Variational Gaussian Copula Inference

TL;DR

This paper introduces a flexible variational inference method using Gaussian copulas and Bernstein polynomials to better capture dependencies and marginal distributions in hierarchical Bayesian models.

Contribution

It proposes a semiparametric, automated variational Gaussian copula approach that preserves dependencies and flexibly models univariate marginals in complex Bayesian models.

Findings

Effective in modeling complex dependencies

Flexible in characterizing univariate marginals

Automated and adaptable framework

Abstract

We utilize copulas to constitute a unified framework for constructing and optimizing variational proposals in hierarchical Bayesian models. For models with continuous and non-Gaussian hidden variables, we propose a semiparametric and automated variational Gaussian copula approach, in which the parametric Gaussian copula family is able to preserve multivariate posterior dependence, and the nonparametric transformations based on Bernstein polynomials provide ample flexibility in characterizing the univariate marginal posteriors.