Scalable Semi-Modular Inference with Variational Meta-Posteriors

TL;DR

This paper introduces scalable variational methods for semi-modular inference, enabling flexible evidence combination and model misspecification control using variational meta-posteriors with normalizing flows.

Contribution

It develops novel variational techniques for approximating Cut and SMI posteriors, including a variational meta-posterior for efficient multi-cut analysis.

Findings

Normalising Flow-based variational approximations improve accuracy

Meta-posterior approach reduces computational complexity

Methods effectively handle model misspecification

Abstract

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.