In recent years, the inconsistency in Bayesian deep learning has garnered
increasing attention. Tempered or generalized posterior distributions often
offer a direct and effective solution to this issue. However, understanding the
underlying causes and evaluating the effectiveness of generalized posteriors
remain active areas of research. In this study, we introduce a unified
theoretical framework to attribute Bayesian inconsistency to model
misspecification and inadequate priors. We interpret the generalization of the
posterior with a temperature factor as a correction for misspecified models
through adjustments to the joint probability model, and the recalibration of
priors by redistributing probability mass on models within the hypothesis space
using data samples. Additionally, we highlight a distinctive feature of Laplace
approximation, which ensures that the generalized normalizing constant can be
treated as invariant, unlike the typical scenario in general Bayesian learning
where this constant varies with model parameters post-generalization. Building
on this insight, we propose the generalized Laplace approximation, which
involves a simple adjustment to the computation of the Hessian matrix of the
regularized loss function. This method offers a flexible and scalable framework
for obtaining high-quality posterior distributions. We assess the performance
and properties of the generalized Laplace approximation on state-of-the-art
neural networks and real-world datasets.

Bayesian 深度学习的不一致性引起了越来越多的关注，温度调节或广义后验分布通常提供了解决这个问题的直接有效方法。本研究引入了一个统一的理论框架，将 Bayesian 不一致性归因于模型规范不当和先验不足，提出了广义 Laplace 近似方法来获得高质量的后验分布。