Bayesian不确定性量化其实没那么可靠，本质是优化问题的伪装。
Position: There Is No Free Bayesian Uncertainty Quantification
- 用优化视角重新解释贝叶斯更新，揭示其内在等价性
- 提出评估贝叶斯推断质量的新指标，发现传统方法可能失真
- 适合关注模型可信度、推理机制的理论研究者阅读
由于直观吸引力，贝叶斯方法在现代机器学习和深度学习中广泛用于建模与不确定性量化。当在参数空间设定先验分布时，可自然获得参数分布，通常被解释为模型不确定性。本文通过分析贝叶斯更新的等价优化表示，挑战了这种贝叶斯不确定性量化的有效性；提出与优化视角一致的替代解释，构建评估贝叶斯推断阶段质量的度量，并指出未来研究方向。
原文摘要 · Abstract (English)
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.
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