# Vector Copula Variational Inference and Dependent Block Posterior Approximations

arXiv: https://arxiv.org/abs/2503.01072 · HTML: https://mlsanity.com/paper/2503.01072/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 56 references that are in the map.
- First posted on arXiv 3 Mar 2025.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Optimal transport mapping via input convex neural networks](https://mlsanity.com/paper/1908.10962/) (2019)
- [Model Selection in Bayesian Neural Networks via Horseshoe Priors](https://mlsanity.com/paper/1705.10388/) (2017)
- [Structured Variational Learning of Bayesian Neural Networks with Horseshoe Priors](https://mlsanity.com/paper/1806.05975/) (2018)
- [Gaussian variational approximation with a factor covariance structure](https://mlsanity.com/paper/1701.03208/) (2017)
- [Gaussian variational approximation with sparse precision matrices](https://mlsanity.com/paper/1605.05622/) (2016)
- [Variational Gaussian Copula Inference](https://mlsanity.com/paper/1506.05860/) (2015)
- [Gaussian variational approximation for high-dimensional state space models](https://mlsanity.com/paper/1801.07873/) (2018)
- [Partially factorized variational inference for high-dimensional mixed models](https://mlsanity.com/paper/2312.13148/) (2023)
- [Streamlined Variational Inference for Linear Mixed Models with Crossed Random Effects](https://mlsanity.com/paper/1910.01799/) (2019)
- [Flexible Variational Bayes based on a Copula of a Mixture](https://mlsanity.com/paper/2106.14392/) (2021)
- [Implicit copula variational inference](https://mlsanity.com/paper/2111.09511/) (2021)
- [Fast and Accurate Estimation of Non-Nested Binomial Hierarchical Models Using Variational Inference](https://mlsanity.com/paper/2007.12300/) (2020)
- [The multirank likelihood for semiparametric canonical correlation analysis](https://mlsanity.com/paper/2112.07465/) (2021)
- [Bayesian Approaches to Shrinkage and Sparse Estimation](https://mlsanity.com/paper/2112.11751/) (2021)
- [Large Skew-t Copula Models and Asymmetric Dependence in Intraday Equity Returns](https://mlsanity.com/paper/2308.05564/) (2023)

## Built on by (most cited first, 1 of 1)

- [Stepwise Variational Inference with Vine Copulas](https://mlsanity.com/paper/2603.22959/) (2026)

## Abstract (arXiv)

The key to VI is the selection of a tractable density to approximate the Bayesian posterior. For large and complex models a common choice is to assume independence between multivariate blocks in a partition of the parameter space. While this simplifies the problem it can reduce accuracy. This paper proposes using vector copulas to capture dependence between the blocks parsimoniously. Tailored multivariate marginals are constructed using learnable transport maps. We call the resulting joint distribution a ``dependent block posterior'' approximation. Vector copula models are suggested that make tractable and flexible variational approximations. They allow for differing marginals, numbers of blocks, block sizes and forms of between block dependence. They also allow for solution of the variational optimization using efficient stochastic gradient methods. The approach is demonstrated using four different statistical models and 16 datasets which have posteriors that are challenging to approximate. This includes models that use global-local shrinkage priors for regularization, and hierarchical models for smoothing and heteroscedastic time series. In all cases, our method produces more accurate posterior approximations than benchmark VI methods that either assume block independence or factor-based dependence, at limited additional computational cost. A python package implementing the method is available on GitHub at https://github.com/YuFuOliver/VCVI_Rep_PyPackage.