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arXiv · 2406.19195

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

Zeqin Yang·Weilin Chen·Ruichu Cai·Yuguang Yan·Zhifeng Hao·Zhipeng Yu·Zhichao Zou·Jixing Xu·Zhen Peng·Jiecheng Guo
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Abstract

Long-term treatment effect estimation is a significant but challenging problem in many applications. Existing methods rely on ideal assumptions, such as no unobserved confounders or binary treatment, to estimate long-term average treatment effects. However, in numerous real-world applications, these assumptions could be violated, and average treatment effects are insufficient for personalized decision-making. In this paper, we address a more general problem of estimating long-term Heterogeneous Dose-Response Curve (HDRC) while accounting for unobserved confounders and continuous treatment. Specifically, to remove the unobserved confounders in the long-term observational data, we introduce an optimal transport weighting framework to align the long-term observational data to an auxiliary short-term experimental data. 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 a long-term HDRC estimator building upon the above theoretical foundations. Extensive experiments on synthetic and semi-synthetic datasets demonstrate the effectiveness of our approach.

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Zeqin Yang, Weilin Chen, Ruichu Cai, Yuguang Yan, Zhifeng Hao, Zhipeng Yu, Zhichao Zou, Jixing Xu, Zhen Peng, Jiecheng Guo. 2024-06-27. Estimating Long-term Heterogeneous Dose-response Curve: Generalization Bound Leveraging Optimal Transport Weights. https://arxiv.org/abs/2406.19195

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