Use of model reparametrization to improve variational Bayes

TL;DR

This paper introduces a model reparametrization technique for variational Bayes that reduces posterior dependence in hierarchical models, leading to improved accuracy and convergence, especially for large datasets.

Contribution

The authors propose a novel reparametrization method based on Gaussian approximations to enhance variational Bayes inference in hierarchical models.

Findings

Reparametrized variational Bayes improves accuracy over traditional methods.

The approach accelerates convergence in hierarchical models.

Effective for large datasets via divide and recombine strategy.

Abstract

We propose using model reparametrization to improve variational Bayes inference for hierarchical models whose variables can be classified as global (shared across observations) or local (observation specific). Posterior dependence between local and global variables is minimized by applying an invertible affine transformation on the local variables. The functional form of this transformation is deduced by approximating the posterior distribution of each local variable conditional on the global variables by a Gaussian density via a second order Taylor expansion. Variational Bayes inference for the reparametrized model is then obtained using stochastic approximation. Our approach can be readily extended to large datasets via a divide and recombine strategy. Using generalized linear mixed models, we demonstrate that reparametrized variational Bayes (RVB) provides improvements in both accuracy and convergence rate compared to state of the art Gaussian variational approximation methods.