An Axiomatic Assessment of Entropy- and Variance-based Uncertainty Quantification in Regression
This work addresses a gap in uncertainty quantification for regression, offering foundational principles for researchers and practitioners, though it is incremental in extending axiomatic studies from classification to regression.
The paper tackled the lack of formal assessment of uncertainty measures in regression by introducing axioms to evaluate entropy- and variance-based methods, providing theoretical insights and practical guidelines for reliable uncertainty quantification.
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 uncertainty quantification in regression, offering theoretical insights and practical guidelines for reliable uncertainty assessment.