Nonparametric Heterogeneous Long-term Causal Effect Estimation via Data Combination

Long-term causal inference has drawn increasing attention in many scientific domains. Existing methods mainly focus on estimating average long-term causal effects by combining long-term observational data and short-term experimental data. However, it is still understudied how to robustly and effectively estimate heterogeneous long-term causal effects, significantly limiting practical applications. In this paper, we propose several two-stage style nonparametric estimators for heterogeneous long-term causal effect estimation, including propensity-based, regression-based, and multiple robust estimators. We conduct a comprehensive theoretical analysis of their asymptotic properties under mild assumptions, with the ultimate goal of building a better understanding of the conditions under which some estimators can be expected to perform better. Extensive experiments across several semi-synthetic and real-world datasets validate the theoretical results and demonstrate the effectiveness of the proposed estimators.

@article{chen2025_2502.18960,
  title={ Nonparametric Heterogeneous Long-term Causal Effect Estimation via Data Combination },
  author={ Weilin Chen and Ruichu Cai and Junjie Wan and Zeqin Yang and José Miguel Hernández-Lobato },
  journal={arXiv preprint arXiv:2502.18960},
  year={ 2025 }
}