Variational Gaussian Copula Inference

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.