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From Aleatoric to Epistemic: Exploring Uncertainty Quantification Techniques in Artificial Intelligence

Tianyang Wang, Yunze Wang, Jun Zhou, Benji Peng, Xinyuan Song, Charles Zhang, Xintian Sun, Qian Niu, Junyu Liu, Silin Chen, Keyu Chen, Ming Li, Pohsun Feng, Ziqian Bi, Ming Liu, Yichao Zhang, Cheng Fei, Caitlyn Heqi Yin, Lawrence KQ Yan

TL;DR

Uncertainty Quantification (UQ) addresses the reliability of AI in high-stakes settings by distinguishing aleatoric and epistemic uncertainty and by estimating predictive distributions. The predictive distribution is often expressed as $p(y|x)=\int p(y|x,\theta)\,p(\theta|D)\,d\theta$, combining data-driven likelihood with parameter uncertainty. The paper surveys six technique families—probabilistic methods, ensembles, sampling-based, generative models, deterministic methods, and hybrids—along with calibration, sharpness, and task-specific metrics. It presents applications in healthcare, autonomous systems, and financial technology, and discusses challenges such as scalability and integration with explainable AI, offering directions for future research.

Abstract

Uncertainty quantification (UQ) is a critical aspect of artificial intelligence (AI) systems, particularly in high-risk domains such as healthcare, autonomous systems, and financial technology, where decision-making processes must account for uncertainty. This review explores the evolution of uncertainty quantification techniques in AI, distinguishing between aleatoric and epistemic uncertainties, and discusses the mathematical foundations and methods used to quantify these uncertainties. We provide an overview of advanced techniques, including probabilistic methods, ensemble learning, sampling-based approaches, and generative models, while also highlighting hybrid approaches that integrate domain-specific knowledge. Furthermore, we examine the diverse applications of UQ across various fields, emphasizing its impact on decision-making, predictive accuracy, and system robustness. The review also addresses key challenges such as scalability, efficiency, and integration with explainable AI, and outlines future directions for research in this rapidly developing area. Through this comprehensive survey, we aim to provide a deeper understanding of UQ's role in enhancing the reliability, safety, and trustworthiness of AI systems.

From Aleatoric to Epistemic: Exploring Uncertainty Quantification Techniques in Artificial Intelligence

TL;DR

Uncertainty Quantification (UQ) addresses the reliability of AI in high-stakes settings by distinguishing aleatoric and epistemic uncertainty and by estimating predictive distributions. The predictive distribution is often expressed as , combining data-driven likelihood with parameter uncertainty. The paper surveys six technique families—probabilistic methods, ensembles, sampling-based, generative models, deterministic methods, and hybrids—along with calibration, sharpness, and task-specific metrics. It presents applications in healthcare, autonomous systems, and financial technology, and discusses challenges such as scalability and integration with explainable AI, offering directions for future research.

Abstract

Uncertainty quantification (UQ) is a critical aspect of artificial intelligence (AI) systems, particularly in high-risk domains such as healthcare, autonomous systems, and financial technology, where decision-making processes must account for uncertainty. This review explores the evolution of uncertainty quantification techniques in AI, distinguishing between aleatoric and epistemic uncertainties, and discusses the mathematical foundations and methods used to quantify these uncertainties. We provide an overview of advanced techniques, including probabilistic methods, ensemble learning, sampling-based approaches, and generative models, while also highlighting hybrid approaches that integrate domain-specific knowledge. Furthermore, we examine the diverse applications of UQ across various fields, emphasizing its impact on decision-making, predictive accuracy, and system robustness. The review also addresses key challenges such as scalability, efficiency, and integration with explainable AI, and outlines future directions for research in this rapidly developing area. Through this comprehensive survey, we aim to provide a deeper understanding of UQ's role in enhancing the reliability, safety, and trustworthiness of AI systems.
Paper Structure (41 sections, 21 equations, 4 figures, 1 table)

This paper contains 41 sections, 21 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Fundamentals of Uncertainty Quantification
  3. Types of Uncertainty
  4. Mathematical Foundations of UQ
  5. UQ in AI Decision-Making
  6. Sources of Uncertainty in AI Systems
  7. Advances in Uncertainty Quantification Techniques
  8. Probabilistic Methods
  9. Ensemble Learning Methods
  10. Sampling-Based Methods
  11. Generative Models
  12. Deterministic Methods
  13. Others
  14. Evaluation Metrics for Uncertainty Quantification
  15. Calibration Metrics
  16. ...and 26 more sections

Figures (4)

  • Figure 1: Receiver Operating Characteristic (ROC) Curve illustrating the trade-off between TPR and FPR. The Area Under the ROC Curve (AUROC) quantifies the overall ability of the classifier to discriminate between classes.
  • Figure 2: Calibration Plot showing the relationship between predicted confidence and observed accuracy. The closer the calibration curve is to the diagonal line, the better the model is calibrated.
  • Figure 3: Trade-Off between Calibration and Sharpness. Models aim to achieve high sharpness while maintaining good calibration. Points represent different models or configurations.
  • Figure 4: Regression Plot with Predicted Confidence Intervals. The blue line represents the predicted mean, while the red dashed lines denote the confidence intervals. The true function is shown in black.