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Granger causality analysis, as one of the most popular time series causalitymethods, has been widely used in the economics, neuroscience. However,unobserved confounders is a fundamental problem in the observational studies,which is still not solved for the non-linear Granger causality. The applicationworks often deal with this problem in virtue of the proxy variables, who can betreated as a measure of the confounder with noise. But the proxy variables hasbeen proved to be unreliable, because of the bias it may induce. In this paper,we try to "recover" the unobserved confounders for the Granger causality. Weuse a generative model with latent variable to build the relationship betweenthe unobserved confounders and the observed variables(tested variable and theproxy variables). The posterior distribution of the latent variable is adoptedto represent the confounders distribution, which can be sampled to get theestimated confounders. We adopt the variational autoencoder to estimate theintractable posterior distribution. The recurrent neural network is applied tobuild the temporal relationship in the data. We evaluate our method in thesynthetic and semi-synthetic dataset. The result shows our estimatedconfounders has a better performance than the proxy variables in the non-linearGranger causality with multiple proxies in the semi-synthetic dataset. But theperformances of the synthetic dataset and the different noise level of proxyseem terrible. Any advice can really help.

Estimating Granger Causality with Unobserved Confounders via Deep Latent-Variable Recurrent Neural Network