Factor copula models have been recently proposed for describing the joint distribution of a large number of variables in terms of a few common latent factors. In this paper, we employ a Bayesian procedure to make fast inferences for multi-factor and structured factor copulas. To deal with the high dimensional structure, we apply a variational inference (VI) algorithm to estimate different specifications of factor copula models. Compared to the Markov chain Monte Carlo (MCMC) approach, the variational approximation is much faster and could handle a sizeable problem in a few seconds. Another issue of factor copula models is that the bivariate copula functions connecting the variables are unknown in high dimensions. We derive an automatic procedure to recover the hidden dependence structure. By taking advantage of the posterior modes of the latent variables, we select the bivariate copula functions based on minimizing the Bayesian information criterion (BIC). The simulation studies in different contexts show that the procedure of bivariate copula selection could be very accurate in comparison to the true generated copula model. We illustrate our proposed procedure with two high dimensional real data sets.

中文翻译：

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高维结构化因子 copula 的变分推理

最近提出了因子 copula 模型，用于根据一些常见的潜在因子来描述大量变量的联合分布。在本文中，我们采用贝叶斯程序对多因子和结构化因子 copula 进行快速推理。为了处理高维结构，我们应用变分推理 (VI) 算法来估计因子 copula 模型的不同规格。与马尔可夫链蒙特卡罗 (MCMC) 方法相比，变分近似要快得多，并且可以在几秒钟内处理一个相当大的问题。因子 copula 模型的另一个问题是连接变量的双变量 copula 函数在高维中是未知的。我们推导出一个自动程序来恢复隐藏的依赖结构。通过利用潜在变量的后验模式，我们选择基于最小化贝叶斯信息准则 (BIC) 的双变量 copula 函数。不同环境下的模拟研究表明，与真实生成的 copula 模型相比，双变量 copula 选择的过程可能非常准确。我们用两个高维真实数据集来说明我们提出的程序。