  NOTE: This preprint has a flawed theoretical formulation. Please avoid it and
refer to the ICLR22 publication https://openreview.net/forum?id=q7n2RngwOM.
Also, arXiv:2109.15062 contains some new ideas on unobserved Confounding.
  As an important problem of causal inference, we discuss the identification
and estimation of treatment effects under unobserved confounding. Representing
the confounder as a latent variable, we propose Intact-VAE, a new variant of
variational autoencoder (VAE), motivated by the prognostic score that is
sufficient for identifying treatment effects. We theoretically show that, under
certain settings, treatment effects are identified by our model, and further,
based on the identifiability of our model (i.e., determinacy of
representation), our VAE is a consistent estimator with representation balanced
for treatment groups. Experiments on (semi-)synthetic datasets show
state-of-the-art performance under diverse settings.
