This paper introduces a generalized representation of Bayesian inference. It is derived axiomatically, recovering existing Bayesian methods as special cases. We use it to prove that variational inference (VI) based on the Kullback-Leibler Divergence with a variational family Q produces the uniquely optimal Q-constrained approximation to the exact Bayesian inference problem. Surprisingly, this implies that standard VI dominates any other Q-constrained approximation to the exact Bayesian inference problem. This means that alternative Q-constrained approximations such as VI targeted at minimizing other divergences and Expectation Propagation can produce better posteriors than VI only by implicitly targeting more appropriate Bayesian inference problems. Inspired by this, we introduce Generalized Variational Inference (GVI), a modular approach for instead solving such alternative inference problems explicitly. We explore some applications of GVI, including robustness and better marginals. Lastly, we derive black box GVI and apply it to Bayesian Neural Networks as well as Deep Gaussian Processes, where GVI comprehensively outperforms competing methods.

提出了一种基于优化的贝叶斯推论的新颖泛化方法，称为三原则规则，并通过GVI（广义变分推论）的探索得出应用，包括提高了贝叶斯神经网络和深高斯过程的预测性能和适当的边际。

广义变分推断：推导新后验分布的三个参数