An Axiomatic Assessment of Entropy- and Variance-based Uncertainty Quantification in Regression

Uncertainty quantification (UQ) is crucial in machine learning, yet most (axiomatic) studies of uncertainty measures focus on classification, leaving a gap in regression settings with limited formal justification and evaluations. In this work, we introduce a set of axioms to rigorously assess measures of aleatoric, epistemic, and total uncertainty in supervised regression. By utilizing a predictive exponential family, we can generalize commonly used approaches for uncertainty representation and corresponding uncertainty measures. More specifically, we analyze the widely used entropy- and variance-based measures regarding limitations and challenges. Our findings provide a principled foundation for UQ in regression, offering theoretical insights and practical guidelines for reliable uncertainty assessment.

@article{bülte2025_2504.18433,
  title={ An Axiomatic Assessment of Entropy- and Variance-based Uncertainty Quantification in Regression },
  author={ Christopher Bülte and Yusuf Sale and Timo Löhr and Paul Hofman and Gitta Kutyniok and Eyke Hüllermeier },
  journal={arXiv preprint arXiv:2504.18433},
  year={ 2025 }
}