De-confounding Representation Learning for Counterfactual Inference on
  Continuous Treatment via Generative Adversarial Network
Yonghe Zhao Qiang Huang Haolong Zeng Yun Pen Huiyan Sun
Counterfactual inference for continuous rather than binary treatment
variables is more common in real-world causal inference tasks. While there are
already some sample reweighting methods based on Marginal Structural Model for
eliminating the confounding bias, they generally focus on removing the
treatment's linear dependence on confounders and rely on the accuracy of the
assumed parametric models, which are usually unverifiable. In this paper, we
propose a de-confounding representation learning (DRL) framework for
counterfactual outcome estimation of continuous treatment by generating the
representations of covariates disentangled with the treatment variables. The
DRL is a non-parametric model that eliminates both linear and nonlinear
dependence between treatment and covariates. Specifically, we train the
correlations between the de-confounded representations and the treatment
variables against the correlations between the covariate representations and
the treatment variables to eliminate confounding bias. Further, a
counterfactual inference network is embedded into the framework to make the
learned representations serve both de-confounding and trusted inference.
Extensive experiments on synthetic datasets show that the DRL model performs
superiorly in learning de-confounding representations and outperforms
state-of-the-art counterfactual inference models for continuous treatment
variables. In addition, we apply the DRL model to a real-world medical dataset
MIMIC and demonstrate a detailed causal relationship between red cell width
distribution and mortality.