Stochastic Approximation Cut Algorithm for Inference in Modularized Bayesian Models

TL;DR

This paper introduces SACut, a new stochastic approximation algorithm for sampling from the cut distribution in modularized Bayesian models, with proven convergence and bias reduction capabilities.

Contribution

The paper proposes SACut, a novel parallelizable stochastic approximation algorithm with theoretical convergence guarantees for inference in modularized Bayesian models.

Findings

Proves convergence of SACut samples to an approximate distribution.

Shows bias decreases geometrically with tuning parameter.

Demonstrates reduced computation time via parallelization.

Abstract

Bayesian modelling enables us to accommodate complex forms of data and make a comprehensive inference, but the effect of partial misspecification of the model is a concern. One approach in this setting is to modularize the model, and prevent feedback from suspect modules, using a cut model. After observing data, this leads to the cut distribution which normally does not have a closed-form. Previous studies have proposed algorithms to sample from this distribution, but these algorithms have unclear theoretical convergence properties. To address this, we propose a new algorithm called the Stochastic Approximation Cut algorithm (SACut) as an alternative. The algorithm is divided into two parallel chains. The main chain targets an approximation to the cut distribution; the auxiliary chain is used to form an adaptive proposal distribution for the main chain. We prove convergence of the samples drawn by the proposed algorithm and present the exact limit. Although SACut is biased, since the main chain does not target the exact cut distribution, we prove this bias can be reduced geometrically by increasing a user-chosen tuning parameter. In addition, parallel computing can be easily adopted for SACut, which greatly reduces computation time.