  As an important problem in causal inference, we discuss the estimation of
treatment effects (TEs). 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 TEs. Our VAE also
naturally gives representations balanced for treatment groups, using its prior.
Experiments on (semi-)synthetic datasets show state-of-the-art performance
under diverse settings, including unobserved confounding. Based on the
identifiability of our model, we prove identification of TEs under
unconfoundedness, and also discuss (possible) extensions to harder settings.
