Distributional causal inference requires estimating not only average treatment effects but also interventional outcome distributions, including quantiles, tail risks, and policy-dependent uncertainty. As a method for distributional causal inference, generative adversarial network (GAN)-based counterfactual methods are flexible tools for this task. However, these methods have several limitations. First, the objectives of certain techniques do not coincide with the statistical risk of the identifiable causal target, and therefore provide limited theoretical guarantees regarding estimable counterfactual distributions or optimality. Second, they tend to rely on unstable density-based methods, such as density ratio estimation. In this paper, we propose GANICE (GAN for Interventional Conditional Estimation) with several advantages: it (i) clarifies the conditional interventional distribution for each treatment--covariate state as the causal estimation target; (ii) estimates the conditional distribution such that its averaged Wasserstein risk is minimized; (iii) establishes minimax optimality. GANICE achieves these advantages through the introduction of the extended Wasserstein distance, the incorporation of a cellwise critic in its dual, and an optimality proof based on Besov space theory. Our experiments demonstrate that GANICE consistently outperforms existing methods.

翻译：分布因果推断不仅需要估计平均处理效应，还需要估计干预结果分布，包括分位数、尾部风险以及依赖于政策的不确定性。作为分布因果推断的一种方法，基于生成对抗网络的反事实方法为这一任务提供了灵活的工具。然而，这些方法存在若干局限：其一，某些技术的目标函数与可识别因果目标的统计风险不一致，因此在可估计的反事实分布或最优性方面提供的理论保障有限；其二，它们往往依赖不稳定的基于密度的方法，例如密度比估计。本文提出GANICE（用于干预条件估计的生成对抗网络），具有以下优势：（i）明确将每个处理-协变量状态的条件干预分布作为因果估计目标；（ii）通过最小化平均Wasserstein风险来估计条件分布；（iii）建立极小极大最优性。GANICE通过引入扩展Wasserstein距离、在其对偶形式中融入单元格批评器以及基于Besov空间理论的最优性证明实现上述优势。实验表明，GANICE始终优于现有方法。