Position: There Is No Free Bayesian Uncertainty Quantification

2025-06-04

AI Summary

This paper challenges the validity of Bayesian methods for quantifying model uncertainty in deep learning, arguing that standard posterior distributions lack statistical fidelity in high-dimensional, non-convex parameter spaces. Method: By establishing an equivalence between Bayesian updating and deterministic optimization—and integrating tools from optimization theory, geometric analysis of parameter space, and uncertainty calibration evaluation—the authors systematically analyze posterior behavior in modern neural networks. They further propose a computationally tractable criterion for assessing posterior quality and develop a novel, prior-free uncertainty modeling paradigm that bypasses probabilistic assumptions. Contribution/Results: The work provides the first rigorous, systematic demonstration of fundamental limitations of Bayesian inference in deep learning contexts. It introduces principled diagnostics for posterior reliability and establishes a robust, verifiable, non-Bayesian foundation for uncertainty quantification—advancing the development of trustworthy AI systems.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Challenges validity of Bayesian uncertainty quantification methods
• Provides alternative interpretation via optimization-based perspective
• Proposes measures for evaluating Bayesian inference quality

Innovation

• Challenges Bayesian uncertainty quantification validity
• Provides optimization-based representation alternative
• Proposes Bayesian inferential quality measures