Position: There Is No Free Bayesian Uncertainty Quantification

TL;DR

This paper critically examines Bayesian uncertainty quantification in machine learning, arguing that it lacks a solid foundation and proposing alternative interpretations and measures for assessing its quality.

Contribution

It challenges the validity of Bayesian uncertainty quantification, offers an optimization-based perspective, and suggests new ways to evaluate Bayesian inference.

Findings

Bayesian uncertainty quantification can be misinterpreted as true uncertainty.

An alternative interpretation aligns Bayesian methods with optimization perspectives.

Proposes measures to assess the quality of Bayesian inference.

Abstract

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.