due to the steadily increasing relevance of machine learning for practical applications, many of which are coming with safety requirements, the notion of uncertainty has received increasing attention in machine learning research in the last couple of years. In particular, the idea of distinguishing between two important types of uncertainty, often refereed to as aleatoric and epistemic, has recently been studied in the setting of supervised learning. In this paper, we propose to quantify these uncertainties with random forests. More specifically, we show how two general approaches for measuring the learner's aleatoric and epistemic uncertainty in a prediction can be instantiated with decision trees and random forests as learning algorithms in a classification setting. In this regard, we also compare random forests with deep neural networks, which have been used for a similar purpose.