Position: There Is No Free Bayesian Uncertainty Quantification
This work addresses foundational issues in uncertainty quantification for researchers and practitioners using Bayesian methods, but it is incremental as it critiques existing approaches without introducing a new paradigm.
The paper challenges the validity of Bayesian uncertainty quantification in machine learning by discussing its optimization-based representation and proposing alternative interpretations and quality measures, without presenting specific numerical results.
Due to their intuitive appeal, Bayesian methods of modeling and uncertainty quantification have become popular in modern machine and deep learning. When providing a prior distribution over the parameter space, it is straightforward to obtain a distribution over the parameters that is conventionally interpreted as uncertainty quantification of the model. We challenge the validity of such Bayesian uncertainty quantification by discussing the equivalent optimization-based representation of Bayesian updating, provide an alternative interpretation that is coherent with the optimization-based perspective, propose measures of the quality of the Bayesian inferential stage, and suggest directions for future work.