The Cut posterior and related Semi-Modular Inference are Generalised Bayes methods for Modular Bayesian evidence combination. Analysis is broken up over modular sub-models of the joint posterior distribution. Model-misspecification in multi-modular models can be hard to fix by model elaboration alone and the Cut posterior and SMI offer a way round this. Information entering the analysis from misspecified modules is controlled by an influence parameter $\eta$ related to the learning rate. This paper contains two substantial new methods. First, we give variational methods for approximating the Cut and SMI posteriors which are adapted to the inferential goals of evidence combination. We parameterise a family of variational posteriors using a Normalising Flow for accurate approximation and end-to-end training. Secondly, we show that analysis of models with multiple cuts is feasible using a new Variational Meta-Posterior. This approximates a family of SMI posteriors indexed by $\eta$ using a single set of variational parameters.
翻译:剪切后部和相关的半模块推论是用于模子贝亚斯证据组合的通用贝亚斯方法。 分析分解于联合后部分布的模块型子模型。 多模式模型的偏差很难单独通过模型的拟订来修正, Cut 后部和 SMI 提供了一种圆形方法。 从错误指定的模块输入分析的信息由与学习率有关的影响参数$\eta美元控制。 本文包含两个实质性的新方法。 首先, 我们给出了与证据组合的推断目标相适应的切切和SMI外部相近的变异方法。 我们用整齐化流程对一组变异后部进行参数的精确近似和端对端培训。 第二, 我们表明,使用新的Variational Meta- Posteriors 进行多重切换模型分析是可行的。 这相当于一个使用单一的变异参数以 $\eta$指数指数的SMI 后部。