# Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods

arXiv: https://arxiv.org/abs/1910.09457 · HTML: https://mlsanity.com/paper/1910.09457/

## Key facts

- Cited by 913 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Oct 2019.

## Built on by (most cited first, 30 of 913)

- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [A Survey of Machine Unlearning](https://mlsanity.com/paper/2209.02299/) (2022)
- [Generating with Confidence: Uncertainty Quantification for Black-box Large Language Models](https://mlsanity.com/paper/2305.19187/) (2023)
- [Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons](https://mlsanity.com/paper/2201.07766/) (2022)
- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [Rho-1: Not All Tokens Are What You Need](https://mlsanity.com/paper/2404.07965/) (2024)
- [Quantifying Aleatoric and Epistemic Uncertainty in Machine Learning: Are Conditional Entropy and Mutual Information Appropriate Measures?](https://mlsanity.com/paper/2209.03302/) (2022)
- [AI Transparency in the Age of LLMs: A Human-Centered Research Roadmap](https://mlsanity.com/paper/2306.01941/) (2023)
- [Decomposing Uncertainty for Large Language Models through Input Clarification Ensembling](https://mlsanity.com/paper/2311.08718/) (2023)
- [DEUP: Direct Epistemic Uncertainty Prediction](https://mlsanity.com/paper/2102.08501/) (2021)
- [Uncertainty Quantification and Confidence Calibration in Large Language Models: A Survey](https://mlsanity.com/paper/2503.15850/) (2025)
- [A Deeper Look into Aleatoric and Epistemic Uncertainty Disentanglement](https://mlsanity.com/paper/2204.09308/) (2022)
- [On Verbalized Confidence Scores for LLMs](https://mlsanity.com/paper/2412.14737/) (2024)
- [A Survey on Uncertainty Quantification Methods for Deep Learning](https://mlsanity.com/paper/2302.13425/) (2023)
- [LUQ: Long-text Uncertainty Quantification for LLMs](https://mlsanity.com/paper/2403.20279/) (2024)
- [Active Learning for Deep Object Detection via Probabilistic Modeling](https://mlsanity.com/paper/2103.16130/) (2021)
- [Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review](https://mlsanity.com/paper/2303.10462/) (2023)
- [Uncertainty-aware Reward Model: Teaching Reward Models to Know What is Unknown](https://mlsanity.com/paper/2410.00847/) (2024)
- [Classifier Calibration: A survey on how to assess and improve predicted class probabilities](https://mlsanity.com/paper/2112.10327/) (2021)
- [Prior and Posterior Networks: A Survey on Evidential Deep Learning Methods For Uncertainty Estimation](https://mlsanity.com/paper/2110.03051/) (2021)
- [Mutual Information Alleviates Hallucinations in Abstractive Summarization](https://mlsanity.com/paper/2210.13210/) (2022)
- [Pitfalls of Epistemic Uncertainty Quantification through Loss Minimisation](https://mlsanity.com/paper/2203.06102/) (2022)
- [A Survey on Autonomous Driving Datasets: Statistics, Annotation Quality, and a Future Outlook](https://mlsanity.com/paper/2401.01454/) (2024)
- [Training Uncertainty-Aware Classifiers with Conformalized Deep Learning](https://mlsanity.com/paper/2205.05878/) (2022)
- [Deep Ensembles Work, But Are They Necessary?](https://mlsanity.com/paper/2202.06985/) (2022)
- [Trustworthy clinical AI solutions: a unified review of uncertainty quantification in deep learning models for medical image analysis](https://mlsanity.com/paper/2210.03736/) (2022)
- [A Survey of Uncertainty Estimation Methods on Large Language Models](https://mlsanity.com/paper/2503.00172/) (2025)
- [Uncertainty in Natural Language Generation: From Theory to Applications](https://mlsanity.com/paper/2307.15703/) (2023)
- [When Does Confidence-Based Cascade Deferral Suffice?](https://mlsanity.com/paper/2307.02764/) (2023)
- [Quantile Regression for Distributional Reward Models in RLHF](https://mlsanity.com/paper/2409.10164/) (2024)

## Abstract (arXiv)

The notion of uncertainty is of major importance in machine learning and constitutes a key element of machine learning methodology. In line with the statistical tradition, uncertainty has long been perceived as almost synonymous with standard probability and probabilistic predictions. Yet, due to the steadily increasing relevance of machine learning for practical applications and related issues such as safety requirements, new problems and challenges have recently been identified by machine learning scholars, and these problems may call for new methodological developments. In particular, this includes the importance of distinguishing between (at least) two different types of uncertainty, often referred to as aleatoric and epistemic. In this paper, we provide an introduction to the topic of uncertainty in machine learning as well as an overview of attempts so far at handling uncertainty in general and formalizing this distinction in particular.