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.
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