Consistency of Adversarially Estimated Confounding Variable Models


I have a theoretical question here based on Dustin’s paper: .

If I have a confounding latent variable, z, that interacts with both x and y and I’m interested in determining the causal impact of x on y, will modeling this with adversarially with maximum likelihood yield consistent or unbiased estimates of the parameters of x–>y. In particular if I use a linear model willl the estimates be unbiased if the true relationship is linear and some sort of best linear estimator if nonlinear? I assume with full information variational inference this will be the case as well? Are there sources and proofs for this. Thanks,