  Individual treatment effect (ITE) estimation requires adjusting for the
covariate shift between populations with different treatments, and deep
representation learning has shown great promise in learning a balanced
representation of covariates. However the existing methods mostly consider the
scenario of binary treatments. In this paper, we consider the more practical
and challenging scenario in which the treatment is a continuous variable (e.g.
dosage of a medication), and we address the two main challenges of this setup.
We propose the adversarial counterfactual regression network (ACFR) that
adversarially minimizes the representation imbalance in terms of KL divergence,
and also maintains the impact of the treatment value on the outcome prediction
by leveraging an attention mechanism. Theoretically we demonstrate that ACFR
objective function is grounded in an upper bound on counterfactual outcome
prediction error. Our experimental evaluation on semi-synthetic datasets
demonstrates the empirical superiority of ACFR over a range of state-of-the-art
methods.
