Variational inference (VI) is a popular method to estimate statistical and econometric models. 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 cyclically monotone transformations. 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 fast and efficient stochastic gradient methods. The efficacy and versatility of the approach is demonstrated using four different statistical models and 16 datasets which have posteriors that are challenging to approximate. 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.

翻译：变分推断（VI）是一种用于估计统计与计量模型的常用方法。VI的关键在于选择一个易于处理的密度函数来近似贝叶斯后验分布。对于大型复杂模型，一种常见做法是假设参数空间划分中多变量块之间相互独立。虽然这简化了问题，但可能降低近似精度。本文提出使用向量Copula来简洁地刻画块间依赖关系。通过可学习的循环单调变换构建定制化的多变量边缘分布。我们将所得联合分布称为“依赖块后验”近似。所提出的向量Copula模型能够实现既易于处理又灵活多变的变分近似。该方法允许使用不同的边缘分布、块数量、块大小以及块间依赖形式。同时支持采用快速高效的随机梯度方法求解变分优化问题。通过四个不同统计模型和16个具有挑战性后验分布的数据集，验证了该方法在有限额外计算成本下的有效性与通用性。在所有案例中，相较于假设块独立或基于因子依赖的基准VI方法，本方法均能产生更精确的后验近似。