A Review of Uncertainty Representation and Quantification in Neural Networks
Kaizheng Wang, Fabio Cuzzolin, Keivan Shariatmadar, David Moens, Hans Hallez · IEEE Transactions on Pattern Analysis and Machine Intelligence · 2025
Effectively estimating the uncertainty attached to neural network predictions thus becomes essential to improve robustness, reliability, and trustworthiness. This paper provides an overview of various methodologies for representing, quantifying, and distinguishing two major types of uncertainties (namely, 'aleatoric' and 'epistemic' uncertainty) in neural networks. The review covers classical probabilistic techniques such as Bayesian neural networks and deep ensembles, methods from generalized probability that leverage uncertainty representations such as Dirichlet distributions, belief functions, random sets, probability intervals, and credal sets, among others. Additionally, interval-based approaches employing interval models are also examined. We discuss the strengths and limitations of various methodologies and identify promising research directions for potential future exploration.