# Variational Gaussian Copula Inference

arXiv: https://arxiv.org/abs/1506.05860 · HTML: https://mlsanity.com/paper/1506.05860/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jun 2015.

## Built on by (most cited first, 12 of 12)

- [Efficient Semi-Implicit Variational Inference](https://mlsanity.com/paper/2101.06070/) (2021)
- [Variational Marginal Particle Filters](https://mlsanity.com/paper/2109.15134/) (2021)
- [Inference and Sampling for Archimax Copulas](https://mlsanity.com/paper/2205.14025/) (2022)
- [Nonparametric Automatic Differentiation Variational Inference with Spline Approximation](https://mlsanity.com/paper/2403.06302/) (2024)
- [Transport Quasi-Monte Carlo](https://mlsanity.com/paper/2412.16416/) (2024)
- [VFDS: Variational Foresight Dynamic Selection in Bayesian Neural Networks for Efficient Human Activity Recognition](https://mlsanity.com/paper/2204.00130/) (2022)
- [Vector Copula Variational Inference and Dependent Block Posterior Approximations](https://mlsanity.com/paper/2503.01072/) (2025)
- [Rotated Mean-Field Variational Inference and Iterative Gaussianization](https://mlsanity.com/paper/2510.07732/) (2025)
- [Natural Gradient Hybrid Variational Inference with Application to Deep Mixed Models](https://mlsanity.com/paper/2302.13536/) (2023)
- [Learning variational autoencoders via MCMC speed measures](https://mlsanity.com/paper/2308.13731/) (2023)
- [Stepwise Variational Inference with Vine Copulas](https://mlsanity.com/paper/2603.22959/) (2026)
- [Structured Nonparametric Variational Inference for Dependent Latent Modeling](https://mlsanity.com/paper/2606.15458/) (2026)

## Abstract (arXiv)

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.