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approximation uncertainty

Approximation uncertainty is a form of epistemic uncertainty in machine learning that arises from having a finite amount of training data, resulting in a discrepancy between the predictor induced by a learning algorithm and the optimal predictor within the chosen hypothesis space. While a chosen model class may have the theoretical capacity to represent the best possible hypothesis, limited sample size or estimation errors introduce uncertainty regarding which specific hypothesis or parameter set best captures the underlying pattern. Unlike aleatoric uncertainty, which reflects irreducible randomness inherent to the data-generating process, approximation uncertainty is reducible through the acquisition of additional training observations. It is also distinguished from model uncertainty, which is the structural error that occurs when the chosen hypothesis space is misspecified and cannot represent the true relationship regardless of sample size.

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Aleatoric and epistemic uncertainty in machine learning: an introduction to concepts and methods

Aleatoric and epistemic uncertainty in machine learning: an introduction to concepts and methods

Eyke Hüllermeier, Willem Waegeman

OrganizationsGhent UniversityPaderborn University

Why you should read this

Clarifies the critical distinction between irreducible data randomness and reducible model ignorance, providing a comprehensive framework for quantifying both aleatoric and epistemic uncertainty to build safer, more reliable machine learning systems.

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.

Added

2026-09-16