Abstract: In order to improve the approximate performance of CVI(Copula Variational Inference), the CHVI (Copula Hierarchical Variational Inference) method is proposed. The main idea of this method is to combine the Copula function in the CVI method with the special hierarchical variational structure of the HVM(Hierarchical Variational Model), so that the variational prior of the HVM obeys the Copula function in the CVI method. CHVI not only inherits the strong ability of the Copula function in CVI to capture the correlation of variables, but also inherits the advantage of the variational prior structure of HVM to obtain the dependencies of the hidden variables of the model, so that CHVI can better capture the relationship between hidden variables. correlation to improve the approximation accuracy. The author validates the CHVI method based on the classical Gaussian mixture model. The experimental results on synthetic datasets and practical application datasets show that the approximate accuracy of the CHVI method is greatly improved compared to the CVI method. 

Key words: variational inference, Copula function, hierarchy, correlation