The capacity to address counterfactual "what if" inquiries is crucial for understanding and making use of causal influences. Traditional counterfactual inference usually assumes a structural causal model is available. However, 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 a given causal model or even directly estimating conditional distributions. We re-cast counterfactual reasoning as an extended quantile regression problem using neural networks. The approach is statistically more efficient than existing ones, and further makes it possible to develop the generalization ability of the estimated counterfactual outcome to unseen data and provide an upper bound on the generalization error. Experiment results on multiple datasets strongly support our theoretical claims.

翻译：处理反事实“如果……会怎样”问题的能力对于理解和利用因果影响至关重要。传统的反事实推断通常假设存在一个结构因果模型。然而在实践中，这种因果模型往往是未知的，并且可能无法识别。本文旨在基于（学习到的）定性因果结构与观测数据执行可靠的反事实推断，无需给定因果模型，甚至无需直接估计条件分布。我们将反事实推理重新表述为使用神经网络扩展的分位数回归问题。该方法在统计上比现有方法更高效，并进一步使得能够发展估计出的反事实结果对未见数据的泛化能力，同时提供泛化误差的上界。在多个数据集上的实验结果有力地支持了我们的理论主张。