  Estimating an individual's potential outcomes under counterfactual treatments
is a challenging task for traditional causal inference and supervised learning
approaches when the outcome is high-dimensional (e.g. gene expressions, impulse
responses, human faces) and covariates are relatively limited. In this case, to
construct one's outcome under a counterfactual treatment, it is crucial to
leverage individual information contained in its observed factual outcome on
top of the covariates. We propose a deep variational Bayesian framework that
rigorously integrates two main sources of information for outcome construction
under a counterfactual treatment: one source is the individual features
embedded in the high-dimensional factual outcome; the other source is the
response distribution of similar subjects (subjects with the same covariates)
that factually received this treatment of interest.
