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Title: Variational inference for high dimensional structured factor copulas Authors:  Hoang Nguyen - Orebro University (Sweden) [presenting]
Pedro Galeano - Universidad Carlos III de Madrid (Spain)
Concepcion Ausin - Universidad Carlos III de Madrid (Spain)
Abstract: 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. We employ a Bayesian procedure to make a fast inference for multi-factor and structured factor copulas. To deal with the high dimensional structure, we apply a Variational Inference (VI) approximation to estimate the different specifications of factor copula models. Compared to the Markov chain Monte Carlo (MCMC) approach, the VI 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 automated 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 Bayesian information criterion (BIC). The simulation studies in different contexts show that the procedure of bivariate copula selection could be at least 80\% accuracy in comparison to the true generated copula model. We illustrate our proposed procedure with high dimensional real dataset.