Scalable Semi-Modular Inference with Variational Meta-Posteriors
This addresses challenges in modular Bayesian evidence combination for researchers in statistics and machine learning, offering incremental improvements to existing methods.
The paper tackles the problem of model-misspecification in multi-modular Bayesian models by developing variational methods for approximating Cut and Semi-Modular Inference posteriors, using Normalising Flows for accurate approximation and a Variational Meta-Posterior to handle multiple cuts efficiently.
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 $η$ 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 $η$ using a single set of variational parameters.