Identifiability of causal effects with non-Gaussianity and auxiliary covariates

Assessing causal effects in the presence of unmeasured confounding is a challenging problem. It has been previously shown that the causal effect is identifiable when noise variables of the treatment and outcome are both non-Gaussian under linear model setting with hidden variables. In this paper, we investigate the problem of identifying the causal effect using the auxiliary covariate and non-Gaussianity from the treatment. Our key idea is to characterize the impact of unmeasured confounders using an observed covariate, assuming they are all Gaussian. We demonstrate that the causal effect can be identified using a measured covariate, and then extend the identification results to the multi-treatment setting. We further develop a simple estimation procedure for calculating causal effects.