Estimating Long-term Heterogeneous Dose-response Curve: Generalization Bound Leveraging Optimal Transport Weights

Long-term causal effect estimation is a significant but challenging problem in many applications. Existing methods rely on ideal assumptions to estimate long-term average effects, e.g., no unobserved confounders or a binary treatment,while in numerous real-world applications, these assumptions could be violated and average effects are unable to provide individual-level suggestions.In this paper,we address a more general problem of estimating the long-term heterogeneous dose-response curve (HDRC) while accounting for unobserved confounders. Specifically, to remove unobserved confounding in observational data, we introduce an optimal transport weighting framework to align the observational data to the experimental data with theoretical guarantees. Furthermore,to accurately predict the heterogeneous effects of continuous treatment, we establish a generalization bound on counterfactual prediction error by leveraging the reweighted distribution induced by optimal transport. Finally, we develop an HDRC estimator building upon the above theoretical foundations. Extensive experimental studies conducted on multiple synthetic and semi-synthetic datasets demonstrate the effectiveness of our proposed method.