# Flexible Variational Bayes based on a Copula of a Mixture

arXiv: https://arxiv.org/abs/2106.14392 · HTML: https://mlsanity.com/paper/2106.14392/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jun 2021.

## Built on by (most cited first, 4 of 4)

- [Wasserstein Gradient Flow over Variational Parameter Space for Variational Inference](https://mlsanity.com/paper/2310.16705/) (2023)
- [Marginally calibrated response distributions for end-to-end learning in autonomous driving](https://mlsanity.com/paper/2110.01050/) (2021)
- [Vector Copula Variational Inference and Dependent Block Posterior Approximations](https://mlsanity.com/paper/2503.01072/) (2025)
- [Stepwise Variational Inference with Vine Copulas](https://mlsanity.com/paper/2603.22959/) (2026)

## Abstract (arXiv)

Variational Bayes methods approximate the posterior density by a family of tractable distributions whose parameters are estimated by optimisation. Variational approximation is useful when exact inference is intractable or very costly. Our article develops a flexible variational approximation based on a copula of a mixture, which is implemented by combining boosting, natural gradient, and a variance reduction method. The efficacy of the approach is illustrated by using simulated and real datasets to approximate multimodal, skewed and heavy-tailed posterior distributions, including an application to Bayesian deep feedforward neural network regression models.