Leveraging a Simulator for Learning Causal Representations for CATE from Post-Treatment Covariates

Treatment effect estimation involves assessing the impact of different treatments on individual outcomes. Current methods rely on observational datasets where covariates are gathered before treatments and outcomes are observed afterward. However, real-world scenarios often deviate from this protocol, leading to both covariate and outcome observed post-treatment. We first establish that this deviation renders treatment effects unidentifiable, necessitating additional assumptions for estimation. We propose SimPONet, which unlike prior methods that assume counterfactual supervision in the training datasets, leverages a simulator that generates related synthetic counterfactual data. This allows extraction of causal representations from post-treatment covariates that aid in identifying treatment effects. The accuracy of such estimates hinges on the quality of the simulator, and we conduct theoretical analyses to establish generalization bounds that assess the CATE error based on the distributional discrepancies between real and synthetic data. In a linear setting, we analytically derive the CATE error, demonstrating the limitations of several baseline methods. Our empirical validation on synthetic and semi-synthetic real world datasets further reinforces SimPONet's effectiveness in precise treatment effect estimation from post-treatment data.