  Heterogeneous treatment effect (HTE) estimation is vital for understanding
the change of treatment effect across individuals or subgroups. Most existing
HTE estimation methods focus on addressing selection bias induced by imbalanced
distributions of confounders between treated and control units, but ignore
distribution shifts across populations. Thereby, their applicability has been
limited to the in-distribution (ID) population, which shares a similar
distribution with the training dataset. In real-world applications, where
population distributions are subject to continuous changes, there is an urgent
need for stable HTE estimation across out-of-distribution (OOD) populations,
which, however, remains an open problem. As pioneers in resolving this problem,
we propose a novel Stable Balanced Representation Learning with
Hierarchical-Attention Paradigm (SBRL-HAP) framework, which consists of 1)
Balancing Regularizer for eliminating selection bias, 2) Independence
Regularizer for addressing the distribution shift issue, 3)
Hierarchical-Attention Paradigm for coordination between balance and
independence. In this way, SBRL-HAP regresses counterfactual outcomes using ID
data, while ensuring the resulting HTE estimation can be successfully
generalized to out-of-distribution scenarios, thereby enhancing the model's
applicability in real-world settings. Extensive experiments conducted on
synthetic and real-world datasets demonstrate the effectiveness of our SBRL-HAP
in achieving stable HTE estimation across OOD populations, with an average 10%
reduction in the error metric PEHE and 11% decrease in the ATE bias, compared
to the SOTA methods.
