The capacity to address counterfactual "what if" inquiries is crucial for understanding and making use of causal influences. Traditional counterfactual inference usually assumes the availability of a structural causal model. Yet, in practice, such a causal model is often unknown and may not be identifiable. This paper aims to perform reliable counterfactual inference based on the (learned) qualitative causal structure and observational data, without necessitating a given causal model or even the direct estimation of conditional distributions. We re-cast counterfactual reasoning as an extended quantile regression problem, implemented with deep neural networks to capture general causal relationships and data distributions. The proposed approach offers superior statistical efficiency compared to existing ones, and further, it enhances the potential for generalizing the estimated counterfactual outcomes to previously unseen data, providing an upper bound on the generalization error. Empirical results conducted on multiple datasets offer compelling support for our theoretical assertions.

翻译：处理反事实"假设"问题的能力对于理解与运用因果影响至关重要。传统的反事实推理通常假设存在结构因果模型，然而在实践中，此类因果模型往往未知且可能不可识别。本文旨在基于（学习到的）定性因果结构与观测数据实现可靠的反事实推理，无需依赖给定的因果模型甚至对条件分布的直接估计。我们将反事实推理重新表述为扩展的分位数回归问题，并通过深度神经网络实现以捕获通用的因果关系与数据分布。所提方法相比现有方法具有更优的统计效率，同时增强了将估计的反事实结果泛化至未见数据的潜力，并提供了泛化误差的上界。在多个数据集上的实证结果为我们的理论论断提供了有力支持。